Deterministic QOS

Quality-of-Service

� Video and audio need Quality-of-Service (QoS)

guarantees:

{ delay

{ jitter

{ throughput

{ loss rate

� A deterministic service gives worst-case guarantees.

Quality-of-Service

� A deterministic service gives worst-case delay guarantees:

Delay � X

.� A statistical service makes probabilistic service

guarantees:

Pr[Delay > X] < " or Pr[Loss] < " :

Multimedia Networks

Sender

TrafficPolicer

Receiver

AdmissionControl

� Multimedia connections have QoS and tra�c

parameters.

� Multimedia networks need resource reservation.

Why is Resource Reservation Di�cult?

� Compressed digital video has a variable bit rate.

0 100 200 300 400 5000

50

100

150

200

Num

ber

of C

ells

Peak Rate

Average Rate

Frame Number

� Problem: How do we provide deterministic QoS without

peak-rate reservation?

Design Space for QoS

On a fundamental level, the design space for QoS is

3-dimensional.

TrafficCharacterization

Scheduling

Admission Control

Peak Rate Allocation

TrafficCharacterization

Scheduling

Admission Control

PeakPeak

Peak

Deterministic QoS

TrafficCharacterization

Scheduling

Admission Control

EmpiricalEnvelope

EDF

Deterministic

Assumptions

� There are P ow classes, Cq is the set of ows in class q.

� We �rst consider a single node.

� Flow j 2 Cq has a delay bound dq.

Design Space for Deterministic QoS

TrafficCharacterization

Scheduling

Admission Control

Empirical E

nvelope

FIFO

Static Priority

WFQ

EDF

Leaky Bucke

t

Peak Rate

Deterministic(sufficient)

Deterministic(necessary+sufficient)

TraÆc Characterization

� Aj(t1; t2) are arrivals from ow j in [t1; t2).

� Denote: AC(:) =P

j2C Aj(:).

� Arrivals from ow j are characterized by a subadditive

deterministic envelope A�j as follows

Aj(t; t+ �) � A�j(�) 8t;8� :

� TraÆc is conditioned (shaped, policed) to comply to A�j .

Practical Deterministic Envelopes

Time

Tra

ffic

σ

ρ

Time

Tra

ffic

σ

ρ

P

Most deterministic envelopes used in practice are Leaky

Buckets (or Token Buckets):

� Simple Leaky Bucket: A�(t) = � + � t.

� Peak-Rate Constrained LB: A�(t) = minfP t; � + � tg.

Best Possible Deterministic Envelopes

8000

6000

4000

2000

004080

120160200

0 50 100 150 200 0 50 100 150 200

A

E*

Cu

mu

lati

veTimeTime

Tra

ffic

� Best deterministic envelope for a given trace is the

empirical envelope E�j :

E�j (�) := supt�0Aj(t; t+ �); for all � � 0 :

Packet Scheduling

Input Links Output Links

Fabric

Scheduler

� A connection j has a delay bound dj .

� Packet scheduling discipline determines delay .

Admission Control

Schedulability Condition:

Given a packet scheduler and a set of connections. The

connections are said to be schedulable if a violation of the

delay bounds will never occur.

Schedulability Condition

=

Delay Bound Test for Admission

Control

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

� Exact Admission Control Test:

d �

Xj2N

A�j(t)� t t � 0

Earliest-Deadline-First (EDF)

32d = 20

d = 30

1d = 10

t=302

23

3 1

45 29

1

� Exact Admission Control Test (Liebeherr/Wrege/Ferrari):

t �

Xj2N

A�j(t� dj) + max

k;dk>tsk t � 0

where maxk;dk>t sk � 0 for t > maxk2N dk

Static Priority (SP)

2

1

33

11

3

2 2

� Exact Admission Control Test (Liebeherr/Wrege/Ferrari):

(9� � dp)

t+ � �

Xj2CpA�j(t) +

p�1Xq=1X

j2CqA�j(t+ �) + maxr>p

sr

for all p; t � 0

Experimental Setup

� Single 155 Mbps switch.

� Three connection groups Low, Medium, High Delay .

Delay Burst

Index Bound Size Rate

j dj Bj rj

Low 1 12 ms 4,000 cells 10-155 Mbps

Medium 2 24 ms 2,000 cells 10-155 Mbps

High 3 36 ms 4,000 cells 10-155 Mbps

Evaluation20

1010

2020

40

4080

80

155

155

10

20

40

80

155

EDF

2010

10

2020

40

4080

80

155

155

10

20

40

80

155

SP

VBR Video Networks with

Deterministic Quality-of-Service

Constraints

J�org Liebeherr

Department of Computer Science

University of Virginia

1

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.

4

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):

10

What is the best A� ?

� De�ne the \Empirical Envelope" E:

E(�) := maxt

A[t; t+ � ]

� E is a time-invariant bound.

� E is best possible time-invariant bound.

E(�) � A�(�) 8A�

11

Constructing the Empirical Envelope

Trace of VBR Video:

1501005000

20

40

200

200

180

160

140

120

100

80

60

Frame Number

Nu

mb

er

of

Cell

s

`Integral' of the Trace:

200150100500

1000

0

2000

3000

4000

5000

6000

7000

8000

9000

Frame NumberC

um

ula

tive N

um

ber

of

Cell

s

Empirical Envelope E

12

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' traf-

�c models.

14

Approximations of the Empirical

Envelope

� Construct an upper bound for the Empirical Envelope with

leaky buckets.

� Result is an approximation of the empirical envelope.

17

Input: E and a time � .

Output: A set of parameter (�i; �i).

Procedure Find Parameters (E, � )

n = 0

While � > 0 Do

n = n+ 1

�n = max

0�t<��1

� � t(�E(t)� tE(� ))

�

�n =E(� )� �n

�

Output (�n; �n)

� = minf t j �n + �n t = E(t)g

End While

End Procedure

Example

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.

18

Workload for Empirical Evaluations

� Lecture:

{ 10-minute MPEG-1 trace showing a videotaped lecture.

{ 160 � 120 pixels per frame; 30 frames per second.

{ Frame pattern is IBBPBB.

� Movie

{ 30-minute MPEG-1 trace of \Jurassic Park".

{ 384 � 288 pixels per frame; 24 frames per second.

{ Frame pattern is IBBPBBPBBPBB.

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)

Average U

tilizatio

n# o

f C

on

necti

on

s

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

s

Delay Bound (ms)

Movie

Max. Utilization with Multi-Level Leaky Buckets

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

0.4

0.3

0.2

0.1

Av

erag

e Utiliza

tion

3 LBs

6 LBs/Envelope

0

Lecture

6 LBs

1 LB

2 LBs 3-5 LBs

0.1

0.2

Av

era

ge

Uti

liza

tio

n

0.4

0.3

60

50

40

30

20

10

00 100 200 300 400 500

Delay Bound (ms)

# o

f C

on

nec

tio

ns 8 LBs/Envelope

Movie

(LB = Leaky Bucket)

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 ms200ms1000ms200 ms

80 ms

MovieLectureDeadline

9080706050403020100

60

50

40

30

0

10

20

# M

ovie

Con

necti

on

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