Deliverable Horizon2020 EUJ-01-2016 723171 5G-MiEdge D3.4 ... · Nature: Report Version: 1 Number of pages: 79 Abstract This deliverable is the final report of Task 3.3. It reports

Deliverable Horizon2020 EUJ-01-2016 723171 5G-MiEdge D3.4

Date : February 2019 Public Deliverable

5G-MiEdge Page 1

5G-MiEdge

Millimeter-wave Edge Cloud as an Enabler for 5G Ecosystem

EU Contract No. EUJ-01-2016-723171

Contractual date: M32

Actual date: M32

Authors: See list

Work package: D3.4 User/application centric orchestration of mmWave edge cloud

Security: Public

Nature: Report

Version: 1

Number of pages: 79

Abstract

This deliverable is the final report of Task 3.3. It reports on the latest activities of Work

Package 3 on the user/application centric orchestration to realize 5G liquid edge cloud.

In particular, the deliverable describes algorithms for jointly optimal allocation of radio,

and computation resources, data prefetching, load distribution, and resilient design

against the drawbacks of mmWave communications.

Keywords

Resource allocation, 5G mobile, Multi-Access edge computing, computation offloading,

data prefetching, load distribution, dynamic resource management

All rights reserved.

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The document is proprietary of the 5G-MiEdge consortium members. No copy or

distribution, in any form or by any means, is allowed without the prior written agreement

of the owner of the property rights.

This document reflects only the authors’ view. The European Community is not liable for

any use hat may be made of the information contained herein.

Authors

Sapienza University of

Rome

Sergio Barbarossa

Francesca Cuomo

Stefania Sardellitti

Mattia Merluzzi

[email protected]

[email protected]

[email protected]

[email protected]

CEA-LETI Nicola di Pietro [email protected]

Tokyo Institute of

Technology

Gia Khanh Tran

Kei Sakaguchi

[email protected]

[email protected]

Intel Valerio Frascolla

Robert Zaus

[email protected]

[email protected]

mailto:[email protected]








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Table of contents

Abbreviations and acronyms ......................................................................................... 5

Executive Summary ........................................................................................................ 8

1 Introduction ............................................................................................................. 9

2 Jointly optimal allocation of radio/computation/storage resources ................. 10

2.1 Optimal assignment and resource allocation for computation offloading ..... 10

2.1.1 Jointly optimal assignment and resource allocation in static scenarios

............................................................................................................ 10

2.1.2 Jointly optimal resource allocation in dynamic scenarios with power

consumption and average delay trade-off ........................................... 23

2.2 Data prefetching algorithm ............................................................................. 32

2.2.1 Overview ............................................................................................ 32

2.2.2 Performance indices ........................................................................... 34

2.2.3 Numerical results ................................................................................ 35

3 Load distribution and clustering via distributed pricing mechanisms ............ 37

3.1 Load distribution ............................................................................................ 37

3.1.1 State of the art ..................................................................................... 37

3.1.2 Contribution ........................................................................................ 38

3.1.3 Scenario and problem description ...................................................... 38

3.1.4 Single user case .................................................................................. 39

3.1.5 Joint allocation of computation load and radio resources: Multi-user

Case .................................................................................................... 44

3.1.6 Numerical results ................................................................................ 45

3.2 Dynamic ON/OFF strategies .......................................................................... 49

3.2.1 Data traffic demand forecast for load distribution and clustering ...... 50

3.2.2 Optimization problem ......................................................................... 52

3.2.3 Numerical analysis ............................................................................. 53

4 Resilient design and detection of network criticalities ...................................... 56

4.1 Robust design based on multi-link communications and block erasure coding

against blocking .............................................................................................. 56

4.1.1 Overview of the contributions ............................................................ 56

4.1.2 Multi-link communications ................................................................ 57

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4.1.3 Block-erasure-correcting codes for robust multi-link communications

............................................................................................................ 58

4.2 Multi-route multiplexing on mmWave mesh backhauling against overloaded

edge cloud ...................................................................................................... 65

4.2.1 System architecture ............................................................................ 65

4.2.2 Optimization problem ......................................................................... 66

4.2.3 Numerical analysis ............................................................................. 68

5 Relevance of the proposed algorithms with the project use cases .................... 70

5.1.1 Omotenashi services ........................................................................... 70

5.1.2 Moving hotspot ................................................................................... 70

5.1.4 Outdoor dynamic crowd ..................................................................... 71

5.1.5 Automated driving .............................................................................. 72

6 Summary ................................................................................................................ 73

7 References .............................................................................................................. 74

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Abbreviations and acronyms

Acronym Description

3GPP 3rd Generation Partnership Project

5G 5th (fifth) Generation

5G-MiEdge Millimeter-wave Edge Cloud as an Enabler for 5G Ecosystem

5QI 5G QoS Identifier

AF Application Function

AMF Access and Mobility management Function

ANDSF Access Network Discovery and Selection Function

AP Access Point

API Application Interface

AS Application Server

BS Base Station

BSSID Basic Service Set Identification

CDN Content Delivery Network

C-Plane Control Plane

CPN Connectivity Provider Network

C-RAN Centralized RAN or Cloud RAN

C/U split Control/User-plane split

D2D Device-to-Device

DC Dual Connectivity

D-RAN Distributed RAN

DN Data Network

DP Data Plane

eMBB Enhanced Mobile Broadband

EPC Evolved Packet Core

ETSI European Telecommunications Standards Institute

GBR Guaranteed Bit Rate

GUI Graphic User Interface

HD High Definition

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HetNet Heterogeneous Network

HomoNet Homogeneous Network

ICN Information-Centric Networks

IEEE The Institute of Electrical and Electronic Engineers

IoT Internet of Things

LADN Local Area Data Network

LCM Life Cycle Management

LoA Levels of Automation

M2M Machine-to-Machine

MAB Multi-armed Bandit

ME Mobile Edge or Multi-access Edge

ME app Mobile Edge application

MEC Mobile Edge Computing or Multi-access Edge Computing

MEH Mobile Edge Host

MEO Mobile Edge Orchestrator

MEP Mobile Edge Platform

MEPM Mobile Edge Platform Manager

MgNB Master gNodeB

MiEdge mmWave Edge cloud

mmWave Millimeter Wave

MSF MEC Service Function

N3IWF Non-3GPP Interwork Function

NEF Network Exposure Function

NFV Network Functions Virtualization

NR New RAT

NSSAI Network Slice Selection Assistance Information

OBU On-Board Unit

OSS Operations Support System

PCF Policy Control Function

PDU Packet Data Unit

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QFI QoS Flow Identifier

QoE Quality of Experience

QoS Quality of Service

RAT Radio Access Technology

RAN Radio Access Network

RL Reinforcement Learning

RNI Radio Network Information

RSS Received Signal Strength

RSU Road Side Unit

sBS Base Station for small cell

SCA Successive Convex Approximation

SDN Software-Defined Network

SgNB Secondary gNodeB

SINR Signal to Interference-plus-Noise Ratio

S-MEH Source ME host

SMF Session Management Function

TA Tracking Area

T-MEH Target ME host

UDM Unified Data Management

UE User Equipment

UOF User plane Optimization Function

UPF User Plane Function

U-Plane User Plane

uRLLC Ultra-Reliable & Low Latency Communications

V2V Vehicle-to-Vehicle

V2X Vehicle-to-Everything

VM Virtual Machine

WP Work Package


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Executive Summary

The project 5G-Miedge aims to merge Multi-Access edge computing and millimeter-

wave (mmWave) communications to enable the 5G ecosystem. Work Package 3 (WP3)

is one of the technical WP and focuses on the design of 5G liquid edge cloud for

user/application centric orchestration. Among all tasks of WP3, this deliverable reports

the results related to task 3.3: “User/application centric orchestration to realize 5G

liquid edge cloud”. The objective is to develop new algorithms for resource allocation

and orchestration. In particular, Task 3.3 is divided in three subtasks dealing with

- joint allocation radio/computation/storage resources,

- load distribution and clustering,

- resilient design of mobile edge computing.

The deliverable is organized in 6 sections and describes algorithms for the following

objectives:

a. Resource allocation for computation offloading

b. Data prefetching

c. Computational load distribution among MEHs

d. Dynamic ON/OFF strategies

e. Robust design analysis of mobile edge computing over mmWave links

f. Multi-route multiplexing on mmWave mesh backhauling against overloaded

edge cloud.


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1 Introduction

The goal of the EU-Japan funded project 5G-Miedge (Millimeter-wave Edge cloud as

an enabler for 5G ecosystem) is to create a synergy between mmWave communication

(Radio Access Network) and Multi-Access Edge Computing. In this holistic view,

radio, computation and storage resources have to be managed jointly, in order to

provide a good experience to the end users, especially in terms of latency and energy

efficiency. This deliverable is part of WP3, which runs from month 4 until month 32.

In particular, it is related to task 3.3 of the project, which focuses on the

user/application centric orchestration to realize 5G liquid edge cloud. More

specifically, this deliverable elaborates on the development of different novel

algorithms regarding the orchestration of the edge cloud resources, namely Radio

Access Points and Mobile Edge Hosts.

This deliverable is split in 6 Sections, and describes algorithms for the following

objectives:

a. Resource allocation for computation offloading

b. Data prefetching

c. Computational load distribution among MEHs

d. Dynamic ON/OFF strategies

e. Robust design analysis of mobile edge computing over mmWave links


edge cloud

In Section 2 new algorithms for the joint radio and computation resource allocation

strategies for computation offloading, and a novel data prefetching algorithm are

presented.

Section 3 presents the problem of load distribution, clustering, and describes dynamic

ON/OFF strategies for the energy efficiency of the edge cloud.

In Section 4, we first present a block erasure channel coding analysis as a way to

counteract blocking events typical of mmWave links. Then we deal with a multi-route

multiplexing strategy to avoid overloaded nodes in the edge cloud while reducing the

energy consumption. Every section and its relative algorithms will be corroborated

with several numerical results to show their performance.

In Section 5 a mapping between the proposed algorithms and the 5G-MiEdge project

use cases is proposed.

Finally, in Section 6, we will draw the deliverable conclusions.


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2 Jointly optimal allocation of radio/computation/storage resources

In this section we present some recent results on an optimal joint allocation of radio,

computation and storage resources. First, computation offloading strategies are

presented in a static scenario, with a novel assignment algorithm to associate user

equipment (UE) to millimeter wave (mmWave) access points (APs) and mobile edge

hosts (MEHs). Then results are extended to a dynamic case, devising an algorithm

based on stochastic optimization. Finally, a novel data prefetching algorithm is

presented.

2.1 Optimal assignment and resource allocation for computation offloading

We now describe resource allocation strategies for computation offloading.

Computation offloading is one of the services enabled by MEC, as detailed described

in [MEC002], enabling resource poor devices to run sophisticated applications by

transferring the computation from UEs to MEHs. Given the edge cloud scenario

depicted in Fig. 2.1, showing a set of UEs, APs and MEHs. We call ‘MiEdge resources’

two main set of items, i.e. communication resources (transmit power and data rate from

UEs to mmWave APs), and computation resources on MEHs. The MEHs are operating

In multi-tasking mode, running a set of virtual machines (VM) serving the applications

offloaded from the UEs. In the following, the computation resources will be measured

in percentage of CPU cycles dedicated from an MEH to a specific UE. In this

subsection, we describe the optimal assignment of those resources to APs and MEHs,

in terms of UE power consumption, and we devise low complexity algorithms for real

time applications, in static and dynamic scenarios. We start in Section 2.1.1 with the

static optimization, and then we generalize the approach to the dynamic case, which

includes scheduling, in Section 2.1.2.

Fig. 2.1 - Edge cloud scenario

2.1.1 Jointly optimal assignment and resource allocation in static scenarios

In this section, we present a novel algorithm for joint assignment of UEs to mmWave

APs and MEHs to run a certain application, together with a joint optimization of radio

and computation resources with the aim of minimizing the UE power consumption

under latency constraints. We first present a brief state of the art and then our novel

approach. These results are mainly based on [Sar18].


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State of the art

Several works investigated computation offloading optimization strategies in Multi-

Access Edge Computing (MEC) systems in the multi-user case [Sar15], [You17],

[Zhao17], [Chen16]. In [Sar15], a joint optimization of radio and computation

resources is investigated, in a multi-user MIMO scenario, taking into account inter-

cell interference. In [You17], the authors aim to minimize the overall energy

consumption at the UE side, in case of TDMA and OFDMA systems, while the authors

of [Zhao2017] propose a joint optimization of offloading decision and allocation of

computation and communication resources. In [Chen16], MEC computation

offloading decision is formulated as a computation offloading game. Only few works

focus on the association of users to APs and MEC servers. In [Sar14], we propose a

sub-optimal association strategy minimizing the UE energy consumption, taking into

account radio and computation parameters jointly. The server selection problem is

studied in [Zhao15] for a multiuser system to decide whether to offload computation

either to the edge server or to the central cloud. In [Ge12], the server selection over

multiple MEC servers is formulated as a congestion game. Another approach for the

Cloud Radio Access Networks (C-RAN) is presented in [Li2017], based on matching

theory.

Contributions

We consider the mmWave edge cloud scenario, composed of multiple APs and

multiple MEHs concurring to serve multiple UEs, as depicted in Fig. 2.1. The

association of a UE to a pair of AP and MEC server depends not only on radio channel

parameters, but also on the availability of computational resources at the MEC server

and the state of the backhaul network. A UE can get radio access from a certain AP,

but its application can run on a MEC server located elsewhere, exploiting wired or

wireless backhaul. We formulate the offloading problem as the jointly optimal

association between UEs, APs and MEHs, and allocation of mobile radio and

computational resources. To solve the resulting mixed-binary problem (as described in

2.1.1.4) with affordable complexity, we propose two alternative sub-optimal strategies:

i) a method based on successive convex approximation (SCA) techniques, as

developed in [Scu17], which extends our previous approach [Sar14] by incorporating

the penalty method recently proposed in [Zhang17];

ii) a method based on matching theory [Roth92], extending the approach of [Saad14]

to deal with computation offloading.

Scenario description and notation

Let us consider a mmWave based cloud access network where multiple users may get

radio access through multiple APs and multiple MEHs. In particular, we consider a

system composed of 𝑁𝑏 mmWave APs, 𝑁𝑐 MEH and 𝐾 mobile users. Denote with

ℐ ≜ {𝑘 ∶ , 𝑘 = 1, … 𝐾} the set of users asking for computation offloading of their

applications to a set of MEHs. From the offloading point of view, we simplify the

classification of applications by assuming that each of them is characterized through

the following parameters: i) the number of bits (𝑏𝑘) to be transmitted from the mobile

user to the MEH to transfer the program execution; ii) the number of CPU cycles 𝜔𝑘

needed to run the application. We denote by 𝐿𝑘 the end-to-end latency requested by


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the 𝑘-th UE to run its application. In case of offloading, the overall latency experienced

by the 𝑘-th UE for accessing the network through the AP 𝑛 when served by MEH 𝑚,

is given by

The first term is the server execution time

𝑇𝑚𝑘exe =

𝑤𝑘

𝑓𝑚𝑘 (1)

where 𝑤𝑘 is the number of CPU cycles to be executed and 𝑓𝑚𝑘 is the number of CPU

cycles/second allocated by the 𝑚-th MEH to the 𝑘-th UE. The second term 𝑇𝑘𝑛tx is the

time spent to send the program state and input (encoded with 𝑏𝑘 bits) from the 𝑘-th

UE to the 𝑛-th AP. The third term 𝑇𝑘𝑛rx is the time necessary for the server to send the

result back to the 𝑘-th UE. Finally, the fourth term 𝑇𝐵𝑛𝑚 is the backhaul delay between

AP 𝑛 and MEC server 𝑚, which is supposed to be constant regardless the size of the

application; This delay enables the transfer of the program execution from the UE to

the MEC server. More specifically, the time 𝑇𝑘𝑛tx necessary for the 𝑘-th UE to transmit

𝑏𝑘 bits over a channel of bandwidth 𝐵 to the 𝑛-th AP is

where 𝑐𝑘 = 𝑏𝑘/𝐵 and 𝑟𝑘𝑛(p𝑘𝑛) is the spectral efficiency, which, in the interference-

free regime, assumes the form

where p𝑘𝑛 is the transmit power of user 𝑘 and 𝛼𝑘𝑛 is an equivalent channel coefficient.

We assume mmWave communications for the radio access and, under Line Of Sight

(LOS) conditions, we use Friis formula to model the path loss. Each pair of UE and

AP is supposed to be equipped with, respectively, 𝑛𝑇 transmit antennas and 𝑛𝑅 receive

antennas. We also denote with 𝑑𝑘𝑛 the distance between UE 𝑘 and AP 𝑛. In a LOS

condition with a single path with isotropic array elements, the channel matrix 𝑯𝑘𝑛 ∈ ℂ𝑛𝑅×𝑛𝑇 between UE 𝑘 and AP 𝑛 is rank one. In this case, the channel coefficient 𝛼𝑘𝑛

is 𝛼𝑘𝑛 = 𝜈𝑘𝑛2 𝜉𝑘𝑛/𝜎𝑛

2, with 𝜉𝑘𝑛 the positive eigenvalue of the rank one matrix 𝑯𝑘𝑛𝑯𝑘𝑛𝐻 ;

𝜎𝑛2 is the noise variance; and the coefficient 𝜈𝑘𝑛 incorporates the path loss. Within this

edge-cloud scenario, the association of a UE to a pair of AP and MEH depends not

only on the radio channel parameters, but also on the computation resources

availability of the MEHs. Therefore, by extending our previous approach in [Sar14],

in the next section we propose an optimization strategy to jointly find the optimal

computation and communication resources allocation and the optimal association

between UEs, APs and MEHs.

Algorithm development

Our goal is now to devise an optimal strategy to assign each UE to an AP and to a

MEH, while jointly optimizing the radio and computation resources allocation. The

objective is to minimize the transmit power consumption of all users, under power

budget and latency constraints. The assignment is performed by properly selecting the

binary values 𝑎𝑘𝑛𝑚 for 𝑘 = 1, … , 𝐾 , 𝑛 = 1, … , 𝑁𝑏 , 𝑚 = 1, … , 𝑁𝑐 , where the


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subscripts 𝑘, 𝑛, and 𝑚 denote, respectively, UE, AP, and MEH indexes. For the sake

of simplicity, we assume that each UE is served by a single AP and a single MEH.

Therefore, for each 𝑘, 𝑎𝑘𝑛𝑚 = 1 if the 𝑘-th UE accesses the network through AP 𝑛

and it is served by the 𝑚-th MEH, while 𝑎𝑘𝑛𝑚 = 0 otherwise. The objective function

we aim to minimize is the sum of the powers spent by all UEs:

where

The resulting optimization problem is:

where we define the function

.

The above constraints have the following meaning: i) the overall latency of the 𝑘-th

must be lower than the maximum value 𝐿𝑘; ii) the total power spent by the 𝑘-th UE

must be lower than a fixed total power budget 𝑃𝑘; iii) the sum of the computational

rates 𝑓𝑚𝑘 assigned by each MEH cannot exceed the server computational capability

𝐹𝑚 ; iv) each UE should be served by one AP-MEH pair. For simplicity we have

incorporated the term 𝑇𝑘𝑛rx in the latency limit 𝐿𝑘 . It can be noted from the latency

expression the interplay between radio access and computational aspects, such

relationship calls for a joint optimization of the radio resources, the transmit power 𝒑

of the UEs and the computational rates 𝒇. Unfortunately, problem 𝒫 is a mixed-binary

problem and, in general, NP-hard. To handle its computational cost with affordable

complexity, in the following we propose two alternative suboptimal strategies.

SCA-based optimization strategy

In this section we propose a suboptimal optimization strategy to solve problem 𝒫 ,

combining our previous approach in [Sar14] with the SCA strategy proposed in

[Scu17], and incorporating an efficient penalty term, recently proposed in [Zhang17],

to relax the binary variables to be real while driving the solution towards the situation


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where each UE is served by a single AP and a single MEH. More specifically, the

penalty method in [Zhang17] is based on the fact that, given the following problem,

with 𝑞 ∈ (0,1), 𝜖 > 0, the optimal solution is binary, i.e. only one element is one and

all the others are zero. Moreover, the minimum value of the objective function is

Therefore, we relax our binary variables 𝑎𝑘𝑛𝑚 to be real and belonging to the

following convex set

and we add a penalty to the objective function so that our relaxed optimization problem

becomes

where 𝜎 > 0 is a penalty parameter and

𝒫 becomes 𝒫𝜎 by introducing the penalty function. However, even by relaxing the

binary variables 𝒂, problem 𝒫𝜎 is still non-convex, since the objective function and

the constraints i), ii) are non convex. In what follows, we exploit the structure of

problem 𝒫𝜎 and building on some recent advances on SCA techniques [Scu17], we

devise an efficient iterative penalty SCA approximation algorithm (PSCA) converging

to a local minimum. To solve the non-convex problem 𝒫𝜎 efficiently, we adopt an

SCA-based algorithm where the original problem is replaced by a sequence of strongly

convex problems. To do this, we start by finding a suitable convex approximation of

the nonconvex objective function that is the sum of the non-convex term 𝑓(𝒑, 𝒂) and

the concave function 𝑃𝜖(𝒂) . Let 𝒙 ≜ (𝒑, 𝒇, 𝒂) be the set of variables and 𝒳 the

feasible set of problem 𝒫𝜎 . Moreover, we denote by 𝒙𝜈 ≜ (𝒑𝜈 , 𝒇𝜈 , 𝒂𝜈) the set of

variables at iteration 𝜈 of SCA. Following [Scu17], the main idea is to approximate

the original nonconvex non-separable term with a strongly convex function, say

𝑓𝑃𝜎(𝐱, 𝐱𝜈), that has the same first order behaviour of the original objective function

at 𝐱𝜈, around the current iterate 𝒙𝜈 ∈ 𝒳. To find a convex approximant of the objective


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function observe that 𝑓(𝒑, 𝒂)has a bilinear structure, since it is the sum of the terms

𝑠𝑘𝑛𝑚(𝑝𝑘𝑛,𝑎𝑘𝑛𝑚) ≜ 𝑝𝒌𝒏𝑎𝑘𝑛𝑚. Therefore, as suggested in [Scu17], 𝑠𝑘𝑛𝑚 can be written

as a difference of convex (DC)

A valid convex upper approximation of𝑠𝑘𝑛𝑚, for any given (𝑝𝑘𝑛,𝜈 𝑎𝑘𝑛𝑚

𝜈 ) ∈ ℝ2, is then

Finally, the concave function 𝑃𝜖(𝒂) can be approximated by its first order

approximation at the iterate 𝒂𝜈, i.e.,

Then, a convex approximation of 𝑓𝑃𝜎(𝐩, 𝐚) can be defined as

where we added quadratic regularization terms to make 𝑓𝑃𝜎(𝐱, 𝐱𝜈), strongly convex

with respect to 𝒙 . Note that, in the above approximation, we use a monotonically

increasing penalty sequence {𝜎𝜈}𝜈 to guarantee that the obtained solution 𝒂 is binary

[ZHANG17]. Now, we show how to reduce the non-convex constraint

𝑔𝑘𝑛𝑚(𝑝𝑘𝑛𝑚, 𝑓𝑚𝑘 , 𝑎𝑘𝑛𝑚) to a convex form. To do so, we can observe that at any feasible

point (p,f,a), 𝑟𝑘𝑛(𝑝𝑘𝑛) > 0 , 𝑓𝑚𝑘 > 0 and 𝐿𝑘 > 𝑇𝐵𝑛𝑚 − 𝜔𝑘𝑎𝑘𝑛𝑚𝑓𝑚𝑘 , for all 𝑘, 𝑛, 𝑚 .

Then, the constraint 𝑔𝑘𝑛𝑚(𝑝𝑘𝑛𝑚, 𝑓𝑚𝑘 , 𝑎𝑘𝑛𝑚) can be rewritten as

which is the sum of the convex term −𝑟𝑘𝑛(𝑝𝑘𝑛) and the convex function

Finally, the non-convex bilinear constraint ℎ𝑚(𝒇, 𝒂) can be replaced by the following

convex approximation

We can now introduce the proposed convex approximation of the nonconvex problem

𝒫𝜎. Given the feasible point 𝒙𝜈 ∈ 𝒳, we have


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where we denoted by �̂�(𝒙𝝂) ≜ (�̂�(𝒙𝝂), �̂�(𝒙𝝂), �̂�(𝒙𝝂)) the unique solution of the

strongly convex optimization problem 𝒫𝜈 , starting from a feasible point 𝒙0 . The

proposed solution method consists in solving iteratively problem 𝒫𝜈, starting from a

feasible point 𝒙0. First we find an optimal solution �̂� of 𝒫𝜈 by setting the penalty

coefficient 𝜎 to zero. Hence, taking this optimal solution as initial point, we iteratively

solve 𝒫𝜈 with an increasing penalty coefficient 𝜎𝜈 . In Algorithm 1, we provide a

formal description of the procedure.

Matching theory based optimization strategy

In this section, we propose an alternative approach to overcome the combinatorial

complexity of the assignment problem by devising an optimization strategy based on

matching theory [Roth92]. Inspired by [Saad14], which uses matching theory for the

uplink selection of AP, we generalize the approach of [Saad2014] to computation

offloading. The assignment problem is formulated as a matching game in which UEs

and AP-MEH pairs rank one another using suitable preference functions associated to

the transmit power used by each UE, to implement computation offloading under

latency constraints. Matching theory is a powerful and simple tool to associate agents

of two different sets using suitable preference lists. A typical matching problem is the

college admission problem [Gale62], where students apply to colleges based on their

preference lists and are accepted based on colleges' preference lists. Each college

cannot accept more students than a certain number, defined as its quota 𝑞. The aim of

matching theory algorithms is to find a stable assignment. An assignment of applicants

to colleges is called unstable if there are two applicants 𝛼 and 𝛽 who are assigned to

colleges 𝐴 and 𝐵 , respectively, although 𝛽 prefers 𝐴 to 𝐵 and 𝐴 prefers 𝛽 to 𝛼 .

Matching theory has been extensively used in economics, and recently introduced in


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wireless networks [Han17]. In the context of C-RAN, the authors in [Li17] find an

assignment of UEs to Radio Remote Head (RRH), Base Band Unit (BBU) and

computing resources to minimize the refusal ratio, i.e. the portion of requests that

cannot meet their deadlines. The preference function is based on the expected latency

that a user would experience choosing a certain triple RRH, BBU, and computing

resource. In [Gale62], the Deferred Acceptance (DA) algorithm is presented and

proved to converge to a stable matching. In the DA algorithm, students apply to their

preferred college, which subsequently accept students based on their preference lists,

rejecting the least preferred ones. Applying matching theory, and in particular the DA

algorithm to problem 𝒫 is not straightforward due to inter-dependencies of utility

functions necessary to build preference lists. In fact, while UEs get accepted by a pair

AP-MEH, the convenience of being assigned to that pair changes due to the need for

resource sharing. As pointed out in [Saad14], in case of interdependent preferences,

the general college admission game becomes complex. In [Saad14], matching is used

only for the uplink selection of AP, and the 𝑅-factor, a parameter that incorporates both

the delay and the packet success rate, is used as utility function. To overcome the

problem of interdependent preferences, the authors propose to divide the problem into

two interdependent subgames: a matching game, where UEs build their preferences

based on the potential 𝑅-factor guarantees (supposing that each AP 𝑛 fills up its quota

𝑞𝑛), and a second subgame, where UEs can request to be transferred to another AP to

improve their 𝑅-factors. Generalizing this approach to our assignment problem, we

first need to define a utility function to build UEs' preference lists. In our joint

allocation of communication and computation resources, we incorporate both

communication and computation parameters in the preference function. For the sake

of simplicity, we assume perfect beamforming and interference-free channels. In

particular, every UE is supposed to be served with the same frequency band at the

same time. We focus instead on the delay caused by computation resource sharing. To

define the utility function, we consider constraint i) of problem 𝒫. Even though we do

not have any a priori information on allocated resources, we can get an approximate

estimation of the minimum transmit power that a user would experience choosing a

certain pair AP-MEH using the delay constraint. To do this, we compute an expected

minimum transmit power in case of a disjoint allocation. In particular, given a certain

allocation of computation resources, the minimum transmit power necessary to meet

the latency constraint can be easily found. As we do not know a priori the assignment

of UEs to each pair AP-MEH, initially we assume that each MEH 𝑚 serves all UEs as

far it does not exceed its quota 𝑞𝑚, in order to consider the maximum computation

delay. Thus, for the first assignment, we compute 𝑓𝑚𝑘, for UE 𝑘 and MEH 𝑚, with a

proportional rule as follows

Replacing the above equation in the execution delay expression given in (1) the

minimum rate to meet the latency constraint 𝐿𝑘 can be written as

Inverting the above equation, the associated minimum transmit power is then


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We define the utility function for UE 𝑘 accessing AP 𝑛 and MEH 𝑚 as

Based on this utility function, each UE builds its preference list. Similarly, each AP

build its preference list based on the best SNR. For simplicity, we assume that all

MEHs can accept an unlimited number of UEs. However, this condition can lead to a

solution very far from the optimum, since a single MEH has limited resources. Indeed,

a first stage for the assignment is not sufficient due to interdependency of the

preference functions of all UEs. For this reason, as in [Saad14], we perform a second

stage with a coalitional game to transfer UEs, given the new conditions, to a more

desirable coalition. A coalition 𝒞𝑛𝑚 is the set of all users associated to AP 𝑛 and MEH

𝑚 . Once UEs are assigned with the DA algorithm, the new proportional disjoint

allocation of computation resources can be computed as follows:

Computing the new approximate computation delays, we can compute the expected

minimum transmit powers towards all links and build the new preference lists. Now,

UEs can request to be transferred from one coalition to another one, based on the new

utility functions. In particular, as in [Saad14], UE 𝑘 requests to be transferred to

coalition 𝒞𝑛′𝑚′ from coalition 𝒞𝑛𝑚 if 𝑈𝑘𝑛′𝑚′ > 𝑈𝑘𝑛𝑚. If more UEs request to be

transferred to a certain coalition, only the UE with the highest SNR is considered for

the transfer. Each transfer is accepted if the following two conditions hold [Saad14]:

1. MEH 𝑚′ does not exceed its quota 𝑞𝑚′

2. The social welfare, represented by the sum of the utility functions of the two

coalitions is improved.

Formally, the second condition can be written as follows:

where

and 𝒞𝑛𝑚\{𝑘} is the set obtained by removing UE 𝑘 from 𝒞𝑛𝑚. This stage stops if there

are no more transfer requests or the social welfare is not improved by any transfer. In

[Saad14] it is proved that, given any initial assignment, this second game will converge

to a Nash-stable partition, where no user has any incentive to execute a transfer. Once

the assignment has been performed, for every MEH, we optimize the radio and

computation resources jointly as in 𝒫, but considering the assignment as given by the

matching algorithm. Note that, the difference between PSCA and the matching

algorithm, is that the PSCA performs the assignment and the joint allocation at the

same time, while the matching first performs the assignment, and then the resources

are jointly allocated.


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Numerical results

To test the effectiveness of the proposed offloading strategy, in Fig. 2.1.1-1 we report

the optimal total transmit power consumption vs. the maximum latency 𝐿𝑘, assumed

equal for all users. To test the effectiveness of the proposed algorithms, we compare

their performance with the optimal results achieved with the exhaustive search. We

consider a network composed of 𝐾 = 4 UEs, a number of APs equal to the number of

MEH, i.e. 𝑁𝑏 = 𝑁𝑐 = 2. The other parameters are set as follows: 𝐹1 = 2.7 ⋅ 109, 𝐹2 =3 ⋅ 108 , 𝑃𝑘 = 1.35 ⋅ 10−1, 𝑞 = 0.7 , where 𝑞 is the order of the norm used in the

penalty function. We can observe that both the PSCA and the matching game

algorithms provide results very close to the exhaustive search algorithm whose

complexity is exponential. Additionally, we consider as comparison term the SNR-

based association method, in both cases where the radio and computational resources

are jointly and disjointly optimized. It can be noted that both proposed approaches

yield considerable power savings with respect to SNR-based methods, taking

advantage of the optimal assignment of each user to a cloud through the most

convenient base station. It has to be remarked that the complexity of the matching-

based algorithm has a polynomial growth with the number of players (UEs and AP-

MEH pairs), although the reached final solution could be suboptimal, as the preference

lists are built based on an approximate a priori knowledge. To further test the

effectiveness of the matching algorithm, in Fig. 2.1.1-2 we show the ratio 𝜌 between

the overall power consumptions achieved with two different association rules (SNR

and matching) and the global optimal solution (exhaustive search), averaged over the

channel realizations. It is interesting to note from Fig. 2.1.1-2 that 𝜌 keeps quite close

to 1 for the proposed matching algorithm.

Fig. 2.1.1-1. – Overall UE transmit power vs. L


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Fig. 2.1.1-2 – Average ratio 𝝆 vs. L

Use case specific system architecture and signaling

For the scenario studied in the previous sections we assume a system architecture as

shown in Fig. 2.1.1-3 below. This is based on the system architecture defined in D1.3,

for the outdoor dynamic crowd use case where the wireless backhaul meshed network

is a non-3GPP network. Note that compared to D1.3 we are adding an NL1' control

interface between UE and the MEHs located in the liquid RAN.

The NL1' interface can be used by the UE to inform the MEH (Mesh master) about the

UE's address and about SNR measurement results of neighbour APs, and subsequently

to request from the MEH (slave) the start of the MEC service. (In section 2.1.1.3, this

request is referred to as "send(ing) of the program state".) In the downlink direction it

can be used by the MEH (Mesh master) to inform the UE about the optimum AP and

the address of the MEH (slave) it shall use for accessing the network and receiving

MEC service.

Fig. 2.1.1-3 – Modified System Architecture of ODC (non-3GPP case)


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Therefore, the 3GPP network provides the control plane for the UE to request the MEC

service from the MSF and trigger corresponding configuration of the MEHs in the non-

3GPP network, whereas the non-3GPP provides data plane to the UE and control plane

for the actual activation of the MEC service.

Fig. 2.1.1-4 shows the signaling procedure in more detail. Upon receipt of the request

for the MEC service, the MSF provides the MEH (Mesh master) with information

required for the local resource optimization, including e.g. the application for which

the MEC service type is requested. Furthermore, the MSF provides the UE with MEC

service info/assist info, including an address which the UE can use to send an Access

Request to the MEH (Mesh master) after performing association with a first AP. The

MEH (Mesh master) collects data, e.g. regarding the availability of computation

resources in the slave MEHs and the SNR associated to the signal sent by the UE,

when received by the associated APs.

When the MEH (Mesh master) performs local optimization, it determines the optimum

association between UE, AP and MEH (slave), configures the APs and MEHs

accordingly and informs the UE about the optimum AP the UE shall use.

The UE then performs re-association with the optimum AP and starts exchanging user

data with the application server (AS). The MEH (slave) is looped into the user plane

and waits for the request from the UE to activate MEC services.

Fig. 2.1.1-4 – Signaling for local optimization of ODC (non-3GPP case)

Information to be exchanged

It is now useful to give a hint about the needed information to be exchanged among

the involved entities to enable the optimization of the communication and computation


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resources when an application is offloaded to a MEH. First of all, let us clarify which

entities are involved in the overall process:

1. UEs

2. APs

3. MEHs

These entities must exchange UE/application related parameters and access-/network-

side related parameters as described below:

UE/application related parameters:

a. The amount of information 𝑛𝑏 (number of bits) necessary to transfer the

application execution from the UE to the MEH, i.e. to activate the MEC service;

b. The computational burden of the application, i.e. the number of CPU cycles

required for its execution, say 𝑤 (CPU cycles)

c. The SNR associated to the signal sent by the UE, when received by the AP;

d. The latency requirement for the application to be offloaded, say 𝐿 (msec),

measuring the overall delay experienced by the UE from the moment it

launches an application remotely and the moment it receives the result back

from the MEH.

Although these parameters are UE or application related, they do not need to be

signalled by the UE in this format. For example, the computational burden of

compressing a video depends on the processor running the task, specifically on the

support of special vector operations or dedicated hardware accelerators. This

information is generally not known to the UE, but it can be stored locally in the MEH

(Mesh master) for each application for which the MiEdge RAN is supporting MEC

services. The same table can also include the number of bits required for the transfer

of application execution from the UE to the MEH (slave) and the latency requirement.

So it is sufficient for the UE to signal the type of application for which MEC services

are requested to the SMF only once, at the beginning. The SMF forwards this

information to the MEH (Mesh master) when it configures the MEH (Mesh master) to

perform resource optimization.

The only parameter that needs to be determined for each UE individually is c), the

SNR associated to the signal sent by the UE, when received by any of the APs. In

section 2.1.1.8 it is assumed that the SNR measurement results of neighbour APs made

by the UE and reported to the MEH (Mesh master) can be used to derive these

parameters.

Access and Network related parameters

If we consider a deployment consisting of sets of MEHs and APs, we assume that a

cluster head (MEH) has an overview of all the available computational and radio

resources of the MEHs and the mmWave APs belonging to its mesh. In that case, the

relevant parameters to be collected are:

a. Current computational load at each MEH (maximum clock frequency and

current computation load);

b. Backhaul delay between each mmWave AP and each MEH;

c. Quota of each MEH, i.e. the maximum number of users that each MEH can

accept.


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The above information has to be kept updated in a rather dynamical way, so to have

fresh knowledge on those relevant parameters. We assume that extracting network-

relevant parameters, such as backhaul delays for example, occurs at a time scale longer

than the time-scale implicit in the optimization of resource allocation.

In general, in the static formulation of computation offloading, the amount of signaling

to be exchanged to enable offloading is much less than the data to be transmitted. In

fact, the signaling only includes the few parameters mentioned above, which need to

be exchanged only when a request of offloading takes place. In Section 2.1.2.6, we

will consider how much the signaling increases in the dynamic formulation.

2.1.2 Jointly optimal resource allocation in dynamic scenarios with power

consumption and average delay trade-off

In this section, we elaborate further on the previous topic, introducing a dynamic

formulation of the problem, considering a scenario where applications create

continuously data to be processed. For instance, let us consider a face recognition

program that receives a video from a camera and elaborates it. Obviously, in this case,

data is continuously generated and the scenario is highly dynamic. Moreover, as

explained in this section, we do not assume any knowledge on the statistics of the data

generation process and the radio channels. In particular, data is stored in a local queue

at the UE before they are transmitted to a MEH through an AP. Similarly, data is stored

in a computation queue at the MEH side before being processed. Here we introduce

the concept of a total-queue composed by the queue at the UE side plus the queue at

the MHE side. To limit the delay of the application, we introduce bounds on the

average total-queue length and on the out-of-service probability, defined as the

probability that the total-queue length exceeds a certain threshold. We now briefly

introduce the state of the art to then present our contribution. This work is mainly

presented in [Mer19] and [Mer19-2]. A computation offloading strategy with UE

assignment based on matching theory was already presented in [D2.4], as part of

[Mer19-3].

State of the art

The dynamic formulation is investigated in [Mao17], where the authors aim to

minimize the long-term average power consumption under constraints on the mean

rate stability of the computation queues with a single MEH. The contribution [Mao16]

investigates the same problem introducing energy harvesting devices. In [Mer19-3],

the authors extend the work [Mao17], to the case of multiple APs and MEHs, devising

an algorithm based on matching theory with transfers with a penalty function

discouraging frequent handovers. In [Yang18] the authors consider a fog-enabled D2D

scenario and propose a strategy to associate mobile devices and offload tasks among

each other. The authors of [Sun17] address the problem of user assignment, with the

aim of minimizing the average delay under energy constraints, while introducing a

penalty function that discourages frequent handovers, and using Multi-armed bandit

to learn the optimal penalty parameter.

All the aforementioned works do not address the problem of dynamic computation

offloading while keeping the computation queues under a certain threshold in order to


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limit the service delay, which is the approach proposed in this deliverable. To the best

of our knowledge, we are aware of only a few works that deal with this problem. In

fact, latency-constrained dynamic computation offloading was first addressed in

[Chen17], where the authors introduce a probabilistic constraint on the computation

queues, written as a bound on the probability of exceeding a certain value, handling it

with extreme value theory. Finally, the work in [Chen18] extends [Chen17] by

considering a scenario with multiple APs and MEHs, and introducing a UEs

assignment strategy based on matching theory.

Contribution

We propose a novel algorithm for dynamic computation offloading, aimed at

minimizing the long-term average power consumption under an average latency

constraint and a bound on the out-of-service probability, defined as the probability that

the overall service time (including communication and computation times) exceed a

certain value. The algorithm defines a policy for radio resource allocation and

scheduling at the MEH, based on the current state of communication and computation

queues. We consider the scenario where a UE offloads all its computations to a MEH

and there is no concurrent (UE/MEH) computation, to avoid continuous back and forth

exchange of program status between the UE and the MEH. We impose constraints on

the sum of the local queues (data to be transmitted from the UEs) and the remote

queues at the MEH (computations to be performed). This sum represents a proper

measure of the overall service delay. Our approach differs from what is proposed in

[Chen17], [Chen18], where constraints on local and remote queues are imposed

separately, and not jointly as in our case. In our case, we provide a truly joint

optimization of radio and computation resources in a dynamic fashion and we are able

to satisfy a constraint on the overall out-of-service probability. The proposed method

requires the solution of a convex problem in each time slot, so that it can be

implemented through efficient numerical tools [Boyd04]. Numerical results assess the

performance of our solution, illustrating how, in its simplicity, it guarantees out of

service probability and average delay constraints.

Scenario and problem formulation

Let us consider a scenario where 𝐾 UEs wish to offload computations to a MEH,

connected to a mmWave AP via a high capacity backhaul, as in the example of Fig.

2.1.2-1. Since we are dealing with a dynamic problem, time is divided in slots of equal

duration 𝛥. In each time slot 𝑡, new computation requests are randomly generated at

the UE side; the radio channel, denoted by ℎ𝑘(𝑡), can also vary over time.


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Fig. 2.1.2-1 - Scenario

Then, letting 𝑝𝑘(𝑡) be the transmit power of UE 𝑘, the maximum data rate between

UE 𝑘 and the AP is given by:

where 𝛽𝑘(𝑡) is the portion of the bandwidth allocated to UE 𝑘, 𝐵 is the total available

bandwidth, and 𝑁0 is the noise power spectral density. We consider a local (at the UE)

queue of bits to be transmitted and a remote (at the MEH) computation queue for each

UE (cf. Fig. 2.1.2-1). The local data queue of UE 𝑘, say, 𝑄𝑘𝑙 (𝑡), takes on input the new

data arrivals 𝐴𝑘(𝑡) , generated with random arrival times, and it is drained by

transferring data to the MEH via the mmWave AP, thus evolving as:

Similarly, the remote computation queue, say, 𝑄𝑘𝑟(𝑡), is fed by the data arriving from

the UEs and drained by the computation power of the MEH, and it evolves as follows:

where 𝑓𝑘(𝑡) is the total computation power (in CPU cycles/s) assigned to UE 𝑘 during

time slot 𝑡; and 𝐽𝑘 denotes the number of bits per CPU cycle, a parameter that depends

on the specific application required by UE 𝑘. The overall delay is then associated to

the sum of the time needed to send the data in the local data and the time to run all

computation requests associated to the remote computation queue:

Our goal is then to find an optimal resource allocation strategy in order to minimize

the long-term average power consumption at each UE, under constraints on the

maximum average queue length (which can be directly related to the average delay by

Little's law [Lit11]) and the out of service probability, i.e. the probability that 𝑄𝑘tot(𝑡)

exceeds a certain value. The problem can be formulated as follows:


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where 𝛹(𝒕) = [{𝑝𝑘(𝑡)}𝑘, {𝑓𝑘(𝑡)}𝑘, {𝛽𝑘(𝑡)}𝑘]; 𝑄𝑘avg

and 𝑄𝑘max are the upper bounds on

the average queue length and on the maximum queue length for the out of service

probability, respectively. 𝜖𝑘 is the out-of-service probability, while 𝑃𝑘 and 𝑓max are the

UE transmit power budget and the computational power of the MEH, respectively. The

constraints have the following meaning: (a) imposes that the average queue length (i.e.,

the average delay) of each UE does not exceed a certain value; (b) ensures that the

probability for the total queue 𝑄𝑘tot to exceed a maximum value does not exceed the

required out-of-service probability; (c) ensures that the transmit power of each UE is

non negative and does not exceed a maximum power budget; (d) ensures that the

fraction of the bandwidth allocated to each user is non negative and is at most 1; (e)

guarantees that the sum of the allocated bandwidth to all UEs does not exceed the

available bandwidth; (f) forces the computation resources allocated to each UE to be

non-negative and not greater than the computation power of the MEH 𝑓max ; (g)

guarantees that the sum of the computation resources allocated to each UE is at most

equal to the computational power of the MEH.

Algorithm development

We tackle problem 𝒯 using tools from stochastic optimization [Nee10]. The starting

point, as in [Nee10], is to introduce virtual queues corresponding to constraints (a) and

(b) in 𝒯. The virtual queues quantify the degree of violation of the imposed constraints.

Denoting by 𝑍𝑘(𝑡) the virtual queue of UE 𝑘 associated to the first constraint, we can

write its evolution as follows:

To introduce the second virtual queue, we recast constraint (b) in the following

equivalent form:

where 𝟏{⋅} is the indicator function. Since the indicator function can be rewritten as


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where 𝑢{⋅} denotes the unitary step function, the virtual queue 𝑌𝑘(𝑡) associated to the

second constraint of 𝒯 can evolves as

where 𝜇 is a step-size used to speed up the convergence of the algorithm. Note that the

use of the step size does not change the problem, since it comes just from the scalar

multiplication of both sides of the constraint by a factor 𝜇 . Having introduced the

virtual queues 𝑍𝑘(𝑡) and 𝑌𝑘(𝑡) for each UE 𝑘, the constraints (a) and (b) of 𝒯 can be

substituted by mean-rate stability constraints of the virtual queues as follows:

The algorithmic solution passes through the definition of the Lyapunov function

where 𝛩(𝑡) = [𝒁(𝑡), 𝒀(𝑡)] are the vectors whose elements are the virtual queues of all

UE’s. Then, the Lyapunov drift is defined as [Nee10]:

where the expectation is taken with respect to the channel and arrival rate realizations,

and it depends on the control policy. The Lyapunov drift defined in leads to the mean-

rate stability of the virtual queues [i.e., (a) and (b) above], but it can also lead to an

unnecessary power consumption. To balance the mean-rate stability and the long-term

average power consumption, we introduce the drift-plus-penalty function [Nee10],

which comprises the Lyapunov drift and a term including the objective function (the

transmit power in this case):

where 𝑉 is a control parameter used to balance the power consumption and the

Lyapunov drift. Using a stochastic optimization approach, our algorithm is based on

the concept of opportunistically minimizing an upper bound of the drift-plus-penalty

function in a per slot fashion. It can be shown that an upper bound of the drift-plus-

penalty function is given by [Mer19-2]:


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where 𝐶 is a positive constant. Since the step function in is non-convex, we exploit its

closest convex upper bound

which is reminiscent of the hinge loss used in support vector machines [Sim18]. Then,

using this upper-bound, we obtain:

where 𝛥𝑅𝑘,max and 𝐴𝑘,max are upper bounds on the data rate and the data arrivals,

respectively. Thus, the algorithm proceeds by greedily minimizing instantaneous

values of the upper bound, thus obtaining the following dynamic control policy:

where 𝒵 is the set of feasible actions according to the constraints (c)-(g) of problem 𝒯.

It is easy to prove that problem 𝒪 is a convex optimization problem, but having a non-

differentiable objective function. To handle the non-differentiability, we first perform

a simple change of variable, in order to use the data rate 𝑅𝑘(𝑡) as a variable instead of

the transmit power 𝑝𝑘(𝑡). In particular, the transmit power can be written as


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Then, exploiting the equivalent epigraph form [Boyd04], it is possible to show that

problem 𝒪 can be equivalently recast as [Mer19-2]

where 𝜴(𝒕) = [{𝑝𝑘(𝑡)}𝑘, {𝑓𝑘(𝑡)}𝑘, {𝛽𝑘(𝑡)}𝑘, {𝜉𝑘(𝑡)}𝑘, {𝛤𝑘(𝑡)}𝑘, {𝛷(𝑡)}𝑘] , and 𝛿𝑘 =𝐴𝑘,max + 𝛥𝑅𝑘,max(𝑡) − 𝑄𝑘

max + 1 . It is easy to see that problem 𝒫 is convex and

differentiable, and can be solved using powerful numerical tools as interior point

methods [Boyd04]. In fact, almost all functions in 𝒫 are linear, except for the

exponential term, which is the perspective function that is known to be convex

[Boyd04]. The overall dynamic procedure is described in Algorithm 2

.

Numerical results

In this section, we show the performance of our algorithm through numerical results

obtained by simulation in the MATLAB environment, using the fmincon function from


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the optimization toolbox. Since problem 𝒫 is convex, fmincon converges to the global

optimal solution very efficiently. We consider a mmWave link with a path loss as in

[SAK15], an available bandwidth of 200 MHz, a noise power spectral density of -174

dBm/Hz, and a mmWave AP at the center of a square of size 100 m. The single MEH

has a computational power 𝑓max = 5 × 109 CPU cycles/s, and the parameter 𝐽𝑘 is set

to 10−1 bits/CPU cycle for all 𝑘. The maximum transmit power of each user is 𝑃𝑘 =500 mW, and each terminal is endowed with a planar array of 4 antennas. At the

receive side, the AP has an array of 16 elements. In Fig. 2.1.2-2, we show the tradeoff

between the average user queue length and the average user transmit power, comparing

our algorithm with the algorithm proposed in [Mao17], which requires only mean rate

stability of the sum of the computation queues. In this evaluation we considered a

scenario with 15 UEs with an arrival rate uniformly distributed between 0 and

𝐴𝑘,max = 6 × 105 bits. The requirements are 𝑄𝑘avg

= 3 × 106 bits, 𝑄𝑘max = 5 × 106

bits and 𝜖𝑘 = 10−2. Simulations are run for 2000 slots with 𝛥 = 10 ms, and are

averaged over 100 channel realizations, given by different positions of the UEs. For

the virtual queue 𝑌_𝑘(𝑡), we used a step-size 𝜇 = 1000. The power/delay tradeoff is

explored by letting the parameter 𝑉 vary along the curves reported in Fig. 2.1.2-2 (as

𝑉 decreases, the average power increases). As we can notice from Fig. 2.1.2-2, the

proposed method obtains a considerable gain with respect to the strategy in [Mao17]

in terms of queue length/power tradeoff. In particular, with the proposed method, the

average queue length approaches the maximum average requirement as 𝑉 increases,

whereas the algorithm in [Mao17] incurs in a much longer total user queue length for

a given power. Note that, since we imposed constraints on the average delay and on

the maximum queue length, our strategy does not arbitrarily decrease the power

consumption as 𝑉 increases, but it reaches a minimum power such that these

constraints are satisfied. The only drawback of increasing 𝑉 , and thus finding the

minimum power value, is the convergence time. On the contrary, the algorithm

proposed in [Mao17] can arbitrarily decrease the transmit power consumption at the

cost of a larger average queue length.

Fig. 2.1.2-2 – Average user sum queue length vs. long-term average power

consumption

10-3

10-2

10-1

Average user transmit power (W)

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Qto

t (t)

106

Algorithm from [Mao17]

Proposed Algorithm

Qavg


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As a further example, in Fig. 2.1.2-3 we show the behavior of the reliability function

defined as 1 − CDF(𝑄𝑘tot(𝑡)), where CDF(⋅) is the cumulative distribution function.

We consider 3 users with different 𝑄𝑘avg

, 𝑄𝑘max , and 𝜖𝑘 , running the simulation for

150000 slots, and considering 𝑉 = 4 × 1016. Each solid curve shows the probability

that 𝑄𝑘tot(𝑡) is greater than the value on the abscissa, while the dotted vertical lines

represent the maximum requirements 𝑄𝑘max, 𝑘 = 1,2,3. From Fig. 2.1.2-3, looking at

the intersections between the curves and the vertical lines, we can notice that all the

users meet the required constraint on the out of service probability. For instance, for

the blue curve, the requirement is not to exceed 𝑄1𝑚𝑎𝑥 for more than once every 10

time slots (1e-1 of outage probability). In fact, the intersection between the blue curve

and the green vertical line is exactly at (1e-1). This means that the probability is 1e-1

as required. The same comment is valid for all other UEs. Finally, in Fig. 2.1.2-4, we

show the instant value of the sum queue length for the 3 UEs with the same simulation

parameters of Fig. 2.1.2-3. In this figure we can notice the effectiveness of the

algorithm in terms of average queue length and, at the same time, the effect of the

bound on the out-of-service probability. Indeed, while the first UE requires an out-of-

service probability 𝜖1 and its queues often exceeds the prescribed threshold 𝑄1max UE

2 and UE 3 present much less peaks exceeding their thresholds, since they require a

much lower value of 𝜖𝑘. At the same time, the bound on the average queue length is

always met by all UEs.

Fig. 2.1.2-3 – Probability that the user sum queue length exceeds the value on

the abscissa


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Fig. 2.1.2-4 – Instant value of the (sum) queue lengths vs. iteration index

Information to be exchanged for dynamic computation offloading

The dynamic formulation requires more exchange of information than the static case.

In the dynamic case, all information about the bits to be transmitted and the number of

computations to be run is embedded in the communication and computation queues.

There are a few parameters that need to be exchanged (mainly coming from the

specific application that is running) only when a new request of offloading arrives,

from the UE to the network:

1. Delay constraints of each application, i.e. 𝑄𝑘𝑎𝑣𝑔

𝑎𝑛𝑑 𝑄𝑘𝑚𝑎𝑥

2. The required out of service probability (𝜖𝑘)

3. The number of bits per CPU cycle (𝐽𝑘)

Then, if computation offloading takes place, within each time slot the parameters to be

exchanged between the UE and the edge cloud are the following:

1. The channel states (ℎ𝑘(𝑡))

2. The updated local queue lengths (𝑄𝑘𝑙 (𝑡))

All other information are available in the edge cloud and must not be exchanged over

the radio interface. Note that this information have to be exchanged at the beginning

of each time slot. The overall amount of signaling is in any case much smaller than the

amount of data to be exchanged.

2.2 Data prefetching algorithm

2.2.1 Overview

We assume a scenario composed of heterogeneous networks with limited backhaul

resource. In such environment, the method to allocate the limited resources greatly

affects the performance of the network. The prefetching of data to MEH in advance


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will reduce access delay significantly, as will be seen in Section 2.2.3, which is

important for latency-sensitive applications.

Prefetching process

This section explains our approach to prefetch user data. It is important to select

appropriate indices of small cell base station (BS) s, user u and traffic n. They are

decided based on context information collected via the control plane (C-plane) of

macrocell BS. Fig. 2.2-1 the area surrounding a small cell BS s, where dotted line

denotes the backhauling toward the small cell BS on which content data are pre-

fetched in advance for a time window Tp before UE1 and UE2 really arrive at their

expected locations marked by red dots.

Fig. 2.2-1 - The area surrounding a small cell s

The Prefetching process steps are as follows:

1) Get user destination information via context information management

framework in the MEC service function (MSF proposed in D1.3).

2) Predict traffic and to-be-connected small cell BS 𝑠 at the destination, which is

defined as a BS which will maximize the UE’s SINR among BSs in the vicinity

of the expected destination of the UE. We assume that the value of SINR

(communication area) can be predicted by measurement and stochastic analyses

to make a power map beforehand.

3) Pick user within time window Tp as target to prefetch when user approaches the

destination.

4) Select user 𝑢 and traffic 𝑛 by dedicated prefetching algorithms explained later.

Prefetching algorithm

In step 4) of the prefetching process mentioned above, a combination of user u and

traffic n is selected by a specific prefetching algorithm. Fig. 2.2-2 shows the traffic

demand at the small cell s. The horizontal and vertical axes show time and traffic

demand, respectively. A user u demands data n whose size is Lu,n at time tu,n. Now, we

consider which traffic backhaul resource CB should be allocated at time t.


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Fig. 2.2-2 - Traffic demand at the small cell s

In our simulation we compare two algorithms. The first one is round robin (RR) which

randomly selects user u and traffic n. The second one is our proposed weighted

proportional fairness (WPF) algorithm, which sets an objective function considering

user context information and selects user u and traffic n to maximize it. The objective

function Ou,n(t) is defined as

,

, ,

p

,

,

( ) ( )( )

( )

u n

u n u n

u

u n

u n

LO t w t

B t

Tw t

t t

where Bu(t) is the allocated backhaul resource to user u until time t, wu,n(t) is a weight

coefficient taking into account the traffic generation time tu,n for user u and traffic n at

time t. wu,n(t) is a ratio of Tp against margin time defined as the difference between tu,n

and t. α is called the proportional fair (PF) coefficient, which changes the priority of

the weight coefficient. The objective function is selected to balance the trade-off

between prefetching priority of large-volume data and traffic of high urgency e.g. UE

are really approaching its expected destination.

2.2.2 Performance indices

We define two indices to evaluate performance of the proposed prefetching algorithm

toward the MEHs.

System rate

System rate R is defined as a total rate of all macro and small cell as follows,

S SM

SM

M S ,M SM S

remremS , ,M , ,

1 1 1s s,

min , min ,j s j

N JJu s ju j u su

j u s j uj s j

W CW C DLR

T T

M SM S

where WM and WS are the available bandwidth at macro cell and small cell. and

are the link capacities for user u, smallcell s, resp.. Ts is the timeslot width. rem

uL

is the instantaneous remaining traffic demand of user u. Ns is the total number of small

cell BSs. JM and JS are the number of sectors at macro cell BS and smallcell BS.

M,u jC

S, ,u s jC

MMj


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is the set of users belonging to a sector jM of macro cell BS and is the set of users

belonging to a sector jS of small cell BS s. rem

,u sD is the data stored in storage for user

u and small cell s, which is expressed in detail as

rem rem

, B ,min ,u s u s uD C T L

where Tu,s is the total timeslot for user u at small cell s decided by the presented

prefetching algorithm. Namely, if not prefetching, limited backhaul restricts small cell

rate and system rate will decrease. However, if prefetching is applied, mmWave high

speed access will be released from the backhaul bottleneck, thus being able to operate

at its full capability. Therefore, the system rate is expected to be increased.

Delay on access

Delay on access τ is defined as the gap between time tu,n at which user demands traffic

and time tu,nend at which all of the demand traffic is delivered. The formula is

represented as follows,

end

, ,u n u nt t .

However, because a timeout is introduced in traffic model, the delay cannot exceed

this value.

2.2.3 Numerical results

Numerical simulation is conducted using our developed simulator presented in D4.1.

Fig. 2.2-3 shows the system rate achieved by the different considered algorithms

defined in previous section, for each backhaul capacity on the condition that the

number of users, the storage limit and the time window are 200, infinity and 500 s,

respectively. In the figure, red circle, green triangle and blue square show WPF

algorithm, RR and without prefetching, respectively. In case of zero or too small

backhaul capacity, traffic almost cannot be offloaded via small cell BSs thus the system

rate is equivalent to only macrocell rate which has about 100 Mbps. In the case of 10

Gbps or more, the system rate even without prefetching achieves the maximum rate.

This means prefetching function is not needed with sufficient backhaul, however, it is

unlikely from the viewpoint of current low optical fiber penetration rate in the world.

The most noteworthy point is at 1Gbps backhaul. The system rate with prefetching is

much bigger than that without prefetching. The result proves that it is possible to

improve deterioration of system rate thanks to effect of prefetching and storage. In

addition, the system rate with WPF algorithm is bigger than that with RR and achieves

about 95% of maximum rate achieved without prefetching at 1 0Gbps backhaul. The

results show the benefit of applying the proposed algorithm.

S,Ss j


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Fig. 2.2-3 - System rate of the different algorithms

Fig. 2.2-4 - Avg. access delay of the different algorithms

Fig. 2.2-4 shows the average access delay of the different algorithms, as defined in

previous section for each backhaul capacity. Only macro cell (zero backhaul capacity)

cannot accommodate most of large demand traffic expected in the next 10 years and

the delay becomes equal to the timeout mentioned above. In particular, WPF with 1

Gbps backhaul capacity reduces to about 33% of the delay without prefetching.


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3 Load distribution and clustering via distributed pricing mechanisms

This section includes contributions on load distribution and clustering algorithms. In

particular, the first part presents novel algorithms to distribute the computational load

among different MEHs, grouping them in small clusters/federation in order to meet

latency requirements of UEs with low power consumption. Then, we will describe an

algorithm for the dynamic ON/OFF of the mmWave edge cloud, to switch off APs

when necessary to minimize the system’s energy consumption.

3.1 Load distribution

This subsection introduces novel algorithms for the computational load distribution

among MEHs. Our goal is to develop optimal strategies to group the APs, endowed

with MEHs and connected among them through a mmWave backhaul network, into

clusters that can efficiently execute the computation tasks offloaded by UEs in a

parallel and distributed way. MEHs’ federation within a cluster has to face many

challenging limitations such as radio and computational resources availability, delay

constraints, and power consumption. Then, we tackle the issue of joint computational

load distribution and communication resource allocation within the MEC clusters to

efficiently execute the computational tasks. We first devise in the single user case

alternative strategies of clustering aiming at minimizing jointly the serving time, the

cluster size and the transmit power consumption. Then we investigate the multi-user

offloading scenario by showing the considerable performance gain ensured by jointly

optimizing the computational and communication resources and the MEHs federation

in clusters.

3.1.1 State of the art

The selection of computing nodes that are federated for computation offloading or

computation caching can significantly influence not only the execution delay but also

the power consumption of the computing nodes. In [OUEIS14] has been analyzed the

impact of the MEC cluster size (i.e., the amount of the small cells endowed with cloud

functionalities performing computing), its topology and the capacity of the backhaul

link on both execution latency of the offloaded application and the power consumption

for computation offloading. The paper shows that an increasing number of the

computing nodes does not always shorten execution delay. Since the computational

resources of MEC servers are limited, a strategy to enhance the computational

capabilities is to group AP-MEHs into computation clusters. If the cloud resources of

the AP-MEH serving a UE are not enough for computing the offloaded task, the

serving AP-MEH has the possibility of distributing the computation load among

neighbor AP-MEHs. Many offloading strategies and methodologies focused on

application partitioning for offloading decision purposes. Graph-based model are used

to partitioning the computation tasks [SMIT12], [WANG04], [VERB13]. In

[KHAl],[AZIM16] map reduce type call graphs are used to split a computation

workload into mapping tasks. Some works [GARG11], [NATH10], [VERMA08],

proposed heuristics algorithms to solve the VM placement problem. A further approach

is to formulate the offloading problem as a Markov Decision Process (MDP)

[LIANG12], [LIANG12-2], [DIVA14].


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3.1.2 Contribution

To the best of our knowledge, only a few works dealt with the computation partitioning

problem in the multi-users case [YANG_CAO15], [YANG12], [YANG12-2], [JIA16],

[YAO17]. Our contribution is to propose strategies for intra-cluster joint

communication and resource management for computation offloading. Resource

management consists of computation load distribution, radio resource allocation, and

computational capacities assignment. In particular, we consider a scalable architecture

where computations can be performed either locally, at the UE if endowed with

sufficient computing capabilities on it, or in a cluster of AP-MEHs depending on

resource availability, latency constraints and energy consumption. Enabling the

formation of federation or clusters of computing resources allows computational load

to be distributed among several MEHs, which further reduces computing latency. We

assume that AP-MEHs nodes communicate and exchange data through mmWave links

enabling high speed wireless backhauling among APs to guarantee short serving time.

3.1.3 Scenario and problem description

Let us consider the edge-cloud network illustrated in Fig. 3.1-1 composed of densely

deployed mmWave AP-MEHs pairs. The nodes can communicate through point-to-

point wireless backhaul connection, assumed in D1.3 of this project, and each of them

is able to provide both the radio access and the computation resources to a set of UEs.

Each UE requests a computational task offloading to the Serving AP-MEH node (SAP-

MEH) which can serve multiple UEs. We do not tackle the problem of user association

with the SAP-MEH so that UEs are already connected to one serving AP-MEH node

to which they can send their computation requests. Furthermore, we do not deal with

the offloading decision process at the UE side, and, therefore, we suppose that the UEs

have already taken the computation offloading decision. We assume, as in [KHAl],

[AZIM16], that the application to be offloaded is splittable into constituent subtasks to

be processed in parallel by using map-reduce type call graphs. The computation task

is characterized by a set of bits/instructions to be processed/computed under some

latency constraint dictated by the handled application. The goal of each SAP-MEH is

to solve the computation task request without violating the latency constraint.

Depending on the system state and its available resources, each SAP-MEH may decide

to either compute UE’s computational task locally (i.e. using its own computational

resources), or build a cluster of helper MEHs in order to distribute computation among

them. An AP-MEH node contributing in a computation cluster for a task coming from

another SAP-MEH is referred to as helper MEH. Each SAP-MEH has to set up a

computation cluster to accommodate the set of computation tasks coming from

different UEs.


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Fig 3.1-1 – Multi-user mmWave edge cloud scenario

3.1.4 Single user case

In this section we focus on the single user scenario, where a UE offloads a computation

task to its serving SAP-MEH node. We consider a set 𝒩 ≜ {1, … , 𝑁} of 𝑁 AP-MEHs

each one endowed with a total computational capacity of 𝐹𝑛 [CPU cycles/sec], for 𝑛 =1, … , 𝑁 . The serving AP-MEH 𝑠 receives a computation task for running 𝑊 CPU

cycles. The maximum time within which the UE wishes to run the application is

denoted with 𝛥app. The SAP-MEHs may choose either to compute the request locally,

or to establish a computation cluster. The computation request, defined by the pair

(𝑊, 𝛥app) , can be satisfied by only using local resources on SAP-MEHs if the

following latency constraint holds:

where the left side represents the minimum computation time that can be achieved at

the serving node. In this case, the overall computational capacity 𝐹𝑠 of the SAP-MEH

should be allocated for the computation of the request. On the other hand, if the above

equation does not hold, then the SAP-MEH tries to form a computation cluster in order

to distribute the computation load. Each of the AP-MEHs in the cluster is accorded a

fraction of the computation load. However, to guarantee service delivery to the mobile

user, resources should be adequately optimized. Therefore, the SAP-MEH has to: i)

choose which AP-MEH nodes to include in the computation cluster and, then,

distribute the computational load among these Helpers; ii) allocate computational

resources at each Helper; iii) manage communication resources for sending and

retrieving necessary data from SAP-MEHs to Helpers and vice versa. Nevertheless,

the SAP-MEH may optimize a clustering process to compute the offloaded task even

if the condition is verified, depending on the strategy adopted for computing each UE’s

request. In the sequel, we propose several strategies for AP-MEHs computation load

partition, which are able to cover different type of applications and application

requirements.

SAP-MEH

Helper

MUE1 MUE2

MUE3

SAP-MEH

SAP-MEH

Helper


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Latency minimization

Our goal in this section is to find the optimal computation load distribution among the

AP-MEHs in the cluster in order to minimize the service latency. In general, the total

overall service latency is measured from the time the request is received by the SAP-

MEH until all data are computed and received back to the SAP-MEH. Then,

where 𝑁 is the number of helper MEHs that can be part of the computation cluster;

𝛥𝑐𝑜𝑚𝑚𝑠𝑛 = 𝛥𝑈𝐿

𝑠𝑛 + 𝛥𝐷𝐿𝑠𝑛 is the sum of the time 𝛥𝑈𝐿

𝑠𝑛 needed for transferring the program

execution from the SAP-MEH 𝑠 to Helper 𝑛, plus the time 𝛥𝐷𝐿𝑠𝑛 necessary to send back

the result to SAP-MEH 𝑠. We assume that when the computation runs on the SAP-

MEH (i.e. 𝑛 = 𝑠), there is no communication delay so that 𝛥𝑐𝑜𝑚𝑚𝑠𝑠 = 0. The delays

𝛥𝐷𝐿𝑠𝑛 and 𝛥𝑈𝐿

𝑠𝑛 depend respectively on the number of bits 𝑁𝐷𝐿𝑛 and 𝑁𝑈𝐿

𝑛 to be sent and

received at helper MEH 𝑛 . These numbers are related to the computation load 𝑊𝑛

allocated to each helper MEH 𝑛 through the following equations:

where 𝜃𝐷𝐿 and 𝜃𝑈𝐿 are coefficients specific of the application that is going to be

offloaded: a small value of these coefficients refers to applications that require the

transfer of few bits, for a given computational load 𝑊𝑛. Clearly, offloading is more

effective for those applications for which 𝜃𝐷𝐿 and 𝜃𝑈𝐿 are small. In the sequel, we

suppose, for simplicity, that both SAP-MEH and helper MEH transmit with the same

power 𝑝𝑠𝑛 and that channel reciprocity holds. Additionally, we assume high data rate

mmWave backhaul connecting the AP-MEHs nodes, and, under Line Of Sight (LOS)

conditions, we use Friis formula to model the path loss [MUD09]. Then, the overall

transmission time can be written as:

where 𝜃 =𝜃𝑈𝐿+𝜃𝐷𝐿

1−𝑃𝐸𝑅 , 𝐵𝑠𝑛 is the bandwidth allocated for transmitting data between

SAP-MEH 𝑠 and helper MEH 𝑛 ; 𝑝𝑠𝑛 is the transmit power which here we assume

equal to its maximum value 𝑝𝑚𝑎𝑥; The channel response is

where ℎ𝑠𝑛 and 𝑑𝑠𝑛 are the channel coefficient and the distance between SAP-MEHs

and helper MEH 𝑛, respectively; 𝑑0 is the far field reference distance; the coefficient

𝜈𝑠𝑛 is defined as


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where 𝜁 incorporates some efficiency terms and the antennas gains, 𝜆 is the

wavelength associated to the carrier frequency, and 𝛽 is the atmospheric absorption

coefficient; 𝛤(𝐵𝐸𝑅) represents the SNR margin for meeting a target 𝐵𝐸𝑅, and 𝑁0 the

noise power. Finally, 1

1−𝑃𝐸𝑅 denotes the average number of retransmissions for

ensuring a target packet error rate 𝑃𝐸𝑅 , by assuming independent errors on each

packet. The packet error rate depends on the bit error rate 𝐵𝐸𝑅 and the transmission

packet size 𝑙𝑠 according to the following equation

Finally, the delay 𝛥𝑐𝑜𝑚𝑝𝑠𝑛 in the latency term represents the time spent by the helper

MEH 𝑛 to execute 𝑊𝑛 CPU cycle. This term depends on the load distribution in the

cluster, and on the computational capacity allocated at each node of the cluster.

Denoting by 𝑓𝑛 the computational capacity allocated by AP-MEH 𝑛, the computation

time 𝛥𝑐𝑜𝑚𝑝𝑠𝑛 is defined as

The strategy we propose in this section aims at finding the optimal load distribution

among AP-MEHs involved in the computation in order to minimize the cluster latency.

This kind of strategies could be requested by the UE to increase the performance

without imposing power consumption constraints nor cluster size limitations. For these

reasons, the system is forced to include all of the active and reachable AP-MEHs in

the computation cluster. This cluster latency depends on the computational load

through the computation time at the involved AP-MEHs, and on the channel quality

through the communication latency. For this strategy, we assume that the SAP-MEH

communicates with the helper MEHs in the cluster by using the same maximum

transmission power, i.e. 𝑝𝑠𝑛 = 𝑝𝑚𝑎𝑥. This implies that all transmission links are fully

used in order to maximize the effective throughput and decrease the total experienced

latency. Then, the optimization problem can be formulated as follows:

where we define 𝐴𝑛 =1

𝑓𝑛+

𝜃

𝐵𝑠𝑛 log(1+𝑎𝑠𝑛𝑝𝑠𝑛 ) if 𝑠 ≠ 𝑛 and 𝐴𝑛 ≜

1

𝑓𝑛 for 𝑛 = 𝑠 . The

solution of 𝒫ℬ1 leads to a load distribution among all active computation nodes, in a

way that makes uniform the experienced latency at each node. This is intuitive since if

two AP-MEHs do not experience the same latency, then we can always adjust the load

distribution in order to decrease the higher latency and increase the lower one to have

a smaller maximal value. Problem 𝒫ℬ1 is a non-smooth problem. However, to find its

optimal solution, we can introduce the auxiliary slack (real positive) variable 𝑡 ≜max𝑛∈𝒩

𝐴𝑛𝑊𝑛, and then solve the following equivalent problem:


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which admits a closed form solution as stated in the following theorem:

Theorem 3.1-1. The convex problem 𝒫ℬ1 ̅̅ ̅̅ ̅̅ and its optimal solution is given by

The proof can be found in [OUEIS19]. Note that the proposed latency minimization

strategy may in some cases result in assigning very small computation loads to those

helpers that experience a very bad communication channel quality with the SAP-MEH,

and, then, take a long time for receiving and transmitting data. Even if energy

consumption is not our goal, this kind of situation where a lot of energy is spent for a

very small amount of computation could be avoided by finding the optimal energy-

latency tradeoff or, alternatively, by adding a pre-selection step that limits the number

of participating Helpers. However, if the main goal is to guarantee quality of the

service and to serve the UEs’ tasks regardless of the energy cost, 𝒫ℬ1 is able to deliver

the optimal solution in closed form.

Cluster sparsification

In this section we aim at developing a selection strategy to reduce the cluster size, and

eventually its energy consumption, by removing helper MEHs that execute very small

computational tasks. The approach we follow can be seen as a sparsification of the

solution resulting from solving problem 𝒫ℬ1 since we force to zero the computational

load of some helper MEHs. To reduce the cluster size we choose as

cost function the 𝑙0 norm of the load vector 𝑾 = [𝑊1, … , 𝑊𝑁], which associates zero

cost to every non used AP-MEH and unit cost to those involved in the computation

cluster. Then the optimization problem can be cast as follows:

where the first constraints guarantee that the maximum latency dictated by the

application is met by each MEH, while the other constraints ensure that the whole task

will be computed. Although problem 𝒫ℬ2 is non-convex due to the non-convexity of

the 𝑙0 -norm, it admits a closed form solution, as shown in detail in [Oue19]. In


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particular, the solution tends to include in the cluster, the helper MEHs that experience

lower latencies, and then, can support larger computation tasks.

Minimization of Cluster Power Consumption

The strategies proposed in the previous sections aim at minimizing the latency or the

cluster size without taking into account the cluster power consumption. Power

consumption is indeed an important issue in MEC networks where the edge cloud

servers are typical femtocell base stations. Our main goal in this section is to exploit

the latency-power consumption trade-off in order to minimize the transmit power in

the cluster while keeping a good quality for the service. Communication power

consumption can be optimized depending on channel quality, computational capacity

offered by each MEH and application latency constraints. Then in the following we

jointly find the optimal transmit powers 𝑝𝑠𝑛 and the percentage of computation load,

𝑊𝑛 accorded to each helper MEH, which minimize the cluster power consumption. We

assume that at the SAP-MEH is assigned the highest load of computation according to

its computational capacity with no communication cost (𝑝𝑠𝑠 = 0). In the case where

computational resources at the SAP-MEH are sufficient for computing the whole

request without violating the latency constraint, i.e. if 𝑓𝑠𝛥𝑎𝑝𝑝 ≥ 𝑊 , the load is

accorded to the SAP-MEH. Otherwise, if 𝑓𝑠𝛥𝑎𝑝𝑝 ≥ 𝑊, the SAP-MEH load will be

equal to 𝑊𝑠 = 𝑓𝑠𝛥𝑎𝑝𝑝. Therefore, to allocate the remaining computational load 𝑊 −

𝑊𝑠, the following optimization problem is solved:

In [OUEIS19] the optimization problem and its solution is described in details. In this

case, the solution tends to assign high computation loads to Helpers with larger

computational capacities and better communication channels.

Minimization of the maximum transmit power

The previous optimization strategy aims at minimizing the overall communication

power consumption. However, it could happen that helper MEHs with very high

computational capacity suffer a high power consumption. In this problem, we address

selfish minimization of the transmit power consumption under application latency

constraints. The optimization problem can be formulated as follows


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The solution of this problem will tend to accord to all helper MEHs an equal power

consumption. If any helper MEH has a greater power consumption than the others, the

load distribution can be modified to decrease the maximal power consumption value.

Note, that this strategy will most likely increase the overall cluster power consumption

comparing to 𝒫ℬ3.

3.1.5 Joint allocation of computation load and radio resources: Multi-user

Case

In this section, we consider the more general case of edge cloud networks where the

AP-MEHs serve multiple users. Despite the fact that almost all previous works

assumed that the cloud computational capacities are sufficient to meet the computing

users' tasks, such some assumption made for the single user case are not true for

multiple users in edge clouds, where APs are femto base stations with limited power

and computational capacities. In the case where there are a lot of users, SAP-MEHs

may receive concurrent requests at the same time and this requires a joint, optimal

allocation of the computational and radio resources among all users in order to

guarantee the application requirements. In this section, we investigate the problem of

the multi-user computation load partitioning and radio/computational resources

allocation to minimize the cluster power consumption under application latency

constraints. The wireless mmWave links among AP-MEHs allow us to consider

interference free transmission. We denote by 𝒦 the set of 𝐾 active users and by 𝒮 the

set of SAP-MEHs. Each user 𝑘 is served by a SAP-MEH 𝑠 ∈ 𝒮. Each SAP-MEH 𝒮

serves users in set 𝒦𝑠 so that 𝒦 = ⋃ 𝒦𝑠|𝒮|𝑠=1 . Each user 𝑘 ∈ 𝒦 sends a computation

request defined by (𝑊𝑘, 𝛥𝑘 ) to its SAP-MEH 𝑠 ∈ 𝒮, where 𝛥𝑘 denotes the maximum

latency for user 𝑘. We denote by: 𝑤𝑘𝑛 and 𝑓𝑘𝑛, respectively, the computation load and

the computation capacity allocated at AP-MEH 𝑛 for computing user's 𝑘 request; 𝑝𝑠𝑛𝑘

the transmit power used to exchange computational data of user 𝑘 between SAP-MEH

𝑠 and Helper 𝑛 . Denote by 𝒑 ≜ (𝑝𝑠𝑛𝑘 )∀𝑘,𝑛≠𝑠 , 𝒇 ≜ (𝑓𝑘𝑛

𝑘 )∀𝑘,𝑛

, 𝒘 ≜ (𝑤𝑘𝑛𝑘 )

∀𝑘,𝑛 , the

transmit powers, the computational rates and loads allocated to each UE, respectively.

The optimization problem can be formulated as follows


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where

Problem 𝒫𝑐 is convex and can be easily solved via efficient numerical tools. From

problem 𝒫𝑐, from 𝒘 it is possible to understand how the cluster is formed. In particular,

only the MEHs 𝑖 with 𝒘𝒊 different from 0 are included in the cluster, while the others

do not take part in the computation. Then, for each user, the cluster of MEH performing

the computation is determined by the solution of problem 𝒫𝑐.

3.1.6 Numerical results

In this section we present some numerical results to assess the effectiveness of the

proposed optimization strategies. We will first focus on the single user case to

investigate the minimum latency, minimum power and clustering size optimization

strategies. Therefore, we consider the multi-user case by showing as the joint

optimization of the computation load, and of the radio and computational resources

leads significant performance improvements with respect to disjoint optimization

approaches.

Single user case

As simulation scenario in our numerical experiments we considered, a street canyon

of 20 m width and 100 m length where the AP deployment on each side of the road

follows a homogeneous Poisson point process of intensity 𝜆. The SAP-MEH is chosen

as the nearest AP to the centroid of the overall set of APs. Helper MEHs whose distance

from the SAP-MEH is less than 40 meters are classified as Near Helpers, whereas the

remaining ones are referred as Far Helpers. The selected values for the simulation

parameters are: 𝑃𝑚𝑎𝑥 = 0.1 W, 𝜃 = 90 , Δ𝑎𝑝𝑝 = 8 msec, 𝑊𝑘 ∈ [104, 2 × 104] , 𝐹𝑛 ∈

[106, 2 × 106]. As path loss model for the mmWave links, we used the measurement-

based outdoor propagation model introduced in [SAK15], [WEI14]. We averaged the

results over 100 random realizations of the APs' positions.


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Resource partition among helpers

In Fig. 3.1-2 we compare the latency and power minimizing strategies, solving

problems 𝒫ℬ1 and 𝒫ℬ3, respectively, by showing how much load can be allocated to

the SAP-MEH and Helpers. We consider as performance metric the fraction of the

computation load 𝜂𝑤 ≜ ∑ 𝑊𝑛/𝑊𝑛∈�̅� where denotes �̅� alternatively, the SAP-MEH

index 𝑠, the set of active Near or Far Helpers, defined as ℋ𝑛, ℋ𝑓, respectively. In Fig.

3.1-2 we plot the average coefficient �̅�𝑊 versus the average percentage 𝒳𝑛𝑒𝑎𝑟 of Near

Helpers among all active Helpers, defined as 𝒳𝑛𝑒𝑎𝑟 ≜ 𝐸[|ℋ𝑛|/|𝒩|] . It can be

observed that the solution of 𝒫ℬ1 tends to better take advantage from all active

Helpers by giving larger computation tasks to both Far and Near Helpers than 𝒫ℬ3.

Furthermore, 𝒫ℬ1 assigns a higher computation load to Near Helpers in order to

achieve a lower maximum latency, since they usually have better channel conditions.

The solution of 𝒫ℬ3, whose objective is to minimize the cluster power consumption,

assigns as much as possible computation load to the SAP-MEH, because its transmit

power consumption is zero.

Fig. 3.1-2– Load distribution on SAP-MEH, near and far helpers for latency and

power minimization algorithms

As further figure of merit, we consider the latency gain with respect to the maximum

latency 𝛥𝑎𝑝𝑝 defined as 𝐺𝐿 ≜𝛥𝑎𝑝𝑝−𝛥

𝛥 where 𝛥 is the overall latency. In Fig. 3.1-3, we

plot the averaged latency gain �̅�𝐿versus the coefficient 𝒳𝑛𝑒𝑎𝑟. It can be noted that 𝒫ℬ1

has the largest latency gain, and the optimization strategies whose goal is minimizing

the power consumption, i.e. 𝒫ℬ3 and 𝒫ℬ4, do not achieve any latency gain. In fact,

these strategies take advantage of all the available time window in order to further

reduce power consumption by pushing the latency-power consumption trade-off to its

limits. Fig. 3.1-3 also shows that when we tend to sparsify the solution in order to

eliminate Helpers with very low computation tasks by solving 𝒫ℬ0 we lose in terms

of latency. However, this loss is traded with power consumption as can be seen in Fig.

3.1-4, where we plot the averaged transmit power consumption gain 𝐺𝑝 =∑ (𝑝𝑚𝑎𝑥−𝑝(𝑖))𝑖

𝑁𝑝𝑚𝑎𝑥

versus the coefficient 𝒳𝑛𝑒𝑎𝑟.


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Figure 3.1-3 - Latency gain of the proposed algorithms.

Fig. 3.1-4. – Power consumption gain for different strategies

We can notice that the power gain achieved by 𝒫ℬ2 is considerable for all helpers

distribution. Since in the case of 𝒫ℬ2 we assumed that transmission power is constant

and equal to 𝑝𝑚𝑎𝑥, the gain in power consumption comes only from the reduction of

the cluster size. For 𝒫ℬ3 and 𝒫ℬ4, transmission power consumption can be controlled,

then the power consumption gain in these cases is a result of both transmission power

adaptation and cluster size reduction.

Multi-user case

The solution of problem Pc jointly forms computation clusters for all users. To evaluate

the performance of the joint clustering optimization, we compare it to the case where

all requests are handled by the SAP-MEH (No Clustering). Fig. 3.1-5 shows the

average power consumption per user in the computation clusters versus the maximum

number of users per SAP-MEH. We can observe as the average power consumption

increases with the number of users to be served, since each user is forced to use less


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of the SAP-MEH computational capacity and to offload more computation to Helpers.

Furthermore, if we increase the minimum latency Δ𝑚𝑖𝑛, defined as Δ𝑚𝑖𝑛 = minkΔ𝑘,

then our clustering strategy is able to achieve very low power consumption. It can be

observed that the transmit power consumption of the No clustering strategy is zero

since it assigns the user computation load to the serving SAP-MEH.

Fig. 3.1-5 – Average user power consumption vs. maximum number of users per

SAP-MEH

However, this power gain is traded with a lower number of accommodated users as

shown in Fig. 3.1-6, where we plot the percentage of satisfied users versus the

maximum number of users for SAP-MEH. A user is satisfied if its computation request

result is delivered without violating the imposed latency constraint. In order to evaluate

this percentage, we try to solve the optimization problem with the total number of

active users in the network. In case of failure of reaching a solution, users that request

higher computation load are eliminated one by one until all considered users are

satisfied. The satisfaction ratio is evaluated for an increasing number of possible active

users per AP-MEH. In Fig.3.1-6 we show as by increasing Δ , the satisfaction ratio

improves as well, since a higher number of users can be served. Furthermore, the

proposed joint optimization strategy performs better than the No clustering method

when the latency constraint is more stringent by taking advantage of the computational

resources of the clustered helpers.


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Fig. 3.1-6 – User satisfaction ratio vs. maximum number of users per SAP-MEH

3.2 Dynamic ON/OFF strategies

In this section, we consider the network architecture as shown in Fig. 3.2-1 where

mmWave edge cloud can be switched on and off in adaptation to the forecasted data

traffic demand. The architecture is a heterogeneous network (HetNet) that is composed

of several mmWave small cells overlaid on top of a conventional macrocell

deployment. The macrocell BS collects context information such as user mobility and

traffic in the C-plane and deals with small and real-time traffic in the user plane (U-

plane). The small cell BS deals with large traffic in the U-plane, so that the utilization

of mmWave high speed access is needed. The optimization presented in this section

will help to find a suitable clustering of users to be serve by the macro cell’s MEH or

the small cell’s MEH. Furthermore, small cells’ MEH can be switched off when

necessary to minimize the system’s energy consumption, within UE’s prescribed

latency constraints.

Fig. 3.2-1 - Illustration of 5G cellular network using mmWave edge cloud


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3.2.1 Data traffic demand forecast for load distribution and clustering

User traffic measurements are used to forecast the statistics of the traffic demand of

UE in the actual environment. The measurement data were provided by an operator as

follows. The total hourly traffic, L, is measured in 100 meters100 meters areas.

2000 ..., 200, 100, 0,

3000 ..., 200, 100, 0,

23 ..., 1, 0,

:for

kbpsin ,,

y

x

T

TyxL

(3–1)

An example of the measured total traffic in one hour from 10:00 to 10:59 (T=10) is

shown in Fig. 3.2-2. A few high load areas are recognizable in the whole area.

Fig. 3.2-2 - An example of the measured total traffic in one hour

By interpolation on the hourly total traffic measurements, the total traffic distribution

at each time is estimated in:

59):23,0[ :for kbpsin ,, ttyxL (3–2)

The number of UEs in that area at the considered time instant, NUE((x,y),t), is estimated

based on the instantaneous total traffic load, L((x,y),t), and the statistics of the traffic

load of each UE. The traffic load of each UE, can be considered to be fixed (equal to

the average traffic load) or dynamic (stochastic process according to the model).

Accordingly, the instantaneous number of UEs can be modeled either statically or

dynamically as shown in Fig. 3.2-3.


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Fig. 3.2-3 - The number of UEs in the 100 meters 100 meters square area at

point (1100,600)

The packet generation of each UE is considered to follow a Poisson process with 8 sec.

average time interval between packets and the length of each packet follows the

Gamma distribution plus a constant bias. The probability density function (PDF) of

the Gamma distribution is defined as follows:

k

x

k

kxxf e

)()(

/

1

(3–3)

where the parameters of the PDF of the packets’ lengths are listed in Table 3.2.1.

Table 3.2.1 - Parameters of the packet length distribution

Shape parameter, k 0.2892

Scale parameter, 2.012105

Traffic bias 4 kbps

Figure 3.2-3 shows the number of UEs in the 100 meters 100 meters square area

located at point (1100,600) for both dynamic and static models.

Traffic demand’s latency constraints

We present the delay tolerance of each traffic in this section. Each UE’s traffic demand

(measured in bps) generated based on the fitting model explained above is associated

with a specific delay tolerance. The value of the delay tolerance is referred from QCI

(QoS Class Identifier) defined in LTE. More specifically, based on their volume, the

generated traffic in this paper is classified into one among five categories (i.e. VoIP,

video call, game, streaming and other TPC based applications) with their associated

value of delay tolerance defined in [TS23.303]. One result of generated traffic

classification in ascending order of traffic volume is visualized in Fig. 3.2-4, where the

x-axis represents different traffic demands of different UEs and the y-axis shows the


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value of the corresponding generated traffic. The color of the traffic represents the

corresponding category of a traffic based on the aforementioned classification process.

Fig. 3.2-4 - Traffic classification and corresponding delay tolerance.

3.2.2 Optimization problem

The optimization presented in this section will help to find a suitable clustering of users

to be served by the macro cell’s MEH or the small cell’s MEH. Furthermore, small

cells’ MEH can be switched off when necessary to minimize the system’s energy

consumption, within UE’s prescribed latency constraints. The objective function is to

improve the system rate over consumed energy of the system. As for BS deployment,

general hexagonal structure with three sector macro cells is assumed where the macro

BS is located at the center of hexagonal structure and mmWave edge clouds are

overlaid on the macro cells randomly. The optimal cell association to the MEH in edge

cloud or to that at the macro cell will help to improve spectral efficiency. The optimal

ON/OFF status of MEHs will help to improve energy efficiency. In order to maximize

the system performance, the system rate over consumed energy r in bits/J which is

defined as the ratio between the total system rate and the total system consumption

power of all BSs is introduced as follows r :

S1SB

1

,SM,MS

,min ,min

PnP

LCW

LCW

ρ

n

s u

us

su

u

uu

s

SM

SM

(3-4)

where MW and sW are the available bandwidth for macro cell and small cell

respectively. M,uC and suC , are link capacity from macro and s-th small cell. M and

sS represent the number of users belong to macro BS and s-th small cell BS

respectively. SN is the total number of small cell BSs deployed within one macrocell

area. uL is predicted traffic demand of user u. This system rate definition expresses


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the balance between achievable rate and traffic demand. If the achievable rate is much

higher than the traffic demand, the user rate equals to the traffic demand and vice versa.

nS £ NS is the total number of activated small cell BSs and NS

is the total number of

small cell BSs deployed within one macro cell area. Lu in bps is a traffic demand of

user u . PB = PM1 +PM0 +NSPS0is the network's baseline consumption power which is

contributed from PM1 (macro BS's surplus consumption power when activated), PM0

(macro BS's power consumption when idle) and PS0 (small cell BS's consumption

power when idle). PS = PS1 +PS0 is the consumption power of an edge cloud where PS1

is the surplus consumption power when the small cell BS is activated.

On the offloading point of view, MEH should accommodate appropriate UEs to

improve system rate efficiently e.g. edge cloud MEH accommodates UE of high traffic

demand. On the energy saving point of view, small cell BSs should be switched off as

many as possible at the expense of degrading the system rate. For a fixed number of

activated small cell BSs, the denominator of r becomes a constant. Therefore, the

joint optimization problem can be decomposed into finding the optimal user

association or clustering to maximize the total system rate for a fixed set of activated

small cell BSs and finding the optimal set of activated BSs to maximize the system

rate over consumed energy.

Furthermore, to guarantee UE’s latency constraint, for each cluster of UEs associating

with MEH in the edge cloud or smallcell BS which are activated, we optimize the

time resource to guarantee UE’s demanded traffic are delivered within their required

latency tolerance. This requirement for each sub-problem at the s-th MEH can be done

via minimizing the following “local traffic consumption” evaluation function at the s-

the activated MEH which is determined by the maximization of (3-4).

su

u

usu

u

u

uu

s LT

CWL

T

CW

S SM Ms

,SM,M (3-5)

subject to a certain set of constraints [GIA18] where u denotes the time resource to

the u-th UE, MT and ST are the length of one time frame of the macro BS and the small

cell BS respectively, sM and sS denote two clusters of UEs within the area of the s-th

small cell associated with the macro MEH and edge cloud MEH respectively. Similar

to the ON/OFF status of edge clouds, the decision of the two clusters depends on the

maximization of (3-4). The optimization problem in (3-5) attempts to minimize the

gaps between the demanded traffic and the available access link throughput.

3.2.3 Numerical analysis

Simulation setup

Macro BSs are deployed in the hexagonal grid and uses 2GHz band. On the other hand,

small cell BSs are deployed non-uniform randomly in the macro cell area which are

apt to be near the hotspot areas of the day. Each small cell BS has three sectors and

employs the frequency reuse with reuse factor 3. Users are dropped into the evaluated

network coverage randomly. The average value of traffic demand of each user is


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assumed to be a 1000 times higher than that of the current traffic, which means 62

Mbps. The remaining simulation parameters can be found in the following Table 3.2.2.

Table 3.2.2 - Simulation parameters. Parameter Value

Bandwidth

(Macro / 60 GHz) 10 MHz / 2 GHz

Number of macro cells 7 (1 evaluate, 6 interference)

Number of macro sectors 3

Number of edge cloud BSs

(per 1 macro cell) 15 (5 per macro sector)

Number of UEs

(per 1 macro cell) time varying

Number of BS antennas

(Macro / 60 GHz) 4 / 8

Number of UE antennas

(Macro / 60 GHz) 2 / 1

Macro ISD 500 m

BS antenna height

(Macro / 60 GHz) 25 m / 4 m

UE antenna height 1.5 m

Tx power

(Macro / 60 GHz) 43dBm / 19dBm

Additional consumption power of BS

(Macro / 60 GHz)

ON: 835W / 60W

OFF: 19W / 2W

Pathloss model

(Macro / 60 GHz)

]dB[]km[log6.371.128 10 d/

ref

ref

10

ref

ref

10

, log2002.82

, log6.2302.82

ddd

d

ddd

d

dPL

Channel model

(Macro / 60 GHz)

3GPP SCME urban macro scenario/

Measurement-based Rician fading model

Noise power density -174 dBm/Hz

Average traffic demand 62 Mbps

Numerical results

The effectiveness of the proposed algorithm can be observed in Fig. 3.2-5, which

depicts the optimization results (BS ON/OFF status) of 60 GHz small cell BSs for two

representative scenarios of low traffic load at 3AM and peak hour at 3PM. As seen in

the evaluated macro cell area of the figure, more small cell BSs are deactivated at 3AM

rather than that at 3PM.


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Fig. 3.2-5 - ON/OFF status (left: 3AM, right: 3PM).

The optimization problem to reduce the system’s energy consumption via deactivating

a certain set of small cells as shown in the above figure might violate the UE’s latency

constraints. Fig. 3.2-6 reveals that such violation might be mitigated by applying (3-

5), where the vertical axis evaluates the satisfaction ratio of user traffic demand as a

KPI of the system, defined as the percentage of UEs with the achievable user rates are

higher than their traffic demands. The black line in the figure show the results of a

homogeneous network (HomoNet: a network architecture of only macro cells without

small cells) for reference. As seen in the figure, the performance of this KPI can be

roughly ranked in ascending order as follows i.e. HomoNet, 60 GHz HetNet (3-4), 60

GHz HetNet (3-4 and 3-5). With only macro BS, conventional HomoNet is obviously

not able to support the future 1000x traffic demand where only roughly 20% of users

are satisfied. mmWave HetNet via merely maximizing (3-4) has unsatisfactory

performance since it only maximizes the system’s energy efficiency without

considering UE’s traffic demand latency tolerance. On the other hand, our proposed

algorithm via furthermore minimizing (3-5) can support UE’s satisfaction at most of

the time.

Fig. 3.2-6 – Satisfaction ratio performance.


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4 Resilient design and detection of network criticalities

In this section, we first introduce an analysis for the resilient design of Mobile edge

computing against mmWave blocking events based on block erasure channel coding.

Then, we presents a method to control mmWave meshed backhaul for efficient

operation of mmWave edge cloud overlay HetNet. One main feature of this algorithm

is backhauling route multiplexing for overloaded mmWave edge cloud base stations

(SC-BSs).

4.1 Robust design based on multi-link communications and block erasure

coding against blocking

One of the major drawbacks of mmWave communications is that they are prone to

blocking events due to human body and obstacles [AC13], [SMM11]. In this section,

we propose away to compensate blocking effects, based on multi-link communications

between a UE and the edge cloud and on error-correcting codes for block-erasure

channels.

4.1.1 Overview of the contributions

In the whole Section 4.1, we focus on latency-constrained uplink communications

from UEs to APs of the edge cloud. In subsection 4.1.2, we briefly introduce the

strategy of exploiting simultaneous multi-link communications to minimize the uplink

information transmission costs at the UE’s side. Next, in subsection 4.1.3, we combine

multi-link communications with error-correcting techniques to counteract the effect of

blocking events.

In general, we can differentiate between long-term blocking events, whose duration is

almost as long as the uplink transmission time of the offloading procedure (or even

more, up to a few seconds [Mac17]), and short-term blocking events that instead last

much less. The latter can be caused, for example, by a bicycle or a car rapidly crossing

the communication path between the UE and an AP.

When short-term blocking happens, a mmWave channel suffers from a high

attenuation that temporarily decreases the achievable rate to almost 0. Substantially, a

mmWave link assumes an “on/off” behavior depending on the absence or presence of

a physical obstacle interrupting the communication path. Thus, brief blocking events

essentially make communication intermittent. To counteract this effect, we presented

in [D2.1] an approach that was first introduced in [BCM17], [BCMC17]. This idea is

based on overprovisioning of radio resources to guarantee an actual average

information transmission rate that takes into account blocking probabilities and

compensates possible information losses.

In Section 4.1.3, we deal with long-term (or “slow”) blocking, whose duration has at

least the same order of magnitude as the latency constraint. For this kind of blocking

events, we propose a coding strategy over multiple links to increase the probability of

recovering the information lost over blocked channels, thanks to the other received

blocks. We define and analyze the properties of the asymmetric block-erasure channel

and we discuss the tradeoff between the benefit of error-correcting codes for this kind

of channel and the related energy costs due to the transmission of redundant bits.


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4.1.2 Multi-link communications

We consider uplink communications from a UE to the MEH and we suppose that the

UE needs to send 𝑛𝑏 total bits to a MEC AP within a fixed maximum delay, i.e. with

an imposed latency constraint. In order to do this, the UE also aims at minimizing its

transmit power to save as much energy as possible. If we call 𝑅 the information

transmission rate employed by the UE and 𝐵 the available bandwidth, then the

communication delay can be written as 𝐷 = 𝑛𝑏/𝐵𝑅. Calling the latency constraint 𝐿,

the UE looks for the minimum transmit power 𝑝 that guarantees that 𝐷 ≤ 𝐿. Notice

that the latter is equivalent to impose that

𝑅 ≥𝑛𝑏

𝐵𝐿=: 𝑅𝑚𝑖𝑛.

That is, the latency constraint can be translated into a constraint on the minimum

acceptable information transmission rate. If we write the uplink UE-AP channel

capacity as 𝐶 = 𝐵 log2(1 + 𝑎𝑝), for some positive constant 𝑎 [dMC+18], and if we

assume that the modulation and coding scheme is properly chosen to achieve 𝐶, then

it is straightforward to show that the goal of minimizing the transmit power 𝑝 while

meeting the rate/latency constraint is achieved by setting 𝑅 = 𝑅𝑚𝑖𝑛 and

𝑝𝑚𝑖𝑛 =2𝑅𝑚𝑖𝑛 − 1

𝑎.

If the communication between the UE and the MEH happens in a single link, the above

transmit power 𝑝𝑚𝑖𝑛 cannot be further decreased without violating the latency

constraint. Nonetheless, an additional reduction is possible by introducing a new

degree of freedom in our scenario. In [dMC18], an analysis is proposed on the

convenience of exploiting simultaneous multi-link communications between the UE

and the MEH. From now on, when we speak of multi-link communications, we mean

that the UE can send different information to different APs via different mmWave links

and over all the available UE-AP links simultaneously. This requires the use of digital

beamforming. We also assume that all the APs can communicate among themselves

with negligible latency through an ideal high-capacity backhaul. In this way, one AP

endowed with a MEH can collect all the information sent by the UE within a negligible

delay. This scenario is consistent with cloud-RAN architecture, where the APs are

simple RRHs and the information is processed in the cloud. We represented this

architecture in Fig. 4.1-1 for the case of two links.

Fig. 4.1-1 - Two-link communication between a UE and the edge cloud.


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A detailed description of multi-beam technologies in mmWave communications with

fixed subarray and full multi-beam antennas is provided in [Hon17]. Although therein

the perspective lies on the AP's side, [dMC18] considers the case of UEs capable of

exploiting these (or equivalent) technologies. One of the aims of [dMC18] is to show

that multi-link communications can be convenient, because they allow to reduce the

overall transmit power with respect to the single-link case under the same latency

constraint (see also [D2.1] and [D4.1])). Let us recall the following definition, which

will be used in the next subsection:

Definition:

Consider 𝑁 communication links between a UE and 𝑁 APs to communicate a MEH;

let us call 𝐶𝑖 = 𝐵 log2(1 + 𝑎𝑖𝑝𝑖) the capacity of the 𝑖 -th link, with 𝑎1 ≥ 𝑎2 ≥ ⋯ ≥𝑎𝑁 > 0. We denote by 𝑁∗, with 1 ≤ 𝑁∗ ≤ 𝑁, the number of links that minimizes the

transmit power of latency-constrained communication. In other words, the minimum

transmit power is achieved by multi-link communication over the best 𝑁∗ links (out

of 𝑁).

[dMC+18] provides the detailed characterization of 𝑁∗ and the related optimal

strategy to split the total 𝑛𝑏 information bits over 𝑁∗ links; for the purposes of this

document, we just need to know that 𝑁∗ exists and can be explicitly and precisely

computed whenever the 𝑎𝑖 and 𝑅𝑚𝑖𝑛 are given. When we talk about the “power-

optimal communication strategy” in the following, we mean the multi-link

communication strategy over 𝑁∗ links that minimizes the total transmit power under

the latency constraint corresponding to 𝑅𝑚𝑖𝑛.

The scenario and the principles stated above are used for the analysis proposed in the

next subsection.

4.1.3 Block-erasure-correcting codes for robust multi-link communications

In deliverable D2.1 [D2.1], we introduced multi-link communication strategies to

tackle short term blocking events, i.e. blocking events that last much less than the

duration of the application. Conversely, when blocking events last longer,

overprovisioning is not effective anymore and other solutions need to be explored.

This can happen when obstacles slowly cross the line-of-sight path between the UE

and the AP and obstruct the link for “long” time intervals, even as long as a few seconds

[Mac17] or more. When this happens, waiting for the channel to be open again takes

too much time. One solution may be to complete the offloading procedure by restarting

it over other links, but this takes time and typically violates the latency constraint. To

overcome this problem, in this section we define and analyze a theoretical framework

to combine error-correcting-coding techniques with multi-link mmWave

communications to simultaneously perform computation offloading and contrast long-

term blocking events that start after the beginning of the offloading procedure, without

the need for retransmissions. Let us suppose to apply the power-wise optimal multi-

link communication strategy proposed in Section 4.1.2 and in [dMC18] over 𝑁 links,

transmitting 𝑛𝑖 bits over the 𝑖 -th link at rate 𝑅𝑖 , with ∑ 𝑛𝑖𝑁𝑖=1 = 𝑛𝑐 and 𝑛1 ≥ 𝑛2 ≥

⋯ ≥ 𝑛𝑁 . The 𝑖 -th channel is the communication link between the UE and its 𝑖 -th

closest AP, situated at distance 𝑑𝑖. Let us call 𝑃𝑖 the blocking probability of the 𝑖-th

link and let us assume that the distances are ordered in decreasing sense, so that 𝑃1 ≥


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𝑃2 ≥ ⋯ ≥ 𝑃𝑁. This is a realistic assumption, because longer line-of-sight paths have a

higher chance to be blocked. Consider, for simplicity, that blocking events are mutually

independent on any two links. In this case, the problem of offloading 𝑛𝑐 bits over

𝑁 links without losing information is equivalent to the problem of transmitting a word

of length 𝑛𝑐 bits over an asymmetric block-erasure channel, for which the 𝑛𝑐 bits are

split into 𝑁 blocks of length 𝑛𝑖 bits and each block has erasure probability 𝑃𝑖 .

Whenever one link is blocked, we suppose that all the bits of the corresponding block

are lost (erased) and this happens independently from block to block. This model is

our generalization [dMC18] of the block-erasure channel described in [Fab06]. We call

it “asymmetric” because we allow all the 𝑛𝑖’s and the 𝑃𝑖’s to be different from each

other. Our idea is to apply block-erasure-coding to multi-link communications to

counteract blocking effects and we start by generalizing and enriching the results of

[Fab06].

Formally, let 𝒞 ⊆ {0,1}𝑛𝑐 be an error-correcting code for the asymmetric block-

erasure channel of rate 𝑅𝒞 = log2|𝒞| 𝑛𝑐⁄ . 𝑛𝑐 is the total number of (coded) transmitted

bits, 𝑛𝑏 denotes the number of uncoded information bits, and 𝑅𝒞 = 𝑛𝑏/𝑛𝑐 is the

coding rate in case of linear codes. The codewords of 𝒞 are written as 𝒙 =(𝒙1|𝒙2| ⋯ |𝒙𝑁), where 𝒙𝑖 is the block of 𝑛𝑖 coordinates transmitted over the 𝑖-th link.

Let us define an erasure pattern 𝒆 as the vector 𝒆 = (𝑒1, 𝑒2, … , 𝑒𝑁) ∈ {0,1}𝑁 such that

𝑒𝑖 = 1 if the 𝑖-th block of a codeword is erased (i.e. if the 𝑖-th UE-AP link is blocked)

and 𝑒𝑖 = 0 otherwise. Thus, 𝒫{𝑒𝑖 = 1} = 𝑃𝑖. For a given 𝒆, we define

𝒞(𝒆) = {𝒙 ∈ 𝓒 ∶ if 𝑒𝑖 = 0 then 𝒙𝑖 = 0 ∀𝑖 = 1, … , 𝑁}.

𝒞(𝒆) is the set of codewords of 𝒞 whose non-zero blocks are only among the erased

blocks identified by 𝒆 . If 𝒞 is a linear code, then we can suppose without loss of

generality that the asymmetric block-erasure channel input is the all-zero codeword 0.

For every given erasure pattern 𝒆 , all the codewords of 𝒞(𝒆) will give the same

channel output as 0. Assuming that a maximum likelihood decoder does not give

priority to any of the codewords of 𝒞(𝒆), the word error probability caused by the

erasure pattern 𝒆 is

𝑃𝑒𝑤(𝒆) = 1 −

1

|𝒞(𝒆)|.

In particular, if 𝒞(𝒆) = {𝟎} and |𝒞(𝒆)| = 1 , the decoder is capable of correctly

decoding the erasure pattern 𝒆. Therefore, for linear codes, the word error probability

associated with the 𝑃𝑖′𝑠 equals

𝑃𝑒𝑤 = 𝑃𝑒

𝑤(𝑃1, … , 𝑃𝑁) ≔ 𝔼𝒆[𝑃𝑒𝑤(𝒆)] = 𝔼𝒆 [1 −

1

|𝒞(𝒆)|],

where the expected value is computed with respect to the distribution of the erasure

pattern.

We give the following definition of diversity: the block-diversity of a code 𝒞 is defined

as

𝛿 = min𝒙,𝒚∈𝒞∶𝒙≠𝒚

|{𝑖 ∈ {1,2, … , 𝑁} ∶ 𝒙𝑖 ≠ 𝒚𝑖}|.


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Notice that for every erasure pattern 𝒆 such that 𝛿 > ∑ 𝑒𝑖𝑁𝑖=1 , there will be no ML-

decoding errors. Therefore, we are interested in designing codes with the biggest

diversity possible. It is clear that, in general, 𝛿 ≤ 𝑁 and we say that a code has full

diversity if 𝛿 = 𝑁 . An upper bound for 𝛿 is given by our generalization of the

Singleton bound defined in [Fab06] for the case where all blocks have the same length.

In our more general setup, we have:

Theorem (Singleton bound [dMC18]):

Let 0 < 𝑅𝒞 ≤ 1 and let ℓ ∈ {1, … , 𝑁} be the only integer such that

∑ 𝑛𝑖

𝑁

1=ℓ+1

< 𝑛𝑐𝑅𝒞 ≤ ∑ 𝑛𝑖

𝑁

𝑖=ℓ

.

Let us call 𝑀 = 1

𝑁−ℓ+1 ∑ 𝑛𝑖

𝑁𝑖=ℓ the average length of the last 𝑁 − ℓ + 1 blocks of a

codeword. Then,

𝛿 ≤ ⌊1 + 𝑁 −𝑛𝑐𝑅𝒞

𝑀⌋ =: 𝛿𝑆𝐵 .

Now, let us define the outage probability as the probability that, due to blocking events,

the received number of bits is less than 𝑛𝑏 = 𝑛𝑐𝑅𝒞 (the number of information bits):

𝑃𝑜𝑢𝑡 = 𝒫 {∑(1 − 𝑒𝑖)𝑛𝑖 < 𝑛𝑐𝑅𝒞

𝑁

𝑖=1

}.

In general, in case of outage, correct decoding is impossible, regardless of the goodness

of the code. Hence, 𝑃𝑒𝑤 ≥ 𝑃𝑜𝑢𝑡 and we are interested in designing coding techniques

that minimize 𝑃𝑜𝑢𝑡, in order to aim at as low 𝑃𝑒𝑤 as possible. The following upper and

lower bounds for the outage probability can be proved:

Theorem [dMC18]:

Let 0 < 𝑅𝒞 ≤ 1, let ℓ ∈ {1, … , 𝑁} be the only integer such that

∑ 𝑛𝑖

𝑁

𝑖=ℓ+1


𝑁

𝑖=ℓ

and, analogously, let 𝑗 ∈ {0, … , 𝑁 − 1} be the only integer such that

∑ 𝑛𝑖

𝑗

𝑖=1


𝑗+1

𝑖=1

.

The outage probability is bounded as follows:


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∑ (𝑁

𝑢) ∏ 𝑃𝑖

𝑁−𝑢

𝑖=1

∏ (1 − 𝑃𝑖)

𝑁

𝑖=𝑁−𝑢+1

𝑗

𝑢=0

≤ 𝑃𝑜𝑢𝑡 ≤ ∑ (𝑁

𝑢) ∏(1 − 𝑃𝑖)

𝑢

𝑖=1

∏ 𝑃𝑖

𝑁

𝑖=𝑢+1

𝑁−ℓ

𝑢=0

.

Several models exist that quantify the blocking probability of mmWave signals

[TBH16], [Gap16], [ABK17], [QHW17], [GDC17]. Let us recall the model proposed

in Corollary 1.1 of [Bai14], that we will exploit for the simulation results presented in

the following: in the bidimensional space, obstacles are assumed to be rectangles with

random length 𝑋, width 𝑊, and centers randomly distributed according to a Poisson

point process with density 𝜇 . Then, the probability that the line-of-sight

communication path between the UE and an AP at distance 𝑑 is not obstructed is:

𝑃𝑜𝑛(𝜇, 𝑑) = exp( − 𝛽𝑑 − 𝑞),

where 𝛽 = 2𝜇𝜋−1(𝔼[𝑊] + 𝔼[𝑋]) and 𝑞 = 𝜇𝔼[𝑊]𝔼[𝑋].

Fig. 4.1-2 Average outage probability as a function of the density of obstacles,

for different values of 𝑹𝓒.

In Fig. 4.1-2, we show the behavior of the outage probability as a function of the

obstacle density 𝜇 . This result is obtained with the blocking probability model

described above, with 𝔼[𝑋] = 𝔼[𝑊] = 2 m. The outage probability is computed by

exhaustive evaluation of the outage probability for 𝑅𝑚𝑖𝑛 = 8 bit/s/Hz and for all

possible erasure patterns 𝒆 ; the outage probability is averaged over random

realizations of a deployment with 𝑁 = 15 APs randomly distributed in a square region

of size 300 m. For every deployment and for every fixed 𝑅𝒞 , the power-optimal

number of links used for offloading is chosen as intended in Section 4.1.2, with

𝑎𝑖 = 𝐺𝑅𝐺𝑇 (𝜆𝑤

4𝜋𝜎𝑛𝑑𝑖)

2

,


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where 𝐺𝑅 = 128 and 𝐺𝑇 = 32 are the antenna gain at the receiver and transmitter side,

𝜆𝑤 = 5 mm is the signal wavelength, 𝜎𝑛 = −82,96 dBm is the Gaussian noise

standard deviation, and 𝑑𝑖 is the distance between the UE and the 𝑖-th closest AP. The

values of 𝔼[𝑋] , 𝔼[𝑊] , and 𝑅𝑚𝑖𝑛 will remain constant for all the simulation results,

unless stated otherwise. As expected, the outage probability decreases with 𝑅𝒞 and

grows with 𝜇.

Fig. 4.1-3 is obtained with the same simulation parameters of Fig. 4.1-2, but its goal

is to show the maximum possible coding rate necessary to maintain the outage

probability smaller than a fixed value. As the intuition suggests, 𝑅𝒞 needs to decrease

when 𝜇 increases, if we want to guarantee a bounded outage probability.

Fig. 4.1-3 The maximum allowed coding rate needed to guarantee that the

outage probability is smaller than a given fixed value.

To code or not to code?

This subsection addresses the following question: assuming that optimal codes can be

designed for the asymmetric block-erasure channel, whose word error probability

achieves the outage probability, in what circumstances are they worth to be used for

power- and latency-constrained computation offloading? Some considerations and

numerical simulations are provided in the sequel.

Employing a code of rate 𝑅𝒞 to fight blocking over 𝑁 links implies an increase in the

number of transmitted bits of a factor 𝑅𝒞−1 : if 𝑛𝑏 information bits are sent in the

uncoded case, they become 𝑛𝑐 = 𝑛𝑏𝑅𝒞−1 ≥ 𝑛𝑏 after encoding. Since we are

considering communication scenarios with an imposed latency constraint that cannot

be violated, this means that any block-erasure-correcting technique entails the

transmission of more bits with respect to an uncoded transmission within the same

amount of fixed time. This means that we need to increase our spectral efficiency and,

consequently, that the power cost of a coded transmission strategy is higher. This also

implies that the power-wise optimal number of links will be in general higher. When


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the error-correcting code is well-designed, this setup achieves the main goal of

allowing the loss of information on some links (due to long-term blocking events),

without compromising the offloading procedure. However, the need to transmit more

bits clearly yields a cost in terms of transmission power that needs to be taken into

account.

Now, in the uncoded scenario, the outage probability equals the probability that at least

one link is blocked and the information sent over it is lost. Therefore, over 𝑁 channels,

the outage probability of the uncoded transmission scheme is 𝑃𝑜𝑢𝑡𝑢𝑛𝑐(𝑁) = 1 −

∏ 1 − 𝑃𝑖𝑁𝑖=1 . Notice that 𝑃𝑜𝑢𝑡

𝑢𝑛𝑐(𝑁) is a strictly increasing function of 𝑁, because for

every 𝑖,

𝑃𝑜𝑢𝑡𝑢𝑛𝑐(𝑖) > 𝑃𝑜𝑢𝑡

𝑢𝑛𝑐(𝑖 − 1) ⇔ ∏ 1 − 𝑃𝑗

𝑖−1

𝑗=1

> ∏ 1 − 𝑃𝑗

𝑖

𝑗=1

⇔ 1 > 1 − 𝑃𝑗 ,

and the latter is always true. Hence, when we restrict ourselves to the uncoded

transmission scheme, we face two completely opposite requirements: the necessity to

keep low (ideally to 1) the number of links to control the outage probability and the

need for increasing it (up to 𝑁∗) to minimize the transmit power. We will show through

numerical results in what terms coding for the block-erasure channel provides

beneficial compromises between the two previous contrasting requisites. In this

perspective, we claim that a fair assessment of the advantages of error-correcting codes

in this scenario needs to consider the tradeoff between transmit power consumption

and achievable outage probability, rather than focusing on each of these two separately.

Fig. 4.1- 4 shows the average transmit power as a function of the density of obstacles,

when the outage probability is constrained below a maximum value (𝑃𝑜𝑢𝑡 ≤ 0.05).

The results are obtained in a scenario with 15 APs deployed in a square region of size

200 m around the UE, where the obstacles' average dimensions are 𝔼[𝑊] = 1 m and

𝔼[𝑋] = 2 m. First of all, notice that if we rely on the uncoded transmission strategy,

the upper bound on the outage probability can be guaranteed only for obstacle densities

𝜇 not much bigger than 175/km2. For higher densities, there always exist deployments

in the considered region such that 𝑃𝑜𝑢𝑡𝑢𝑛𝑐(𝑁) ≥ 𝑃𝑜𝑢𝑡

𝑢𝑛𝑐(1) = 𝑃1 > 0.05. This is the

reason why the red curve in Fig. 4.1- 4 is plotted exclusively for 𝜇 ≤ 175. The figure

depicts the comparison between the power cost of the uncoded and coded transmission

strategies as a function of 𝜇 and averaged over random deployments of the 15 APs.

Recalling the definition of 𝑁∗ given above, the number of links 𝑁𝑢𝑛𝑐 used for uncoded

multi-link offloading is computed for each instance of the AP deployment as:

𝑁𝑢𝑛𝑐 = max{𝑁 ∈ {1, … , 𝑁∗} ∶ 𝑃𝑜𝑢𝑡 ≤ 0.05} ≤ 𝑁∗.


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Fig. 4.1- 4 - Average transmit power in the uncoded and coded case under the

constraint 𝑷𝒐𝒖𝒕 ≤ 𝟎. 𝟎𝟓.

For the coded scheme, instead, the coding rate 𝑅𝒞 was chosen as the maximum that

guarantees 𝑃𝑜𝑢𝑡 ≤ 0.05 , obtained by exhaustive research. Then, the corresponding

number of channels for multi-link offloading was computed according to the criterion

of transmit power minimization, with fixed total transmission rate 𝑅𝑚𝑖𝑛𝑅𝒞−1 and

𝑅𝑚𝑖𝑛 = 8 or 16. The picture clearly shows that well-designed error-correcting codes

may enable offloading in scenarios where the obstacle density makes the outage

probability uncontrollable for the uncoded communication strategy. Moreover, for

“medium” obstacle densities (75 ≤ 𝜇 ≤ 175 ), recurring to error-correcting codes

yields considerable gains in the transmit power for 𝑅𝑚𝑖𝑛 = 16 . Finally, the figure

confirms that in contexts with “few” obstacles (low 𝜇 ), a coded communication

scheme may not be needed, because the outage probability remains bounded and the

power gain provided by the code transmission scheme is reduced.

Using the same main simulation parameters of Fig. 4.1-5, Fig. 4.1-5(a) shows that

error-correcting codes may also be exploited to fully outperform the best possible

outage probability achievable with uncoded transmissions: the latter is obtained by

exclusively transmitting over the best available link and is represented by the constant

blue lines in the figure (averaged over different random AP deployments and for a few

different obstacle densities in an area of 300 m × 300 m). Choosing a small enough

coding rate 𝑅𝒞 allows to both obtain better average outage probabilities and to reduce

the average transmit power, as shown by the combination of Fig. 4.1-5 (a) and Fig.

4.1-5 (b). For instance, an optimal code with 𝑅𝒞 = 0.5 would allow to achieve better

outage probabilities than any uncoded transmission for each of the proposed obstacle

densities and, at the same time, reduce by 5 dBm the average transmit power with

respect to the uncoded strategy that minimizes the outage probability.


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Fig. 4.1-5 Average outage probability (a) and average transmit power (b) as

functions of the coding rate 𝑹𝓒 for different densities of obstacles.

4.2 Multi-route multiplexing on mmWave mesh backhauling against

overloaded edge cloud

4.2.1 System architecture

In such an environment of dynamic crowd scenario, network densification with many

number of mmWave small cells overlaid on the current LTE cells is effective to

accommodate traffic in peak hours. However, many number of small cells leads to the

problem of high CAPEX and OPEX. One solution to relax the problem is to use

mmWave meshed network for the backhauling of small cells since CAPEX can be

reduced by avoiding deployment cost of wired backhaul. Furthermore, OPEX can also

be reduced by introducing dynamic ON/OFF and flexible path creation in the backhaul

network in accordance with the time-variant and spatially non-uniform traffic. Such

flexible control of the backhaul network is enabled by Software Defined Network

(SDN) technology using out-band control interface over the LTE. Here, mmWave

meshed backhaul with SDN comes into place as one suitable candidate for dense urban

scenarios owing to its ultra-wide bandwidth and deployment flexibility with low cost.

This section presents our proposed method to control mmWave meshed backhaul for

efficient operation of mmWave small cell overlay HetNet. One main feature of our

algorithm is backhauling route multiplexing for overloaded mmWave small cell base

stations (SC-BSs). The other feature is the ON/OFF switching control of wireless

interfaces in less loaded spot. Considering practical user distribution modelled from

realistic measurement data, radio backhaul resources should be concentrated on

overloaded mmWave SC-BSs. Inversely, less loaded mmWave SC-BSs should be

deactivated for saving power.

We employ mmWave overlay HetNet shown in Fig. 4.2-1 as a network topology. In

the mmWave overlay HetNet, LTE is assumed to manage the C-plane information, i.e.

user’s location, movement, traffic demand and also dynamic configuration of wireless

backhaul. The LTE macro BS plays a role of mmWave gateway (GW), which is the

only information source of the whole network.


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Fig. 4.2-1 - mmWave meshed network overlaid on a macro cell.

An example of mmWave meshed network to be used in the dense urban scenario is

also depicted in the above figure. Here, mmWave SC-BSs are overlaid on a LTE macro

cell. The SC-BS has integrated backhaul and access of multiple sectors in both access

and backhaul interfaces. A set of LTE macro BS and mmWave SC-BSs forms a -RAN

or micro operator for a target environment e.g. stadium. In our mmWave meshed

network, GW can be connected to the mmWave SC-BS either directly or indirectly

through relay scheme. This latter scheme can perform backhauling of adaptive

topology, and also conduct backhauling route multiplexing toward a dense traffic spot.

Another advantage is that path loss attenuation can be compensated by amplification

per relay. For stable communications and ease of analysis, relay scheme is only able

to be formed among only links which can achieve maximum data rate of IEEE

802.11ad standard to guarantee a highest homogeneous backhauling rate.

4.2.2 Optimization problem

The prominent objective of the traffic & energy management algorithm is to reduce

energy consumption of mmWave meshed network by switching off as many mmWave

SC-BSs as possible in an area while satisfying users’ traffic demands. As it is hard to

optimize ON/OFF status of mmWave SC-BSs and backhaul paths all at once, the

algorithm involves three steps.

The first step (i):

The initial ON/OFF status of SC-BSs is determined based on the traffic demands per

SC-BS. This determines tentative ON/OFF status of each SC-BS considering multi-

RAT selectivity of microwave LTE and mmWave SC-BS and the goal is to reduce the

total power consumption of mmWave network as much as possible. In order to

minimize the total power consumption, LTE should serve as many users as possible

within its available bandwidth and less loaded SC-BSs should be set OFF. As it

is complicated to consider each user individually, all SC-BSs are activated at first and

all users are served by their nearest SC-BS. Then the i-th SC-BS has an aggregated

traffic demand . If can be instead served by macro LTE, LTE needs to allocate

some bandwidth given by Shannon’s capacity as follows.

BLTE

Ti Ti

bi


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where is the approximated SINR (Signal to Interference plus Noise power Ratio)

of signals from LTE macro BS to the i-th SC-BS considering only path loss attenuation.

Therefore, in order to determine tentative ON/OFF status of SC-BS, we have only to

determine which system of LTE or mmWave network should accommodate . When

we define as a state that users around the i-th SC-BS are accommodated by the

k-th sector of LTE macro BS, the problem to be solved is as follows.

where expresses the number of SC-BSs included in . As a result, if is

accommodated by LTE, the corresponding users around the i-th SC-BS will be

accommodated by LTE, and the i-th SC-BS can be set OFF to reduce power

consumption. If the i-th SC-BS is set ON, all the 3 sectors for the i-th SC-BS’s access

structure will be activated regardless of the number of users in the coverage of the i-th

SC-BS and the user location.

The second step (ii):

Initial paths of backhaul network are created to minimize power consumption.

mmWave backhaul links are formed among SC-BSs that are set ON in step (i) to satisfy

user’s traffic demand. In other words, appropriate backhauling routes from any sector

of GW to SC-BS are determined. Using load balancing approach, we determine such

routes by solving the following linear programming problem:

When the number of SC-BS and the number of sectors of GW are denoted by and

respectively, total number of flow equals the product of these.

means the data amount to be transmitted from any sector of GW to any SC-BS,

weights the number of relay hop against x, is the summation of

traffic load accommodated by each sector of GW, is the summation of

traffic supplied to each SC-BS, expresses the ON/OFF state. is

the aggregated traffic demand of each SC-BS, is a mapping matrix

bi =Ti

log2(1+g i )

g i

Ti

iÎGk

|Gk | Gk Ti

NS

NAPNV xÎ RNV

f Î RNV tS Î RNS

tAP Î RNAP

aÎ RNAP TD Î RNAP

WAP Î RNV´NAP


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between and x, is a mapping matrix between and x. The

constraint [A] means the capacity of each sector of GW, [B] ensures satisfaction of

user’s request, [C] assures that the value of traffic is not negative. We then get the

optimal combination of transmitter sector of GW and receiver SC-BS from solving for

x.

The third step (iii):

This step re-activates remaining SC-BSs in an energy efficient manner so as to transfer

the traffic for the isolated SC-BSs [GIA18-2]. Control signaling to manage ON/OFF

status of SC-BSs and to create physical paths between them are transmitted over the

LTE as an out-band control plane. As such, a dynamic and energy efficient mmWave

meshed network is formed.

4.2.3 Numerical analysis

This section shows several examples of simulation analysis for mmWave meshed

networks controlled by the aforementioned algorithm. In this numerical analysis,

several macro cells with ISD of 500m are assumed to be deployed within the 2000m

square areas in Sect. 3.2 and one macro cell is selected as the evaluation cell. Other

simulation parameters are shown in Table 4.2.1.

Table 4.2.1 - Simulation parameters

Parameter LTE mmWave edge cloud

Bandwidth 10MHz 2×2.16GHz

Carrier freq. 2.0GHz 60GHz

Antenna gain 17dBi 26dBi

Antenna height 25m 4m/25m (SC-BS/GW)

Tx power 46dBm 10dBm

Beam pattern 3GPP IEEE802.11ad

Path loss 3GPP [REF]

# of BSs 1 90

Noise density 174dBm/Hz

Examples of the formed mmWave meshed networks are shown in Fig. 4.2-2. As there

are few users in the evaluation area at 3AM, only a few mmWave SC-BSs are activated.

In this case, since there are enough resource blocks in the LTE, most of the users are

connected to the macro BS, while users with very high traffic demand at the right-

bottom activate SC-BSs. On the other hand, at 3PM, a hotspot appears in the upper-

left zone. We can see some backhaul links formed from gateway to the hotspot,

showing the effectiveness of the traffic and energy management algorithm against the

locally intensive traffic. In other word, the proposed approach can alleviate overloaded

edge cloud via multi-route multiplexing mechanism over the mmWave meshed

backhaul.

tAPWS Î RNV´NS tS


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5G-MiEdge Page 69

(a) Formed mmWave meshed network at AM 3:00.

(b) Formed mmWave meshed network at PM 3:00.

Fig. 4.2-2 - Dynamic formation of mmWave meshed network.


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5G-MiEdge Page 70

5 Relevance of the proposed algorithms with the project use cases

The previous sections describe in details the following novel algorithms, devised and

implemented by the 5G-MiEdge consortium under the WP3 activities:

a. Resource allocation for computation offloading;

b. Data prefetching;

c. Computational load distribution among MEHs;

d. Dynamic ON/OFF strategies;

e. Robust design analysis of mobile edge computing over mmWave links;


edge cloud.

Most of those algorithms have a general validity and are scalable enough to provide

advantages to several scenarios and different use cases, dealing with the synergy of

mmWave and MEC technologies. Nevertheless, some of the use cases defined by 5G-

MiEdge in previous deliverables, e.g. a preliminary version in D1.1 [D1.1] and a final

refined version in D 1.3 [D1.3], could benefit more than other use cases. In the

following a brief analysis of the impact of the proposed algorithm on the project use

cases is provided.

5.1.1 Omotenashi services

In Omotenashi services, data prefetching can be realized for foreign passengers who

arrive at the airport and can download their necessary information for their

business/travel trips right away after they get to the destination airport, as well as

download of entertaining contents. Of course, when there are no passengers at night,

the base station (e.g. signage) can be turned off for energy saving, thus the dynamic

ON/OFF algorithms described in section 3.2 also applies to this use case to reduce

OPEX due to energy consumption.

To summarize, the algorithms that can bring benefits to this use cases are:


d. Dynamic ON/OFF strategies.

5.1.2 Moving hotspot

Prefetching contents to be retrieved by users within low latency is important to

maintain a good quality of service. For this reason, the prefetching algorithm described

in section 2.2 well fits the moving hotspot use case. Moreover, multi-route

multiplexing over mmWave mesh backhauling can be applied for the moving hotspot

scenario as well in case they employ mmWave mesh backhauling. Concentrated

contents toward the moving MEH can be separated into several routes and distribute

to the MEH from multiple transmission points (BSs). At the same time, dynamic

ON/OFF strategies can help in reducing energy consumption by turning off BS when

unused.



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5G-MiEdge Page 71



f. Multi-route multiplexing on mmWave mesh backhauling against overloaded edge

cloud.

5.1.3 2020 Tokyo Olympic

The stadium is a typical ultra-dense scenario where thousands of spectators want to

share at the same time contents and personal experiences. The challenging idea of

creating a unique user experience through AR/VR videos requires a very efficient

management of the computation resources of edge servers, in order to avoid large end-

to-end delays. For this reason, distributing computing among edge servers can enhance

the performance of the system and the quality of service perceived by the end users.

Other applicable algorithms are resource allocation strategies for computation

offloading, data prefetching to reduce download delay, and robust design over

mmWave links to guarantee service continuity.





e. Robust design analysis of mobile edge computing over mmWave links.

5.1.4 Outdoor dynamic crowd

The dynamic crowd use case is the typical scenario where resource allocation

strategies for computation offloading defined in section 2 are important to efficiently

manage radio and computation resources in order to provide good quality of service to

the end users, since the limited computation resources of the edge cloud have to be

shared among users with different application requirements and channel conditions.

Computational load distribution is also important to provide low-latency services, and

robust design over mmWave links to guarantee service continuity. Moreover, the

dynamicity of the system (radio channels, computation task arrivals, mobility) has to

be handled via proper dynamic optimization, described in section 2 as well. Finally,

for energy efficiency purposes, it is paramount to be able to switch on and off also at

a certain frequency, the available resource, so to follow the dynamical variations of the

resource requests and to reduce the OPEX via energy saving.







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5G-MiEdge Page 72

5.1.5 Automated driving

Providing reliable communications to mmWave APs in presence of blocking events, is

a fundamental challenge and an important issue. For instance, a seamless service is

important for the automated driving scenario, due to the critical aspects of some

application such as, e.g., safety applications. Indeed, since our use case requires high

data rate (provided by mmWave communications) and low end-to-end latency (10 ms),

blocking events due to obstacles can be detrimental and have negative effects on the

system performance and the capability of maintaining the service.

For this reason, countermeasures such the ones described in section 4.1 can be

necessary for this purpose. Section 4.1is a very general analysis of the effect of a

possible block erasure channel coding strategy, enabled by multi-link communications.

The reliability of the service is enhanced with respect to a single link case prone to

blocking events. Computation offloading is another service that the automated driving

scenario can benefit of, as well as the multi-route multiplexing on mmWave mesh

backhauling against overloaded edge cloud.




In table 5-1, we summarize the mapping between the proposed algorithm and the 5G-

Miedge use cases.

Use case

Algorithm

Omotenashi

Service

Moving

hotspot

2020

Tokyo

Olympic

Outdoor

dynamic

crowd

Automated

driving

Resource allocation for

computation offloading ✓ ✓ ✓

Data prefetching ✓ ✓ ✓ ✓

Computational load

distribution among

MEHs

✓ ✓

Dynamic ON/OFF

strategies ✓ ✓ ✓

Robust design analysis

of mobile edge

computing over

mmWave links

✓ ✓ ✓

Multi-route

multiplexing on

mmWave mesh

backhauling against

overloaded edge cloud

✓


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6 Summary

To summarize, in this deliverable we described the output of the activities related to

WP3, in particular regarding task 3.3: “User/application centric orchestration to realize

5G liquid edge cloud”. In particular, we developed novel algorithms for the following

purposes:

Resource allocation for computation offloading;

Data prefetching;

Computational load distribution among MEHs;

Dynamic ON/OFF strategies;

Robust design analysis of mobile edge computing over mmWave links;

Multi-route multiplexing on mmWave mesh backhauling against overloaded

edge cloud.

Then, the algorithms described in this deliverable aim at realizing an efficient

application centric resource management, taking into account the two aspects of 5G-

Miedge: mmWave communications for the radio access and Multi-Access Edge

Computing, which provide computation and storage resources at the edge of the

network. Indeed, radio, computation and storage aspects are seen as a holistic system

and are optimized to enable the edge cloud functionalities. Finally, the deliverable

describes a mapping between the proposed algorithms and the 5 use cases of 5G-

MiEdge. Indeed, although the algorithms are general and applicable in different

scenarios, they can be used to enable the use cases proposed by the project.


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Documents

Deliverable Horizon2020 EUJ-01-2016 723171 5G-MiEdge D3.4 ... · Nature: Report Version: 1 Number of pages: 79 Abstract This deliverable is the final report of Task 3.3. It reports