Modified Cell Delineation Strategy For Packet Switched Networks

11

Modified Cell Delineation Strategy Modified Cell Delineation Strategy for Packet Switched Networksfor Packet Switched Networks

Department of Computer ScienceDepartment of Computer ScienceBar-Ilan UniversityBar-Ilan University

Department of Communication EngineeringDepartment of Communication EngineeringHolon Academic Institute of TechnologyHolon Academic Institute of Technology

Marina KopeetskyMarina Kopeetskyandand

Avi LinAvi Lin

22

OutlineOutline

The Packet Network Computational ModelThe Packet Network Computational Model

The Packets’ Errors Handling ProblemThe Packets’ Errors Handling Problem

The Modified Cell Delineation StrategyThe Modified Cell Delineation Strategy

Example: the Three-States Cell Delineation Example: the Three-States Cell Delineation

Strategy Realization.Strategy Realization.

33

Talk Key IssuesTalk Key Issues Presenting a new Cell Delineation (CD) Strategy for any Presenting a new Cell Delineation (CD) Strategy for any

Packet Switching technology of a fixed length Data Units Packet Switching technology of a fixed length Data Units (DUs)(DUs)

This special strategy offers algorithms for differentiating This special strategy offers algorithms for differentiating between synchronization failures and other channel and between synchronization failures and other channel and environment errors with a sufficiently high confidence levelenvironment errors with a sufficiently high confidence level

This algorithms’ family is analyzed and optimized.This algorithms’ family is analyzed and optimized. A possible implementation of this strategy is illustrated for A possible implementation of this strategy is illustrated for

the ATM network case:the ATM network case:– The Cell Delineation cycle implementation time is discussed and The Cell Delineation cycle implementation time is discussed and

analyzed. analyzed.

– Numerical results are presented for the case of the standard CD Numerical results are presented for the case of the standard CD protocol. protocol.

44

The Packets’ Errors HandlingThe Packets’ Errors Handling

A new strategy, algorithms and relevant techniques are:A new strategy, algorithms and relevant techniques are:

offered for properly recognize and maintain cell or packet's offered for properly recognize and maintain cell or packet's

boundaries boundaries

designed to tackle and handle general error packets, with the designed to tackle and handle general error packets, with the

major objectives to differentiate in Real Time between major objectives to differentiate in Real Time between

synchronization failures and other noisy environment channel synchronization failures and other noisy environment channel

errors errors

For handling corrections:For handling corrections:

– The algorithms are properly modified for cell The algorithms are properly modified for cell

synchronization recovery and other noisy channel errors synchronization recovery and other noisy channel errors

– corrections are proposed, analyzed and optimized corrections are proposed, analyzed and optimized

55

Introduction and Packet Network Introduction and Packet Network ModelModel

We propose a new Cell Delineation (CD) Strategy We propose a new Cell Delineation (CD) Strategy for any Packet Switching technology with the for any Packet Switching technology with the fixed length Data Units (DUs). A special strategy fixed length Data Units (DUs). A special strategy that differentiates between synchronization that differentiates between synchronization failures and other channel errors with the failures and other channel errors with the sufficiently high confidence level is proposed, sufficiently high confidence level is proposed, analyzed and optimized.analyzed and optimized.

The strategy implementation is illustrated on the The strategy implementation is illustrated on the Asynchronous Transfer Mode (ATM) network Asynchronous Transfer Mode (ATM) network example. The Cell Delineation cycle example. The Cell Delineation cycle implementation time is discussed and analyzed. implementation time is discussed and analyzed. The numerical results are presented for the case The numerical results are presented for the case of the standard Cell Delineation (CD) protocol. of the standard Cell Delineation (CD) protocol.

66

Main Research ConclusionsMain Research Conclusions

The expansion of the number of the CD protocol The expansion of the number of the CD protocol discrete states is necessary in order to construct discrete states is necessary in order to construct the Cell Delineation recovery procedure in the the Cell Delineation recovery procedure in the optimal/near optimal manner.optimal/near optimal manner.

The CD protocol parameters should be chosen The CD protocol parameters should be chosen dynamically based on the traffic transmission dynamically based on the traffic transmission conditions.conditions.

The presented strategy is appropriated to any The presented strategy is appropriated to any fixed cell/packet network technology.fixed cell/packet network technology.

Construction of the distribution function of the CD Construction of the distribution function of the CD protocol cycle time in the precise way.protocol cycle time in the precise way.

77

FixedFixed Cell Network Protocol StructureCell Network Protocol Structure

Payload Field

n bytes

n=48 for ATM

Header

m bytes

m=5 for ATM

H

E

C

H

E

C

L=m+n bytes

88

Classical Cell Delineation Process Classical Cell Delineation Process StructureStructure

SYNCH

HUNT

PRESYNCH

checkbitbyBit

cellscorrecteconsecutivδm

cellscorrect-noneconsecutivαn

CD process parameters should be allocated in a dynamic fashion!

HEC indicates on out of synchronism state

99

Synchronization failures and other channel errors are mixed together and treated in the same way leading to cell drop and information transfer lose.

Thus

• Different types of errors must be treated differently!

•Traffic based Dynamic allocation of the CD process parameters.

Critique of the Standard CD ProtocolCritique of the Standard CD Protocol

1010

Modified Cell Delineation Process Modified Cell Delineation Process StructureStructure

2. recovers and corrects random errors in the cell Header

ERROR state:

1. distinguishes between various errors generated by different sources

SYNCH

HUNT

ERROR

PRESYNCH

1111

The General Cell Delineation The General Cell Delineation Process StructureProcess Structure

SYNCH

HUNT

ERROR

PRESYNCH

FAILURE

FAILURE state is relevant for the channel degradation case

1212

Modified CD Protocol FeaturesModified CD Protocol Features

1.1. The nature of the CD The nature of the CD protocol is its rapid protocol is its rapid execution execution (comparing to the (comparing to the traffic rate) and its traffic rate) and its effectivenesseffectiveness

2.2. There exists a single There exists a single stable state stable state SYNCH.SYNCH.

3.3. The parameter The parameter should be should be determined determined dynamically subject dynamically subject to the following to the following arguments:arguments:

The noisy channel error The noisy channel error flow model in respect to flow model in respect to the current BER;the current BER;

The accumulated The accumulated channel errors history;channel errors history;

The traffic type (CBR, The traffic type (CBR, VBR, ABR or UBR). VBR, ABR or UBR).

stateSYNCHtheinecteddetbeenhave

HECscorrectnon

utivesecconnifstate

HUNTthetofollowsSystem

1313

Modified CD Protocol Features – Modified CD Protocol Features – Cont’d (1)Cont’d (1)

4.4. The incoming cells The incoming cells stream is composed stream is composed of two cells types:of two cells types:

BlackBlack (B) type (B) type erroneous cells erroneous cells

WhiteWhite (W) type cells (W) type cells that are correct onesthat are correct ones

5.5. The random length of The random length of the sequential B-type the sequential B-type cells is studied and cells is studied and analyzed within a analyzed within a certain time window certain time window TT

The near-optimal The near-optimal choice of T is critical choice of T is critical in order to create the in order to create the effective and robust effective and robust delineation strategydelineation strategy

1414

Modified CD Protocol Features – Modified CD Protocol Features – Cont’d (2)Cont’d (2)

6.6. Denote by Denote by B*B* and and W*W* the average lengths the average lengths of B and W-type cells of B and W-type cells streams received streams received within the T time within the T time window respectively, window respectively, thenthen

is very small. is very small.

*)W*B(*B

1515

The ObjectiveThe Objective

We seek a strategy or a mechanism We seek a strategy or a mechanism that will enable to distinguish that will enable to distinguish between non-synchronous and between non-synchronous and other erroneous packets or cells other erroneous packets or cells among sequential B-type cells in a among sequential B-type cells in a precise fashion, enjoying the above precise fashion, enjoying the above features.features.

1616

Main Solution PreliminariesMain Solution Preliminaries

1.1. Evaluate the Evaluate the optimal/minimal optimal/minimal B-Type sequential B-Type sequential cells stream cells stream length, , that length, , that identifies the identifies the synchronization synchronization failure occurrence failure occurrence subject to a subject to a certain certain confidence level .confidence level .

2.2. The near-optimal real time The near-optimal real time implementation of the implementation of the synchronization recovery synchronization recovery strategy depends on:strategy depends on:

The error flow modelThe error flow model of the of the noisy channel in respect to noisy channel in respect to the current BER (Feature 3)the current BER (Feature 3)

The synchronization failuresThe synchronization failures modelmodel that includes that includes dependencies on the dependencies on the current value of the cell current value of the cell non-synchronous state final non-synchronous state final probability as well as one probability as well as one the synchronization failures the synchronization failures history;history;

The different traffic typesThe different traffic types and the Quality of Service and the Quality of Service (QoS) parameters. (QoS) parameters.

minb

1717

Near-optimal Choice of the Time Near-optimal Choice of the Time Window TWindow T

T must be large enough so that the large scale T must be large enough so that the large scale statistics will be stable.statistics will be stable.

T is a function of B* parameter, which depends on T is a function of B* parameter, which depends on the probabilities of the different error types: the probabilities of the different error types:

T=f( traffic model, traffic intensity)T=f( traffic model, traffic intensity)

The value of T must be continuously considered The value of T must be continuously considered for update each time step t.for update each time step t.

The updated value of T is based on its current The updated value of T is based on its current value as well as on the historical values.value as well as on the historical values.

Ergodic Markov Chain in order to predict the new T Ergodic Markov Chain in order to predict the new T value. value.

1818

Modified Cell Delineation StrategyModified Cell Delineation Strategy

1.1. The value of with respect to :The value of with respect to : SYNCHSYNCHERROR ERROR

SYNCHSYNCHERRORERROR

SYNCHSYNCHHUNTHUNT

SYNCHSYNCHHUNT HUNT

Nk,kbmin

kbkb minmin

kbmin

ratetolerancecertainaisNk

iancevarbais min

1919

Modified Cell Delineation StrategyModified Cell Delineation Strategy

2.2. : any number of B-Type cells that have : any number of B-Type cells that have been received within next time windows T, pass to been received within next time windows T, pass to the HUNT state. the HUNT state.

Note: the traffic modeling is needed for error bursts Note: the traffic modeling is needed for error bursts analysis and prediction.analysis and prediction.

3.3. Error sensitiveError sensitive network: network: HUNT->FAILURE, ERROR->FAILUREHUNT->FAILURE, ERROR->FAILURE4.4. HUNT <-> ERROR : no definit limitations on CD HUNT <-> ERROR : no definit limitations on CD

process time executionprocess time execution ERROR-> HUNT: errors cannot be detected using ERROR-> HUNT: errors cannot be detected using

CRCCRC HUNT-> ERROR: HUNT state operations have been HUNT-> ERROR: HUNT state operations have been

failed. failed.

kbmin

2020

Dynamic Assignment of Dynamic Assignment of ParameterParameter

Correct value assignment of will influence:1. The probability of a non-correct decision about

synchronization failure or establishment respectively.2. The robust synchronization recovery after the

synchronization failure occurs.3. Minimization of the cell loss probability.

Then the min number of sequential B-Type cells within a specific time window T is equal to

k,bmin

n

ii

i

n

imin

average

min

CER

CERbb

i

1

1

Denote

minb

kbb minmin cellserroneous

ofnumberaveragei

)i(Piminb

)cellserroneousutivesecconi(probiP

1

CER- Cell Error Rate

2121






2222

Statement of the OptimizationStatement of the Optimization Problem Problem

The problem is to define number The problem is to define number required for deciding on the following required for deciding on the following synchronization failure issues: synchronization failure issues:

Synchronization failure final probability Synchronization failure final probability Probability of non correct decision Probability of non correct decision

about the synchronization failure;about the synchronization failure; Average CD cycle time ;Average CD cycle time ; CD cycle time variance CD cycle time variance VV..

2

ncp

cT

2323

The Objective Function DefinitionThe Objective Function Definition

0

,Nk

kb)k,b(F average

minmin

similarityselfnetworkofcasetheinCB

Aek

2

VV

TTc

22 Subject to:

K is a function of synchronization failures model and synchronization failure final probability

,b

C,B,Aaverage

min

0

should be determined based on the real statistical data of the communication channel

02022

)(glimanddecreases)(gk

2424

* Analysis of the CD Cycle Average * Analysis of the CD Cycle Average TimeTime

The computational strategy is based on the different branches of the CD probabilistic graph execution.

Six general possibilities to cover the CD graph:

1. SYNCH->HUNT->PRESYNCH->SYNCH

2. SYNCH->HUNT->PRESYNCH->HUNT->PRESYNCH->SYNCH

3. SYNCH->ERROR->HUNT->PRESYNCH->HUNT->

PRESYNCH->SYNCH4. SYNCH->ERROR->HUNT->PRESYNCH->SYNCH5. SYNCH->HUNT->ERROR->PRESYNCH->SYNCH6. SYNCH->ERROR->PRESYNCH->SYNCH

2525

* *Analysis of the CD Cycle Average Analysis of the CD Cycle Average Time-Cont’dTime-Cont’d

6

1

3411

26

324125

32411

24

32411

23

32112

32121

43

21

40140016

401400115

40140014

4014003

4014001

2

4014001

i

icc

ikb

ic

bc

ikb

ic

ikb

ic

HUNTabs

ccc

minc

TT

TTT)),(P),(P(T.

TTTT)),(P),(P(T.

TTTT)),(P),(P(T.

TTTT),(P),(PT.

),(P),(P(p̂

PRESYNCHHUNTprobHUNTPRESYNCHprobp̂

TTp̂THUNTPRESYNCHTTT.

TTTb),(P),(PT.

ERRORTT,PRESYNCHTT

,HUNTTT,SYNCHTT

min

min

min

min

Denote

Note: 40 bit=5 bytes for ATM cell Header

2626

* Example of the Three-States * Example of the Three-States CD Strategy RealizationCD Strategy Realization

The CD Process is best described by Semi-Markovian because:

1. 1) The real-time analysis 2. 2) It is possible to include the statistical correlation between the

sequential discrete states of the process. 3. 3) It has the needed ingredients to describe and to differentiate the

different sources of the CD failures. The following failures are considered:

distortion of the cell Header that is caused by channel errors synchronization failures channel failures.

2727

The General Analysis of the Three-States CD Protocol

Using the Following Aspects:

• Different error transmission models (Markov and Bernoulli) of the communication channel

• Basic and Advanced PRESYNCH protocol

• Different models of the synchronization failures: Self-recovery and non-self-recovery synchronization failures.

2828

The Formal Model

GERT (Graphical Evaluation and Review Technique) method: Definition G={V,A} is stochastic if the execution of a specific set of arcs actions is sufficient for a whole network project execution. Set of conditional Moments Generating Functions (MGF) of a

random variable xyg with argument s: xysg

xy eEsM

W-functions: .,, VyxsMpsW xyxyxy

.)()(

)(

0s

0j00s

j

0j

j sWsd

d

0W

1

sd

sMd

0W - general W-function that corresponds to the CD process

execution

2929

W-functions of the typical topological structures

31322312 WWWW ,,, are the W-functions that correspond to the

transitions SYNCHPRESYNCH,HUNTPRESYNCH

,PRESYNCHHUNT,HUNTSYNCH

Consecutive Connection of Arcs

SYNCHPRESYNCHHUNTSYNCH

iyxixyiyxixixy WWMpMpW .

.WWWn

xx,xxn

1

2111

SYNCH HUNT

PRESYNCH

*

3030

Parallel connection of arcs with the transition probabilities mh,...,h,h 21

A various number of recurrences from PRESYNCH to HUNT within a given CD cycle must be taken into consideration

.xzxyxzxy

xzxzxyxyxzxy WW

pp

MpMp)pp(W

PRESYNCH HUNT

22 w,h

nn wh ,

11 w,h

11 w,h

*

3131

Loops or cycles that prevent the next arc execution

.

L

1i

i2332 WWW

PRESYNCH

HUNT

PRESYNCH

SYNCH

HUNT

PRESYNCH

HUNT

PRESYNCH

HUNT

PRESYNCH

HUNT

PRESYNCH

*

3232

Calculation Procedure

13132

2

23123123120i

iWWWWWWWW

121212 MpW

.p 112

112

i

SYNCHabs

st iesM i

.itt i

t is the cell transmission time

iepW HUNTabs

ts i2323

itis the processing time of i bits, itti ,

tis a bit processing time.

13131

13232

2

1

i

PRESYNCHabs

st

i

PRESYNCHabs

st

iepW

iepW

i

i

.3231 p1p

3333

Basic PRESYNCH protocol:

.

ie

),(P),(P),(P),(PW

L

j iPRESYNCHabs

st

LL

i

1 132

2

4014004014001

Advanced CD protocol:

.iπeU)(1

P(1,40)P(0,40)1UP(1,40)P(0,40)1

1W

1i

PRESYNCH

abs

stLδ

1j

j

32

2

i

L

W32

*

3434

Numerical Results

Average cycle time 1M as a function of . Markov error flow model,

,62 10 basic PRESYNCH protocol,

Poisson model of synchronization failures, .1210 Case 1 corresponds to

,2 case 2 corresponds to .14

0.0001

0.001

2 8 14

case 1

case 2

1M

3535

Average cycle time 1M as a function of . Markov error flow model, .6

2 10 Case 1 corresponds to ,2 case 2 corresponds to .14

0.00064

0.00066

0.00068

0.0007

0.00072

0.00074

0.00076

0.00078

0.0008

0.00082

0.00084

0.00086

2 8 14

case 1

case 2

1M

3636

.

,,,elsmodflow

errorMarkovandBernoulli

foroffunctionasp

12

62

10

108

P*

3737

.,,

,,offunctionaasp3612

62

101010

10

3838

0.00E+00

1.00E-07

2.00E-07

3.00E-07

4.00E-07

5.00E-07

6.00E-07

7.00E-07

8.00E-07

2 8 14

Case 1

Case 2

2M as a function of . Markov errorflow model, ,6

2 10 basic PRESYNCH protocol, Poisson model of

synchronization failures, .1210 Case 1 corresponds to ,2 case 2

corresponds to .14

3939

Average CD cycle time cT normal distribution function. Basic PRESYNCH protocol. Case 1 (red) corresponds to ., 22 Case 2 (green) corresponds to ., 88 Case 3 (yellow) corresponds to ., 1414 Markov error flow model, .6

2 10 Self-

recovery synchronization failures, .1210

4040

Average CD cycle time normal distribution function. Advanced PRESYNCH protocol. Case 1 (red) corresponds to ., 142 Case 2 (green) corresponds to ., 82

4141

Time occurrence in the non-synchronous state HUNT nsT normal distribution function. Case 1 (red) corresponds to ., 22 Case 2 (green) corresponds to ., 88 Markov error flow model, .6

2 10 Self-


4242

Average CD cycle time cT distribution function. Basic PRESYNCH protocol. Case 1 (red) corresponds to ., 22 Case 2 (green) corresponds to ., 88 Case 3 (yellow) corresponds toMarkov error flow model, .6

2 10 Self-recovery

synchronization failures, .1210

4343

Average CD cycle time cT distribution function. Advanced PRESYNCH protocol. Case 1 (red) corresponds to ., 142 Case 2 (green) corresponds to ., 82 Markov error flow model, .6

2 10 Self-recovery synchronization failures,

.1210

4444

Time occurrence in the non-synchronous state distribution function.

Case 1 (red) corresponds to ., 22 Case 2 (green) corresponds to ., 88 Markov error flow model, .6

2 10 Self-


4545

Conclusions

1. Referring to both types of error flow model (Bernoulli and Markov) the average cycle time 1M is, essentially, the increasing function of the arguments and . 2. The final probability of the cell non-synchronous state p is the decreasing function of the and arguments. 3. The final probability of cell non-synchronous state p increases by the increment of or . 4. Considering Bernoulli and Markov error flow models, the average cycle time ,M 1 as well as any distribution moment of higher order 2j,j are higher in the second case.

4646






4747

βα, Statement of the Optimization Problem

p - probability of the non-synchronous system state ncp - probability of non-correct decision about synchronization failure in the SYNCH state The objective function:

00 b,a,bpapp,pH ncnc

a and b - the parameters that define the relative weight of the variables p and ncp in the combined optimization problem. The main goal is to find ncp,pHmin considering the constraint imposed on the average cycle time 1M :

.ncp,pHmin

*MM

1

The continuous function .),(H 0

4848

Example Basic CD protocol, Markov error flow model,

.62 10 Non-self-recovery synchronization

failures, ,1210 .b,a, 118

ncp as a function of

1E-841E-801E-761E-721E-681E-641E-601E-561E-521E-481E-441E-401E-361E-321E-281E-241E-201E-161E-121E-08

0.00011

2 4 6 8 10 12 14

4949

ncp,pH values in the range

52

1.40E-07

-1.10E+00

-8.80E-01

-6.60E-01

-4.40E-01

-2.20E-01

0.00E+00

2.20E-01

2 4 6 8 10

5050

ncp,pH values in the range 155

1.00E-07

1.00E-06

1.00E-05

1.00E-04

5 6 7 8 9 10 11 12 13 14 15

5151

Conclusions

In the range 5 ncp,pH is the drastically increasing function of the argument. In the range 65 ncp,pH increases

slowly. At the point 6 ncp,pH has its maximum value.

For 6 ncp,pH is a very slowly decreasing function.

Using small values of 6 is very dangerous. The reason is that the probability of non-correct decision about synchronization failure is very high in this case.

For ,7 the influence of ncp on

ncp,pH is extremely small. Besides, ncp decreases drastically in the mentioned range. The optimal (minimal) ncp,pH value is investigated on the right end. The higher is the smaller the ncp,pH value is.

For the other values of the CD process parameters the result can be different.

5252






5353

Future PerspectivesFuture PerspectivesNew research issues in High Speed New research issues in High Speed

Network EngineeringNetwork Engineering

Optimal/near-optimal choice of the Optimal/near-optimal choice of the HEC Generating PolynomialHEC Generating Polynomial

Forward Error Correction Technique Forward Error Correction Technique in improving the CD process in improving the CD process characteristicscharacteristics

Defining of the precise CD strategy Defining of the precise CD strategy model that is based on the real model that is based on the real numerous data of the noisy channelnumerous data of the noisy channel

Business

Modified Cell Delineation Strategy For Packet Switched Networks