Queueing Models with Vacations and Their Applications

vi Preface A variety of queueing models have been proposed and analyzed to evaluate the pelformance of systems such as computer, communication and manufacturing systems. Among them, queueing systems with vacations have been extensively studied in the last two decades since those have a lot of applications in those real systems. For example, in most computer systems, a processor is shared among various types of jobs and hence is not available all the time to each type of jobs. From the view point of a specific job type, it alternately handles jobs of the type or jobs of the other types. To reflect the occasional inavailability of the processor in queueing systems, the server is regarded to take vacations. Although a large number of works for the queueing systems with vacations have been carried out, there are still unsolved problems expressed by service disciplines, buffer control policies and the non-Poissonian arrival process. In this dissertation, we study such queueing models with vacations. We focus our attention to a finite parameter which characterizes the way of service and effects the system performance. First of all, we consider queueing systems with vacations and a finite buffer under three service disciplines and study the difference among those waiting time distributions in detail. Three disciplines considered here are (1) first-come first-served (FCFS), (2) random scheduling and (3) last-come first-served (LCFS). Secondly, we analyze the M/G/l/K system with vacations under the buffer control policy called push-out scheme and investigate how the buffer policy effects the waiting time distribution. We consider following two buffering policies: Non-Preemptive-Buffering (NPB) and Preemptive-Buffering (PB), and investigate the mean waiting time and the coefficient variation of the waiting time for each policy. Finally, we focus the queueing models with vacations in which the alTival process is not POissollian. Most of the previous works on vacation models have assumed that customers arrive to the system according to a stationary Poisson process. The assumption of Poisson arrivals is fit to model the arrival process of data messages, and pelf0l1nance measures, such as the mean waiting time, are given by simple formulas. According to the evolution of the communication technology, however, such diverse traffic as packetized voice and video can be integrated into data networks. Poisson process may not be suitable to describe bursty traffic such as voice and video, where there exits a fair amount of correlation and variation. Thus, queueing models with …