Jitter
Analysis in ATM networks handling Self-Similar traffic" |

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