VBR Video Networks with

Deterministic Quality�of�Service

Constraints

J�org Liebeherr

Department of Computer Science

University of Virginia

�

Outline

� VBR Video

� Deterministic QoS Networks

� Video Tra�c Characterization

� Best Possible and Approximations

� Scheduling and Admission Control

� Best Possible and Tradeo�s

� Empirical Evaluation with MPEG traces

�

Video Networks

Video requires Quality�of�Service �QoS� guarantees�

� Delay

� Delay Variation �Jitter�

� Throughput

� Error Rate

QoS guarantees di�cult to satisfy if video is variable�bit rate�

�

MPEG Video Compression

MPEG compression uses three variable�size frame types�

� Intra�coded �I� frames

� Predictive�coded �P� frames

� Bidirectionally predictive�coded �B� frames

PP I

1 2 3 4 5 6 7 8 9 10

I B B B B B B

�� MPEG encoders generate variable�bit rate �VBR� video��

Quality�of�Service Network

� Tra�c Characterization

� Admission controland policing mechanisms

Sender

AdmissionControl

Receiver

TrafficPolicer

�

Types of Quality�of�Service

� Deterministic Servicegives worst�case guarantees�

� The delay of the kth packet on connection j

Dkj � dj �k

� Statistical Servicegives probabilistic guarantees�

Prob�

Dkj � dj�

� zj �k

�

Statistical Service

Advantages�

� Can achieve high utilization

Disadvantages�

� Stochastic models are complex�

� Tra�c policing di�cult or impossible�

� Complex admission control�

�

Deterministic Service

Advantages�

� Policing is well�dened�

� Can consider a no loss model�

� E�cient admission control�

Not known�

� Utilization�

�

In this Talk � � �

Find the best possible utilization

with a deterministic service�

Tra�c Characterization

For QoS networks with deterministic service we need a

worst�case tra�c characterization�

� A�t� t� � is actual tra�c in interval �t� t� � �

� Worst�case characterization of tra�c is a function A� with�

A�t� t� � � A���� �t���

A� is a time�invariant bound of the actual tra�c�

� A� must be sub�additive�

A��t�� t�� � A��t�� �A��t���

�

What is the best A� �

� Dene the �Empirical Envelope E�

E��� �� maxt

A�t� t� �

� E is a time�invariant bound�

� E is best possible time�invariant bound�

E��� � A���� �A�

��

Constructing the Empirical Envelope

Trace of VBR Video�

1501005000

20

40

200

200

180

160

140

120

100

80

60

Frame Number

Num

ber

of

Cell

s

�Integral� of the Trace�

200150100500

1000

0

2000

3000

4000

5000

6000

7000

8000

9000

Frame NumberC

um

ula

tiv

e N

um

ber

of

Cell

s

Empirical Envelope E

��

Searching for a �more practical� A� �

�� Use few parameters�

�� Accurately describe actual tra�c�

�� Be sub�additive�

�� Enforceable by simple policing mechanisms�

Here�

�Leaky bucket�and �Multi�level leaky bucket�tra�c

models�

��

Leaky Bucket

� Describes tra�c by a rate � and a burst size ��

A���� � �� � � �

Token Generator

Net-

workpacket arrival

σ

ρ

time

A*(t)

��

Multi�Level Leaky Bucket

� Describes tra�c by multiple rate�burst pairs ��i� �i��

A�j��� � mini

f�i� �i � �g

Token Generator

Net-

workpacket arrival

A*(t)

timeσ2

σ1

ρ32ρ

1ρ

��

Approximations of the Empirical

Envelope

� Construct an upper bound for the Empirical Envelope with

leaky buckets�

� Result is an approximation of the empirical envelope�

��

Empirical Evaluation

Determine the maximum utilization on a link � � �

� � � � with empirical envelope�

� � � � with leaky bucket tra�c policing�

� Single link with �� Mbps

� Workload on link is obtained from MPEG traces�

��

Workload for Empirical Evaluations

� The Princess Bride

� ���minute MPEG trace�

� ���x��� pixels per frame�

� Frame pattern is IBBPBBPBBPBBPBB�

� Advertisements�

� ���minute TV commercials for graphics products

� ���x��� pixels per frame�

� Frame pattern is IBBPBB�

�

Scheduling Policy

Output LinksInput Links Fabric

Scheduler

� Operates at the output port of the switch�

� Decides which packet to transmit next�

�

Scheduling and Network Utilization

� First�Come�First�Served �FCFS�

� Simplest� o�ers only one delay bound�

� Earliest�Deadline�First �EDF�

� Sophisticated� optimal in terms of schedulability�

� Static Priority �SP�

� Compromise� o�ers xed number of delay bounds�

��

First�Come�First�Served �FCFS�

3 2 1

Admission Control Test�

� Exact Test�

d �

Xj�N

A�j�t� t t � �

��

Earliest�Deadline�First �EDF�

32d = 20

d = 30

1d = 10

t=302

23

3 1

45 29

1

Admission Control Test�

� Exact Test �Liebeherr�Wrege�Ferrari��

t �

Xj�N

A�j�t dj� � max

k�dk�tsk t � �

where maxk�dk�t sk � for t �maxk�N dk

��

Static Priority �SP�

2

1

33

11

3

2 2

Admission Control Test�

� Exact Test �Liebeherr�Wrege�Ferrari��

��� � dp�

t� � �

Xj�Cp

A�j�t� �

p��Xq��

Xj�Cq

A�j�t� �� �max

r�psr

for all p� t � �

��

More Admission Control Tests

FCFS Exact d �X

j�N

A�j�t�� t� t � ��

SP Exact ��� � dp� t� � �X

j�CpA�j�t� �

p��Xq��

Xj�Cq

A�j�t� �� �max

r�p

sr

� p� t � ��

EDF Exact t �X

j�N

A�j�t� dj� � max

k�dk�tsk t � ��

SP Su�cient � t �X

j�CpA�j�t� dp� �

p��Xq��

Xj�Cq

A�j�t� �max

r�p

sr �p� t � dp�

SP Su�cient � dp �

pXq��

Xj�Cq

A�j�dp� �max

r�p

sr �p�

��

Empirical Evaluations

Questions�

� What is the impact of the scheduling method �

� What is the impact of the accuracy of admission control�

� Same MPEG traces as before�

��

Conclusions

� Deterministic networks can achieve high utilization for VBR

tra�c�

� Deterministic VBR can do much better than peak rate

allocation

� Utilization a�ected by three factors�

� Tra�c Characterization�

� Scheduling Method�

� Accuracy of Admission Control�

��

Maximum Achievable Utilization

1

0.75

0.5

0.2520

40

60

80

100

120

Average Rate

00 100 200 300 400 500

Peak Rate

Envelope

Delay Bound (ms)A

vera

ge U

tilizatio

n# o

f C

on

nec

tio

ns

Lecture

140

120

100

80

60

40

20

0

1

0.75

0.5

0.25

0 100 200 300 400 500

Average Rate

Envelope

Peak Rate

Av

erag

e Utiliza

tion#

of

Co

nn

ecti

on

sDelay Bound (ms)

Movie

��

Achievable Utilization Using Multi�Level

Leaky Buckets4 LBs

5 LBs

2 LBs

1 LB

0 100 200 300 400 500Delay Bound (ms)

# o

f C

on

nec

tio

ns

100

80

60

40

20

Av

erag

e Utiliza

tion

3 LBs

6 LBs/Envelope

0

0.8

0.6

0.4

0.2

Lecture

4 LBs

5 LBs

2 LBs

1 LB

0 100 200 300 400 500Delay Bound (ms)

# o

f C

on

nec

tio

ns

100

80

60

40

20

Av

erag

e Utiliza

tion

3 LBs

6 LBs/Envelope

0

0.8

0.6

0.4

0.2

Movie

�

Achievable Utilization Using Di�erent

Schedulers

0 10 20 30 40 50 60 70 80 90

80ms30ms10 ms

20 ms200ms

1000ms80 ms

Movie

Peak Rate

200 msLecture

Deadline

# M

ovie

Con

nec

tion

s

0

10

20

# Lecture Connections

30

50

60

40

0

EDF

�

Peak Rate

80ms30ms10 ms

20 ms200ms

1000ms200 ms80 ms

MovieLectureDeadline

9080706050403020100

60

50

40

30

0

10

20

# M

ovie

Con

nec

tion

s

# Lecture Connections

FCFS

Achievable Utilization Using Di�erent

Schedulers

0 10 20 30 40 50 60 70 80 90

80ms30ms10 ms

20 ms200ms

1000ms80 ms

Movie

Peak Rate

200 msLecture

Deadline

# M

ovie

Con

nec

tion

s

0

10

20

# Lecture Connections

30

50

60

40

0

EDF

��

9080706050403020100

Peak Rate

80ms30ms10 ms

20 ms200ms

1000ms200 ms80 ms

MovieLectureDeadline

# M

ovie

Con

nec

tion

s

# Lecture Connections

60

50

40

30

0

10

20

Static Priorities

Putting it All Together

� Delay bounds for Lecture and Movie � ms and ��ms

� Benchmark case Empirical envelope� EDF� exact condition

� Trade�o�� case three leaky buckets� SP� su�cient condition

��