Modelling queue sizes in an expedited forwarding DiffServ router with service differentiation

This paper studies a single-server non-preemptive priority queue with two traffic classes in order to model Expedited Forwarding Per-Hop Behaviour in the Differentiated Services (DiffServ) architecture. Generally, queueing models assume infinite queue capacity but in a DiffServ router the capacity for high priority traffic is typically small to prevent this traffic from monopolizing the output link and hence causing starvation of low-priority traffic. The presented model takes the exact (finite) high-priority queue capacity into account. Analytical formulas for the system content of each class are determined as well as the high-priority packet loss ratio. For each class, service of a packet takes a (different) general independent distribution. The issues this causes are resolved by using the spectral decomposition theorem. Numerical examples indicate the considerable impact of the finite capacity on the system performance.