Traffic Models

1
Traffic Models

• Shaju Stephen
• Xin Pan
• October 30, 2009
• University of Ottawa
• This report was prepared for Professor L.
  Orozco-Barbosa in partial fulfillment of the
  requirements for the course ELG/CEG 4183

2
Outline

• Introduction
• Improving the traffic
• Traffic characterization
• Traditional models
• Recent trends
• Comparison
• Questions
• References

3
Introduction

• Traffic model
• -Purpose
• -Key issues
• -Key terms
• -Importance

4
Improving the Traffic

• Bandwidth
• Queue size at routers
• Routing mechanisms
• Admission control
• Scheduling mechanisms

5
Traffic Characterization

• Measurement based
• Deterministic based
• Statistical based

6
Traditional Models

• Renewal traffic models
• Poisson Processes
• Bernoulli Processes
• Markov-based traffic models
• Markov-Modulated Processes (MMP)
• Markov-Modulated Poisson Process (MMPP)

7
Traditional Models

• Autoregressive traffic models
• Linear Autoregressive (AR) Processes
• Moving Average (MA) Processes
• Autoregressive Moving Average (ARMA) Processes
• Autoregressive Integrated Moving Average (ARIMA)
  Processes

8
Poisson Processes

• Poisson model is the oldest traffic model.
• A Poisson process can be characterized as a
  renewal process.
• The superposition of independent Poisson
  processes results in a new Poisson process whose
  rate is the sum of the component rates.

9
Markov Model

• MMP is continuous-state, discrete-time process,
  can model the workload arriving synchronously at
  the system.
• In MMPP, the interarrival time can be arbitrarily
  distributed, and depend on both states straddling
  each interarrival interval.

10
Markov Model
0.5
Head
0.5
I
0.5
0.5
0.5
0.5
Tail
11
Recent Trends

• TES traffic models (Transform-Expand-Sample)
• Self-similar traffic models
• Fractional Gaussian Noise (FGN)
• FARIMA model

12
Self-Similar Models

• Significance
• Causes
• Drawback

13
FARIMA Model

• Describe both SR and LR
• Model identification
• Parameter estimation
• Diagnostic checking

14
Comparison

• Traditional traffic models
• analytically tractability in the corresponding
  queuing systems.
• generally capture short-range dependence.

• Recent traffic models
• are difficult to solve analytically.
• can describe both SRD and LRD.

15
Comparison
16
Questions

• 1)What is the purpose of a traffic model?
• 2)Name a scheme used in traffic characterization
• 3)Self-similar models do not describe long range
  dependence (True/false)

17
Questions

• 4) Name two traditional traffic models
• 5) What is the computational complexity of FARIMA
  model
• a) O(N) b)
  O(N2)
• 6) What are the essential differences between
  Poisson Model and Self-Similar Models

18
References

• A. Neidhardt and J. L. Wang, The Concept of
  Relevant Time Scales and Its Application to
  Queuing Analysis of Self-similar Network
  Traffic, Proc. IEEE Intl. Conf. On Network
  Protocols, Oct. 1996.
• D. Bertsekas and R. Gallager. Data Networks.
  Prentice-Hall, Second Edition, 1992.
• M. E. Crovella and A Bestavros, Self-similarity
  in world wide web traffic evidence and possible
  causes, IEEE/ACM Transactions on Networking,
  1997.
• V. Paxson and S. Floyd, Wide Area Traffic The
  Failure of Poisson Modeling, IEEE/ACM
  Transactions on Networking, 1995.