Post on 30-Jan-2020
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