Parameter estimation is a long-lasting topic in queueing systems and has attracted considerable attention from both academia and industry. In this thesis, we design a parameter estimation framework for a tandem queueing system that collects end-to-end measurement data and utilizes the finite mixture model for the maximum likelihood (ML) estimation. The likelihood equations produced by ML are then solved by the iterative expectation-maximization (EM) algorithm, a powerful algorithm for parameter estimation in scenarios involving complicated distributions. We carry out a set of experiments with different parameter settings to test the performance of the proposed framework. Experimental results show that our method performs well for tandem queueing systems, in which the constituent nodes' service time follow distributions governed by exponential family. Under this framework, both the Newton-Raphson (NR) algorithm and the EM algorithm could be applied. The EM algorithm, however, is recommended due to its ease of implementation and lower computational overhead. / Graduate / hangli@uvic.ca

The Internet has been more and more intensively used in recent years. Although network infrastructure has been regularly upgraded, and the ability to manage heavy traffic greatly increased, especially on the core networks, congestion never ceases to appear, as the amount of traffic that flow on the Internet seems to be increasing at an even faster rate. Thus, congestion control mechanisms play a vital role in the functioning of the Internet. Active Queue Management (AQM) is a popular type of congestion control mechanism that is implemented on gateways (most notably routers), which can predict and avoid the congestion before it happens. When properly configured, AQMs can effectively reduce the congestion, and alleviate some of the problems such as global synchronisation and unfairness to bursty traffic. However, there are still many problems regarding AQMs. Most of the AQM schemes are quite sensitive to their parameters setting, and these parameters may be heavily dependent on the network traffic profile, which the administrator may not have intensive knowledge of, and is likely to change over time. When poorly configured, many AQMs perform no better than the basic drop-tail queue. There is currently no effective method to compare the performance of these AQM algorithms, caused by the parameter configuration problem. In this research, the aim is to propose a new analytical model, which mainly uses discrete-time queueing theory. A novel transient modification to the conventional equilibrium-based method is proposed, and it is utilised to further develop a dynamic interactive model of responsive traffic and bottleneck queues. Using step-by-step analysis, it represents the bursty traffic and oscillating queue length behaviour in practical network more accurately. It also provides an effective way of predicting the behaviour of a TCP-AQM system, allowing easier parameter optimisation for AQM schemes. Numerical solution using MATLAB and software simulation using NS-2 are used to extensively validate the proposed models, theories and conclusions.