Delay Analysis for a Discrete-Time GI-D-c Queue with Arbitrary-Length Service Times

In this paper, we consider a discrete-time GI-D-c queueing system with general independent arrivals, deterministic service times of arbitrary length, multiple servers, an infinite buffer size and a first-come-first-served queueing discipline. A relationship between the probability distributions of the system contents and the packet delay is established. By means of this relation, an explicit expression for the generating function of the packet delay is obtained from the known generating function of the system contents, derived in previous work. In addition, some important characteristics of the packet delay, namely the mean, the variance and the tail distribution of the packet delay, are derived through some mathematical manipulations. Numerical examples are presented to illustrate the analysis.