A discrete time queueing model for end-to-end delay and jitter analysis

In this paper we consider a discrete time queueing model to calculate end-to-end delays and jitter in packet networks. The arrival process is formed by a discrete time renewal (foreground stream) and a batch process (background stream). By this model we are able to trace the foreground stream as it passes through a multiplexer where it will be disturbed by crossing packet streams (background traffic). In particular we have analyzed the distribution of the time between two successive departures. By approximating the output foreground stream with a renewal stream and applying this as the input to the next node, by applying the queueing model recursively, we get an end-to-end description. Especially the evolution of the jitter, but also the end-to-end delay will be analyzed more accurately than given by the conventional convolutions approach. Some numerical examples are given and discussed for both evolution of jitter and end-to-end delay. For the end-to-end delay we also compare the results with those obtained by convolution.