Two Discrete-Time Queuing Systems Modeling And Performance Analysis

The application of discrete-time queueing systems is widely. Especially, computers and communications technology have substantially promoted the application of discrete-time queueing systems. Discrete-time queueing systems with infinite servers have been successfully applied in the modeling and analysis of high-speed computer, digital communication and optical network. Two-phase queuing systems have been discussed in the past for their applications in various areas,such as computer, communication, manufacturing and other stochastic systems. In many computer and communication service systems, the situation in which arriving packets receive batch mode service in the first phase followed by individual services in the second phase is common. Compared with the previous studies, the novel method in this paper is simple and promote the research of discrete-time queueing systems.Firstly, we give the current research and the research methods of discrete-time queueing systems,and introduce the basic knowledge on the topic. Then we introduce a novel approach named as bivariate stochastic processes to analyzing the nonhomogeneous discrete-time and batch arrival queueing system with infinite servers.Using this novel approach,we obtain probability generating functions(PGFs) for the joint instantaneous-state distributions of arrival process and departure processes. As a special case, we give an elaborate analysis on the instantaneous-state and steady-state performance measures. Finally, we discusss the queue length, average waiting time of packets and the effect of batch size on waiting timein a discrete-time two-phase queuing system, and give the numerical example analysis for verifying the reliability of the results.