Methods for performance evaluation of networks : fast simulation of loss systems and analysis of Internet congestion control

Abstract

Performance evaluation of modern telecommunication networks by means of mathematical modeling frequently results in a situation, whereby an exact analytical solution poses a difficult problem in terms of computational evaluation. In this thesis, two such problems are studied and a different approach for easing the computational burden is developed in each case.

The first part of the thesis considers the problem of evaluating blocking probabilities in loss systems, which are often used as models for the call scale behavior of modern networks. In this case, the solution to the problem can be given a well known analytical expression, but in practice it can not be used for computing the blocking probabilities due to the prohibitive size of the state space of the system. Then one can use simulation to obtain estimates of the blocking probabilities. For increasing the efficiency of the simulation, i.e., for reducing the variance of the estimates, several novel and increasingly more efficient methods are presented. Noticeable variance reductions are obtained by applying the method of conditional expectations. However, even greater variance reductions are gained by using importance sampling. In the thesis several importance sampling based methods are presented, of which the inverse convolution approach provides variance reductions surpassing all previously reported results in the literature.

In the second part of the thesis, the problem of congestion control in the Internet is studied. Specifically, the focus is on modeling the interaction between the TCP rate control algorithm and the RED buffer management mechanism. By using various analytical approximations, a novel dynamic model is derived for describing the interaction between an idealized TCP source population and a RED controlled buffer. Ultimately, the model consists of a set of coupled retarded functional differential equations (RFDEs) governing the time dependent expectations of the stochastic system state variables. This model is used to explore the dependency of the equilibrium of the system on the parameters of the physical system. Additionally, methods are derived allowing the stability of the system to be analyzed. In particular, sufficient and necessary conditions are obtained for the RFDE system, such that the system is asymptotically stable.