Discrete-time multiserver queues with geometric service times

Abstract

In this paper, a discrete-time multiserver queueing system with infinite buffer size and general independent arrivals is considered. The service times of packets are assumed to be independent and identically distributed according to a geometric distribution. Each packet gets service from only one server. In the paper, the behavior of the queueing system is studied analytically by means of a generating-functions approach. This results in closed-form expressions for the mean values, the variances and the tail distributions of the system contents and the packet delay. Some numerical examples are given to illustrate the analysis. Scope and purpose Discrete-time queueing models are widely used to study the behavior of various types of telecommunication and computer systems. Most of the existing studies of discrete-time multiserver queueing models assume that the service times of the customers are constant. Recently, however, there has been an increased interest in discrete-time models with non-deterministic service times, due to the more and more complicated and irregular service mechanisms in nowadays telecommunication networks. In view of this, this paper focuses on a discrete-time queueing system with multiple servers and geometrically distributed service times. We show that the queueing model can be analyzed by means of a generating-functions approach. The results of the analysis are important to evaluate performance measures such as packet loss and delay in communication and computer networks.