Discrete-time queueing systems and their applications to network performance evaluation

With the increasing complexity and sophistication of communication systems, modeling and performance evaluation are becoming critical issues in the design and operation of such systems. To evaluate the performance of computer communication protocols, extensive help is needed from mathematical models, mainly from queueing models. Most of the literature in queueing theory deals with continuous-time models. However, most of the modern computer and communication systems are discrete-time basis. Moreover, the traffic sources in these systems exhibit a diverse mixture of traffic characteristics such as burstiness and correlated inputs which have not been fully studied in the literature. In this work, we use Markov Modulated Bernoulli Processes (MMBPs) to characterize the bursty traffic manifest in some network systems.The probability generating functions (PGFs) of the queue length and the waiting time distributions for all the queueing models are derived. The methodology presented in this dissertation provides a new insights and builds a bridge that links together the PGFs of the queue length and the waiting time distributions which had been treated separately and independently in the literature. It is worthwhile to note that this is the first work that derives the PGF of the waiting time distribution for queuing systems with MMBP inputs.This research was motivated by the desire to analytically gain insight into the performance of discrete-time network systems. This work consists of four discrete queueing models and their applications to network performance evaluations. The first is the analysis of discrete-time G/G/1 queues, G/G/1 vacation queues and their application to the evaluation of the performance of time division multiplexing systems. The second is the analysis of discrete-time cyclic-service queues and their application to the evaluation of the performance of token-ring networks. The third is the analysis of...