Video VBR Networks with Deterministic Quality-of-Service Constraints
Jorg Liebeherr
Department of Computer Science University of Virginia
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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
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Video Networks
Delay
Video requires Quality-of-Service (QoS) guarantees:
Delay Variation (Jitter) Throughput Error Rate QoS guarantees di cult to satisfy if video is variable-bit rate.
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MPEG Video Compression
MPEG compression uses three variable-size frame types: Intra-coded (I) frames Predictive-coded (P) frames Bidirectionally predictive-coded (B) frames
I 1
B 2
B 3
P 4
B 5
B 6
P 7
B 8
B 9
I 10
=) MPEG encoders generate variable-bit rate (VBR) video.
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Quality-of-Service Network
Tra c Characterization Admission controland policing mechanisms
Admission Control Sender Receiver
Traffic Policer
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Types of Quality-of-Service
Deterministic Servicegives worst-case guarantees. { The delay of the kth packet on connection j
k Dj dj
8k
Statistical Servicegives probabilistic guarantees.
k Prob Dj dj
zj
8k
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Statistical Service
Advantages:
Can achieve high utilization
Disadvantages:
Stochastic models are complex. Tra c policing di cult or impossible. Complex admission control.
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Deterministic Service
Advantages:
Policing is well-de ned. Can consider a "no loss" model. E cient admission control.
Not known: ? Utilization.
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In this Talk : : : Find the best possible utilization with a deterministic service.
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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 ( )
8t 8
A is a time-invariant bound of the actual tra c. A must be sub-additive, A (t1 + t2) A (t1) + A (t2):
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What is the best A ?
De ne the \Empirical Envelope" E : E ( ) := max A t t + ] t
E E
is a time-invariant bound. is best possible time-invariant bound. E( ) A ( ) 8A
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Constructing the Empirical Envelope
200 180 160
Number of Cells
Trace of VBR Video:
Cumulative Number of Cells
`Integral' of the Trace:
9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0 50 100 150 200
140 120 100 80 60 40 20 0 0 50 100 150 200
Empirical Envelope E
Frame Number
Frame Number
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Searching for a "more practical" A ?
1. Use few parameters. 2. Accurately describe actual tra c. 3. Be sub-additive. 4. Enforceable by simple policing mechanisms.
Here: `Leaky bucket'and `Multi-level leaky bucket'tra c
models.
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Leaky Bucket
Describes tra c by a rate and a burst size .
A ( )= +
Token Generator
A*(t)
Netpacket arrival work
time
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Multi-Level Leaky Bucket
Describes tra c by multiple rate-burst pairs ( i i).
Aj ( ) = minf i + i i
Token Generator
g
A*(t)
3 1
Netpacket arrival work
2 1
2
time
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Approximations of the Empirical Envelope
Construct an upper bound for the Empirical Envelope with leaky buckets. Result is an approximation of the empirical envelope.
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Empirical Evaluation
Determine the maximum utilization on a link : : :
: : : with empirical envelope. : : : with leaky bucket tra c policing.
Single link with 45 Mbps Workload on link is obtained from MPEG traces.
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Workload for Empirical Evaluations
The Princess Bride { 90-minute MPEG trace. { 320x240 pixels per frame. { Frame pattern is IBBPBBPBBPBBPBB. Advertisements: { 10-minute TV commercials for graphics products { 160x120 pixels per frame. { Frame pattern IBBPBB.
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Scheduling is Policy
Scheduler Input Links Fabric Output Links
Operates at the output port of the switch. Decides which packet to transmit next.
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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.
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First-Come-First-Served (FCFS)
3 2 1
Admission Control Test:
j 2N
Exact Test: X d Aj (t) ; t
t 0
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Earliest-Deadline-First (EDF)
1 3 45 d1 = 10 d2 = 20 d3 = 30 2 29 1 23 t=30
Admission Control Test:
j 2N
Exact Test (Liebeherr/Wrege/Ferrari): X t Aj (t ; dj ) + kmax sk t 0 d >t
k
where maxk dk>t sk 0 for t > maxk2N dk
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Static Priority (SP)
1 1 2 2 2 1
3
3
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Admission Control Test:
j 2Cp
Exact Test (Liebeherr/Wrege/Ferrari): (9 d p ) pX X ;1 X t+ Aj (t) + Aj (t + ) + max sr r>p
q=1 j 2Cq
for all p t 0
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More Admission Control Tests
FCFS Exact SP Exact EDF Exact SP Su cient 1 SP Su cient 2
d
X
j 2N
Aj (t) ; t8 t 0.
X
j 2C
p
(9
t t dp
dp) t +
X
j 2N X
p
Aj (t) +
k
Aj (t ; dj ) + k d >t sk max Aj (t ; dp) +
q
Aj (t + ) + max sr r>p q=1 j 2C 8 p t 0. t 0.
q
p;1 XX
p;1 XX
q
j 2C p XX q=1 j 2C
q=1 j 2C
Aj (t) + max sr r>p
8p.
8p
t dp.
Aj (dp) + max sr r>p
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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.
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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.
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Maximum Achievable Utilization
120
# of Connections
1 Envelope 0.75 0.5 Peak Rate 0.25
140
1 Average Rate
# of Connections
100 80 60 40 20 0 0
Average Rate
120 100 80 60 40 20 0 0 100
Average Utilization
0.75 0.5 Envelope Peak Rate 200 300 400
0.25
Average Utilization
100
200
300
400
500
500
Delay Bound (ms)
Lecture
Delay Bound (ms)
Movie
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Achievable Utilization Using Multi-Level Leaky Buckets
100 6 LBs/Envelope 5 LBs 0.8 100 6 LBs/Envelope 5 LBs 0.8
Average Utilization
Average Utilization
# of Connections
# of Connections
80 0.6 60 40 20 0 0 100 200 300 400 500 0.2 1 LB 2 LBs 3 LBs 4 LBs 0.4
80 0.6 60 40 20 0 0 100 200 300 400 500 0.2 1 LB 2 LBs 3 LBs 4 LBs 0.4
Delay Bound (ms)
Lecture
Delay Bound (ms)
Movie
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Achievable Utilization Using Di erent Schedulers
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# Movie Connections
50 40 30 20 10 0 0 0 10 20
Deadline Lecture Movie 200 ms 1000ms 80 ms 200ms 20 ms 80ms 10 ms 30ms Peak Rate
# Lecture Connections
30
40
50
60
70
80
90
EDF
30
60
# Movie Connections
50 40 30 20 10 0 0 10 20 30 40
Deadline Lecture Movie 200 ms 1000ms 80 ms 200ms 20 ms 80ms 10 ms 30ms Peak Rate
50
60
70
80
90
# Lecture Connections
FCFS
Achievable Utilization Using Di erent Schedulers
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# Movie Connections
50 40 30 20 10 0 0 0 10 20
Deadline Lecture Movie 200 ms 1000ms 80 ms 200ms 20 ms 80ms 10 ms 30ms Peak Rate
# Lecture Connections
30
40
50
60
70
80
90
EDF
31
60
# Movie Connections
50 40 30 20 10 0 0 10 20 30 40
Deadline Lecture Movie 200 ms 1000ms 80 ms 200ms 20 ms 80ms 10 ms 30ms Peak Rate
50
60
70
80
90
Static Priorities
# Lecture Connections
Putting it All Together
Delay bounds for Lecture and Movie: 30 ms and 50ms Benchmark case: Empirical envelope, EDF, exact condition \Trade-o " case: three leaky buckets, SP, su cient condition
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