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Jitter Analysis in ATM networks handling Self-Similar traffic"
This page contains information about my Undergrad thesis. Here is a brief description about this work (you would have already found this information on my research page):
My undergrad. thesis combined two aspects of research going on in the field of ATM networks during the late 1990's namely : Jitter Analysis and Self-Similar Traffic.  Traditionally Jitter Analysis was performed on  networks in which the traffic was assumed to be of  Poisson nature.  But pioneering research by Willinger et al brought out the fractal or self-similar nature of Ethernet traffic.  Subsequent research proved that even ATM networks handled Self-Similar Traffic. Thus, two of my friends and I tried to develop a mathematically tracatable approximation of the self-similar behavior. We propose a heavy tailed distribution called the 2-parameter discrete Pareto (2-PDP) process. This is used as the density function of the self-similar arrival process. The 2-PDP has two parameters that can be varied to generate self-similar arrivals with any mean and any hurst parameter. Simulation results show that this approximates self-similar arrivals for a certain range of the hurst parameter. We then use this density function and perform jitter analysis on an ATM network handling self-similar traffic. We consider a tagged periodic stream(CBR) multiplexed with background traffic that is of fractal nature flowing through  an ATM network and studied the jitter in the tagged stream. The buffer overflow probability is calculated theoretically using the 2-PDP and also through simulation of the above mentioned scenario. The theoretical and experimental values are then compared.

The Co-Authors of this paper are two of my classmates:  Prasanna Krishnamoorthy and Krithi Rao ( Both are Pursuing their MS in Univ. of Texas, Dallas)
The following links give the various chapters in my thesis.  The first two chapters can be skipped by people who are already familiar with the concept of Self-Similarity.  It is advisable for beginners to go through the first two chapters before they read the rest of the thesis.

1 Chapter 1: Introduction

2 Chapter 2: Self Similarity and Long Range Dependence

3 Chapter 3: An Analytical Approach to Estimate Jitter:

In this chapter an analytical approach to estimate jitter is given.  Section 3.1 deals  with the analytical derivation of jitter for the CBR traffic when multiplexed with   Poisson traffic. This is basically a review of the work done in [RG92](see references). Section 3.2 ; shows how this derivation can be modified to calculate jitter when the CBR traffic is multiplexed with self-similar background traffic. The proofs for all the expressions derived in this section are given in Appendix A.  In this section a new distribution function has been proposed. We call this a "2 Parameter-Discrete Pareto Process".

4 Chapter 4: System Simulation

In order to do the jitter analysis, self-similar traffic traces needed to be generated. This was done using algorithm proposed by Vern Paxson[VP97, see references]. This algorithm will be referred to as the Fast FFT method in the rest of the paper. Section 4.1 deals with this algorithm. An ATM multiplexer, carrying self-similar background traffic and the periodic stream of interest (CBR traffic) was then simulated and the cell delay variation was obtained. This is described in Section 4.2.

5 Chapter 5:Conclusions and References

6 Appendix A:Conclusions and References
Appendix A contains the proof of all the theorems and equations given in Chapter 3

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