Models for calculating end-to-end delay in packet networks

In this paper we consider an analytical model to calculate end-to-end delays in packet networks. To be more specific we consider a particular path in the network and we approximate the end-to-end delay by assuming that the waiting times in each node are independent and that both the input and output streams at each node are Poisson processes. With these assumptions (approximations) the end-to-end delay yields the convolution of the waiting times in each queue. If the service times in each queue are identically distributed the corresponding convolution may be heavily simplified, and closed form expressions are derived in terms of derivative with respect to the load parameter. We put special emphasis on the case with constant service times since this is an important case for applications. Numerical examples show that end-to-end delays in chains up to 20 nodes may be analysed without numerical difficulties. We also give the corresponding results for a chain containing two groups of links with different capacity in each group. This is a particularly interesting case and makes it possible to model a path in an IP network that includes both access and core links. Numerical examples are given and discussed for the various models.