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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
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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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
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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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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Reichs equation (contd.)
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Reichs equation (contd.)
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
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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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
Events and processes: universal concepts
Deterministic traffic models and network calculus
Scheduling
Application to a packet voice example
Connection setup: RSVP approach
Application to a packet voice example
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Application to a packet voice example
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, upper bound on delay:
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May also use
worst-case X
Outline
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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
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
Deterministic traffic models and network calculus
Scheduling
Application to a packet voice example
Connection setup: RSVP approach
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
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