On Processor Sharing (PS) and Its Applications to Cellular Data Network Provisioning

IFIP Performance 2007

On Processor Sharing (PS) and Its Applications to Cellular Data Network Provisioning

Yujing Wu, Carey Williamson, Jingxiang Luo

Department of Computer ScienceUniversity of Calgary


Motivation Insensitivity of network performance to

the traffic details is a desirable property, since it facilitates robust traffic engineering.

Example: Erlang B call blocking formula

How about 3G cellular data networks? Are performance measures sensitive to the detailed traffic characteristics (e.g., flow size distribution, flow inter-arrival time, number of flows, correlations) or not?


Synopsis of Paper Q: Processor Sharing (PS) = insensitivity?

Egalitarian Processor Sharing (EPS): yes Discriminatory Processor Sharing (DPS): no

DPS is a better model of cellular networks with Proportional Fairness (PF) scheduling

Insensitivity study carried out for DPS DPS is “approximately insensitive” EV-DO simulation study verifies DPS results

Results do not hold for differentiated services


Key Contributions Improve the understanding of PS

Prove the strict insensitivity of EPS in a relevant new case (i.e., finite capacity EPS)

Systematically investigate the approximate insensitivity of DPS by simulation

Apply these findings to traffic engineering for the downlink in 3G cellular data networks Practical insensitivity when PF scheduling is used Sensitivity when supporting differentiated

services


Outline

Motivation & Contributions Modeling cellular data networks EPS and DPS results Simulation of a cellular system Service differentiation Summary


Downlink Model for a Cellular Data Network

dataflow 1

dataflow 2

dataflow n

MS

MS

MS

PFscheduler

current feasible rate: r( i )

TDM

.. . .. .

1.667msframe

forward link

C(t)

CAC

)(

)(maxarg)(

n1,...,j tT

trti

j

j

flow arrivals

feasible rate of flow j at slot t

realized throughput of flow j up to slot t

schedule flow i at slot t

propagation loss, shadowing, fast fading


Modeling Cellular Networks

The downlink of the cellular system behaves like a PS queue with respect to the flow-level performance

With different assumptions about rate variations, the system can be abstracted to different models.

Homogenous rate variation (idealized situation): the feasible rate fluctuates around the mean for all active flows, and these fluctuations are statistically identical for all users.

Heterogeneous rate variation: the feasible rate fluctuations around the mean for active flows are statistically different. PF allocates more time to users with lower variability in the feasible rate.

EPS

DPS


Traffic model I: Poisson flow arrivals

The flow size distribution is general.

Poisson process


Traffic model II: Poisson session arrivals

Flows in a session

session arrival epochs (Poisson process)

1. distribution of number of flows per session

2. flow size distribution3. think time distribution4. correlation in successive flow

and think time statistics

general session structure

flexibility to model more realistic traffic.


Outline



EPS Queue Results Insensitivity has been proven for:

Poisson flow arrivals without blocking [Cohen; Kelly]

Poisson session traffic with infinite capacity [Bonald et al. 2001abc; Bonald 2006; Borst 2003]

We prove that the joint queue length distribution, mean number of active flows, and blocking probabilities are insensitive to the session structure in the finite-capacity EPS queue fed by Poisson session arrivals.


Finite Capacity EPS system Model the system by a queueing network

with a restricted state space. Apply results from stochastic queueing

network theory for the proof. (see paper) Value? Assuming homogenous rate

variation in the cellular system, we can replace the complicated Poisson session traffic with simple Poisson flows with exponentially distributed flow sizes. The simplified model will suffice for provisioning purposes.


DPS Queue Results Rigorously speaking, performance is

sensitive to the traffic details [Bonald 2004] Insensitive bounds and limiting

approximations exist. [Fayolle 1980; van Kessel 2005; Bonald 2004; Boxma 2006]

Do the insensitivity properties of EPS systems approximately carry over to DPS for certain parameter choices?


DPS Model of 3G System M flow types Within type m, lm subclasses reflecting

unequal sharing of time slots Assume all flows are geographically

placed uniformly at random in the cell site, independent of their types.

MmwwwWmlmmmm ,,1 ],,,,[ ,2,1,

MmwwwWW lm ,1 ],,,[ 21 ],,,[ 21 MWWWW


DPS Simulation Model Single class of traffic, but different flow weights Finite-capacity: at most 15 concurrent flows Two types of Poisson session traffic

Type 1: 5 flows/session (deterministic) , LN flow size (mean 2, CV 3), HyperExp thinking time (mean 1, CV 3)

Type 2: Geo dist. for flow/session (mean 10), exp dist. thinking time (mean 0.05), flow sizes being one of five dist. (Deterministic, Exp, HyperExp, LN, Pareto)

Change session details of type 2 and compare the results to those in the case where both types are Poisson flows with exponentially distributed sizes.


DPS Simulation Results

Wi=[1, 2], i=1, 2 Wi=[1, 10], i=1, 2


DPS Observations

Flow details (session structure) have little impact on the first-order system performance unless the weights among different flows are highly skewed (e.g., the weight ratio is 10 or more).

In practical cellular systems, the unequal slot sharing among flows caused by PF scheduling and by heterogeneous rate variations is only modest (e.g., weight ratio is less than 2).

It is conjectured that traffic details do not affect the metrics relevant to network provisioning.


Outline



EV-DO System Model Simulate a shared downlink data channel of

the central cell site surrounded by interfering cells (6 direct neighbours, and 12 outer cells).

All BSs transmit at full power on the downlink.

The channel model includes propagation loss, slow fading, and fast fading.

Flows are placed uniformly at random in the center cell, and users do not move during flow transmission. Each active flow has a time-varying SINR updated at every slot.


Static User Scenario

Node ID

1 2 3 4 5 6

Slot share

18.4% 18.4%

17.9%

16.9%

14.6% 13.7%

xx xx xx

node 1

node 6 PF unfairness exists, but it is not extreme!

BS


Dynamic User Scenario

Poisson flow arrivals

flow size: m=50kB

Poisson session arrivals

flows per session: geometric dist., m=30;

think time: exp dist., m=5s

flow size: m=50KB

No blocking

Approximate insensitivity!


Outline



Service Differentiation Deliberately treat traffic unequally

at the type level (i.e., strict priority) To what extent does the weight

asymmetry among traffic types change the insensitivity property?

A DPS system with two types of Poisson flow arrivals, each with a single subclass. 1 ],,1[ aaW


DPS with Differentiated Service

2a

Change flow size distribution of high priority traffic type

Change flow size distribution of low priority traffic type


Service Differentiation Results

Compared to the bias among subclasses, the bias among traffic types manifests sensitivity in a much more dramatic way.

Depending on the traffic priority, variability in the flow size distribution has different impacts.

Using simple traffic models may lead to under-estimation or over-estimation of performance in the cellular system when differentiated services are deployed.


Summary Studied EPS/DPS models of cellular networks Extended the theoretical analysis of the EPS

insensitivity to a new finite-capacity case. Showed that the first-order performance of

DPS systems is approximately insensitive to the session structure in relevant regime for practical parameter settings.

Simple and robust traffic engineering is possible for cellular systems using DPS for PF scheduling.

The introduction of differentiated services may pose a great challenge for future cellular network provisioning.

Documents

On Processor Sharing (PS) and Its Applications to Cellular Data Network Provisioning