Statistical Multiplexing:
Basic Principles
Carey Williamson
University of Calgary
1
Introduction
Statistical multiplexing is one of the
fundamental principles on which ATM
networking is based
 Everyone understands the basic concept
of stat mux, but figuring out how to do
it right is still a hard problem
 LOTS of papers on it, but probably as
many “answers” as authors!

2
Agenda
This presentation: one sample paper
 Woodruff and Kositpaiboon,
“Multimedia Traffic Management
Principles for Guaranteed ATM
Network Performance”
 IEEE JSAC, Vol . 8, No. 3, April 1990

3
Overview of Paper
Identifies several high-level general
principles regarding statistical
multiplexing, traffic management,
and call admission control
 Presents simulation results to illustrate
quantitatively the regions where
statistical multiplexing makes good
sense and where it does not

4
Main Principles
Reasonable bandwidth utilization
 Robustness to traffic uncertainties
 Simplicity
 Node architecture independence

5
Maximum Link Utilization
1.0
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
Deterministic Multiplexing
for Peak/Mean = 2
0.5
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
0.5
Deterministic Multiplexing
for Peak/Mean = 20
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
Deterministic Multiplexing
for Peak/Mean = 2
0.5
Deterministic Multiplexing
for Peak/Mean = 20
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
0.5
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
0.5
Statistical Multiplexing
for Peak/Mean = 2
when average burst B = 10
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
0.5
Statistical Multiplexing
for Peak/Mean = 2
when average burst B = 100
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
B = 10
Peak/Mean = 2
B = 100
0.5
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
Statistical Multiplexing
for Peak/Mean = 20
when average burst B = 10
0.5
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
Statistical Multiplexing
for Peak/Mean = 20
when average burst B = 100
0.5
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
Peak/Mean = 20
B = 10
0.5
B = 100
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Maximum Link Utilization
1.0
B = 10
Peak/Mean = 2
B = 100
0.5
B = 10
Peak/Mean = 20
B = 100
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Best region for statistical multiplexing
Maximum Link Utilization
1.0
B = 10
Peak/Mean = 2
B = 100
0.5
B = 10
Peak/Mean = 20
B = 100
0.0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
Buffer Requirements
30
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
Buffer Requirements
30
Utilization = 10%
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
Buffer Requirements
30
Utilization = 50%
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
Buffer Requirements
30
Utilization = 90%
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Utilization = 10%
Deterministic
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Utilization = 10%
Geometric
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Utilization = 50%
Deterministic
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Utilization = 50%
Geometric
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Utilization = 90%
Deterministic
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Utilization = 90%
Geometric
0
0.0
Granularity of Source
(Peak rate/Link rate)
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
G
U = 90%
U = 50%
D
G
G
D
0
0.0
Granularity of Source
(Peak rate/Link rate)
D
1.0
Buffer Size/Avg Burst Length
30
Effect of Burst Size Distribution
Best region
for
statistical
multiplexing
G
U = 90%
U = 50%
D
G
G
D
0
0.0
Granularity of Source
(Peak rate/Link rate)
D
1.0
Summary
A nice paper describing the general
principles to follow in call admission
control, statistical multiplexing, and
traffic management
 Quantitative illustration of performance
effects, and illustration of when
statistical multiplexing works and when
it does not

31
Summary (Cont’d)

General traffic management principles:
–
–
–
–
Reasonable bandwidth utilization
Robustness
Simplicity
Node architecture independence
32
Summary (Cont’d)
Simulation observations:
 Easier to multiplex “small” things than
“big” things (peak to link ratio)
 The burstier the traffic sources (peak to
mean ratio), the greater the potential
gains of statistical multiplexing, but the
harder it is to multiplex traffic safely
and still guarantee performance

33
Summary (Cont’d)
Easier to multiplex homogeneous traffic
than it is for heterogeneous traffic
 The larger the average burst length, the
harder it is to multiplex the traffic
 The larger the average burst length, and
the greater the variation in burst size,
the more buffers you will need in your
system in order to multiplex effectively

34