The response time distribution of a discrete-time queue under a generalized batch arrival process

Abstract

In this paper we obtain the response time distribution of a single server, discrete-time queue, fed by an aggregate extension of the well-known on/off source. Essentially, at each active slot, we allow for a variable number of units of workload (packets, cells, messages, etc.) to enter the queue. So, the resulting input traffic is a batch-on/off process. The server is deterministic, with a service time corresponding to the transmission of a workload unit. We follow an exact analytical procedure, and we provide an effective algorithm to compute the solution. Moreover, this work has been performed under very general conditions, since no particular distributions are assumed for the random variables characterizing the batch-on/off process: on and off periods, and batch sizes. Also, the fact of obtaining the complete response time distribution, allows for the calculation of other parameters than the mean, such as the jitter, for instance, or higher order moments. This becomes essential when analyzing the performance of finite capacity resources in the context of digital communication systems, especially when real time services are supported. Finally, numerical results are provided.