Statistical Multiplexing: Basic Principles

1
Statistical Multiplexing Basic Principles

• Carey Williamson

University of Calgary
2
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!

3
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

4
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

5
Main Principles

• Reasonable bandwidth utilization
• Robustness to traffic uncertainties
• Simplicity
• Node architecture independence

6
1.0
Maximum Link Utilization
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
7
1.0
Deterministic Multiplexing for Peak/Mean 2
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
8
1.0
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
9
1.0
Deterministic Multiplexing for Peak/Mean 2
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
10
1.0
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
11
1.0
Statistical Multiplexing for Peak/Mean 2 when
average burst B 10
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
12
1.0
Maximum Link Utilization
0.5
Statistical Multiplexing for Peak/Mean 2 when
average burst B 100
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
13
1.0
B 10
Peak/Mean 2
B 100
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
14
1.0
Statistical Multiplexing for Peak/Mean 20 when
average burst B 10
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
15
1.0
Statistical Multiplexing for Peak/Mean 20 when
average burst B 100
Maximum Link Utilization
0.5
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
16
1.0
Peak/Mean 20
B 10
Maximum Link Utilization
0.5
B 100
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
17
1.0
B 10
Peak/Mean 2
B 100
Maximum Link Utilization
0.5
B 10
Peak/Mean 20
B 100
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
18
Best region for statistical multiplexing
1.0
B 10
Peak/Mean 2
B 100
Maximum Link Utilization
0.5
B 10
Peak/Mean 20
B 100
0.0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
19
Buffer Requirements
30
Buffer Size/Avg Burst Length
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
20
Buffer Requirements
30
Buffer Size/Avg Burst Length
Utilization 10
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
21
Buffer Requirements
30
Buffer Size/Avg Burst Length
Utilization 50
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
22
Buffer Requirements
30
Utilization 90
Buffer Size/Avg Burst Length
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
23
Effect of Burst Size Distribution
30
Utilization 10
Buffer Size/Avg Burst Length
Deterministic
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
24
Effect of Burst Size Distribution
30
Utilization 10
Buffer Size/Avg Burst Length
Geometric
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
25
Effect of Burst Size Distribution
30
Utilization 50
Buffer Size/Avg Burst Length
Deterministic
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
26
Effect of Burst Size Distribution
30
Utilization 50
Geometric
Buffer Size/Avg Burst Length
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
27
Effect of Burst Size Distribution
30
Utilization 90
Deterministic
Buffer Size/Avg Burst Length
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
28
Effect of Burst Size Distribution
30
Utilization 90
Geometric
Buffer Size/Avg Burst Length
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
29
Effect of Burst Size Distribution
30
G
Buffer Size/Avg Burst Length
U 90
D
G
G
U 50
D
D
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
G
G
30
Effect of Burst Size Distribution
30
Best region for statistical multiplexing
G
Buffer Size/Avg Burst Length
U 90
D
G
G
U 50
D
D
0
Granularity of Source (Peak rate/Link rate)
0.0
1.0
G
G
31
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

32
Summary (Contd)

• General traffic management principles
• Reasonable bandwidth utilization
• Robustness
• Simplicity
• Node architecture independence

33
Summary (Contd)

• 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

34
Summary (Contd)

• 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