End-to-end delay models with priority

In this paper we consider an analytical model to calculate end-to-end delays in packet networks implementing non-preemptive priority. The aim is to study the end-to-end delay for real time services in an IP network where some kind of differentiation between flows is possible (i.e. DiffServ). 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 for high priority traffic 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. 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 for up to 20 nodes may be analysed without numerical difficulties.