Analysis of discrete-time batch-service queueing systems

Abstract

In this dissertation, we consider a discrete-time single-server queueing system having finite buffer capacity and a Bernoulli arrival process. The system has a finite number M of waiting places and a batch service random capacity Y. A service period is initialized when a service-starting threshold \``a\`` of waiting customers is reached. The system is denoted accordingly by $Geo/G^{a,Y}/1/M$. This queueing system is motivated by manufacturing environments with batch service workstations, e.g., in machines for computer components and chip productions. We first derive departure-epoch probabilities using the embedded Markov chain technique. Next, we establish two relationships for the steady-state probabilities of the queue lengths at two epochs: departure and random. These relationships for the steady-state probabilities at two different epochs can be implemented for numerical computations and useful performance measures such as the loss probability can be obtained. As this queueing system can be potentially useful in various other field such as production, transportation, traffic processes and various related systems, the results in this thesis would be useful not only to queueing researchers but also to practitioners who wish to evaluate the performance of their real systems. Further, many of the analytical and computational results of batch service queueing systems can now be recast in this framework. Moreover, the approach used in this thesis seems to be applicable to a much wider range of queueing systems with more general batch arrival and batch service. This dissertation also presents an exact analysis of the steady-state queue-length distribution of the Geo/G/1 queue with disasters which remove all workloads from the system whenever they occur. We first present the steady-state queue-length distribution of the Geo/G/1 queue with disasters. Then, by using this result, we analyze the Geo/G/1 queue with multiple working vacations in which the server wor...