Flow-level performance analysis of data networks using processor sharing models

Abstract

Most telecommunication systems are dynamic in nature. The state of the network changes constantly as new transmissions appear and depart. In order to capture the behavior of such systems and to realistically evaluate their performance, it is essential to use dynamic models in the analysis. In this thesis, we model and analyze networks carrying elastic data traffic at flow level using stochastic queueing systems. We develop performance analysis methodology, as well as model and analyze example systems. The exact analysis of stochastic models is difficult and usually becomes computationally intractable when the size of the network increases, and hence efficient approximative methods are needed. In this thesis, we use two performance approximation methods. Value extrapolation is a novel approximative method developed during this work and based on the theory of Markov decision processes. It can be used to approximate the performance measures of Markov processes. When applied to queueing systems, value extrapolation makes possible heavy state space truncation while providing accurate results without significant computational penalties. Balanced fairness is a capacity allocation scheme recently introduced by Bonald and Proutière that simplifies performance analysis and requires less restrictive assumptions about the traffic than other capacity allocation schemes. We introduce an approximation method based on balanced fairness and the Monte Carlo method for evaluating large sums that can be used to estimate the performance of systems of moderate size with low or medium loads. The performance analysis methods are applied in two settings: load balancing in fixed networks and the analysis of wireless networks. The aim of load balancing is to divide the traffic load efficiently between the network resources in order to improve the performance. On the basis of the insensitivity results of Bonald and Proutière, we study both packet- and flow-level balancing in fixed data networks. We also study load balancing between multiple parallel discriminatory processor sharing queues and compare different balancing policies. In the final part of the thesis, we analyze the performance of wireless networks carrying elastic data traffic. Wireless networks are gaining more and more popularity, as their advantages, such as easier deployment and mobility, outweigh their downsides. First, we discuss a simple cellular network with link adaptation consisting of two base stations and customers located on a line between them. We model the system and analyze the performance using different capacity allocation policies. Wireless multihop networks are analyzed using two different MAC schemes. On the basis of earlier work by Penttinen et al., we analyze the performance of networks using the STDMA MAC protocol. We also study multihop networks with random access, assuming that the transmission probabilities can be adapted upon flow arrivals and departures. We compare the throughput behavior of flow-optimized random access against the throughput obtained by optimal scheduling assuming balanced fairness capacity allocation.