4 - Stream Sessions -- Deterministic Network Analysis

7/25/2019 4 - Stream Sessions -- Deterministic Network Analysis

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Stream Sessions:Deterministic Network Analysis

Hongwei Zhanghttp://www.cs.wayne.edu/~hzhang

Acknowledgement: this lecture is partially based on the slides of Dr. D. Manjunath


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Outline

Events and processes: universal concepts

Deterministic traffic models and network calculus

Scheduling

Application to a packet voice example

Connection setup: RSVP approach


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Outline



Scheduling




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Introduction


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Introduction (contd.)


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Model and notation

Assume outputqueueing

time


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Model and notation (contd.)

Also called non-idling scheduler


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Model and notation (contd.)


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Some simple analysis For work-conserving/non-idling schedulers


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Some simple analysis (contd.)


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Finite buffer: a first look


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Finite buffer: conservation law

See Exercise 4.1 (page 126 of R0)


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Outline



Scheduling




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Network calculus

A view of network calculus: Work with sample paths of a random process.

Networks see a sample path of a random process, e.g., X(t, )

Network calculus is a sample path analysis in which the sample path satisfies

certain properties.

It can be assumed that these properties are satisfied by all sample paths. Thus

network calculus or the deterministic analysis is a worst-case analysis.

An example objective is to obtain X(t)from A(t) and C of a work conserving

scheduler

We are also interested in other processes such as D(t)and otherperformance

parameters such as worst-case latency


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Reichs equation


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Reichs equation (contd.)


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Combine equations (-1) and (0), we get Reichs Equatoin

The supremum is achieved when s = v, i.e., the last time

before t when buffer was empty


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An equation for the departure process D(t)


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Interpretation of Reichs Equation

t

A(t)

X(t)A(s)

timeb

this line has slope C,and valueA(s) +C.(ts) att

s t

A(t)

X(t)

D(t)

time


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Alternative/direct derivation of D(t) equation


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Direct derivation of D(t) (contd.)


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A convolution operation


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Convolution operation (contd.)


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Remarks


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Remarks (contd.)


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Illustration

slope rA(t) B(t)s

t

slopeC

t

slope r

t

slopeC

B(t)

(B*A)(t)

B()+A(t-)


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Compare * with standard convolution


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An example


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Properties of *


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Service curves


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Example network elements: packetizer


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Example elements: constant rate server


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Network elements: coder + packetizer


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Network elements in tandem


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Latency rate servers in tandem


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Delay in a service element

D

A

timet1 ut2


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Stream traffic, QoS, envelop, regulator


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Regulator example: leaky bucket


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LB becomes empty

buffer becomes empty

buffer nonempty

amount of data in the buffer

departure proces

time

s

LB full

LB nonempty

amount of tokens in LB

Token arrivalprocess


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E(t) = 0 for t < 0


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Sequence of regulators


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An example


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Network performance and designWith envelop E(t)


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Otherwise, Cmin is notthe minimum capacity(see book R0)


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Theory applied in practice: an example


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Outline



Scheduling




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Scheduling


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Generalized processor sharing (GPS)


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Virtual time in GPS


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Arrival, service, departure processes in GPS

jkd j

kqueueintopacketarrivingththeofinstantdeparturethe

)(

=


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Implementing a GPS scheduler


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the departure instant will be the serviceinitiation instantfor the next packet inthe same queue as the departing packet


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Packetized GPS


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Example of PGPS


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Properties of PGPS


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PGPS d WFQ


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PGPS and WFQ


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Envelope of a peak-rate-controlled process shaped by a (, ) regulator; alsoshown is the lower service curve given to the source at WFQ server with min.

rate c, total link rate C, and max. packet length Lmax

Outline


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Outline



Scheduling





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, upper bound on delay:


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May also use

worst-case X

Outline


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Outline



Scheduling



RSVP and IntServ


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RSVP and IntServ

Receiver

Traffic source

with shaper

Packet

network

Router

Router

Router

Router


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k= `k110 c C

LAN

KK1

cc

10

WAN - LAN router

max packetlengthL

(, , R)


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How to compute c in RSVP?


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How to compute c in RSVP?

Summary


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Summary Events and processes: universal concepts


Scheduling



Additional reading


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Additional reading

Yuming Jiang, A Basic Stochastic Network Calculus,

ACM SIGCOMM06

Maximum-(virtual)-backlog-centric (m.b.c) stochastic arrival

curveand stochastic service curve

Homework #3


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Homework #3 Chapter 4 of R0

Exercise 4.1 (page 126)

Problems 4.3, 4.6

Distribution of points: total = 100

30 points for Exercise 4.1 and Problem 4.3 each

40 points for Problem 4.6

4 - Stream Sessions -- Deterministic Network Analysis

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