Mixed finite-/infinite-capacity priority queue with general class-1 service times

This paper studies a single-server queue with two traffic classes in order to model Expedited Forwarding Per-Hop Behaviour in the Differentiated Services architecture. Generally, queueing models assume infinite queue capacity but in a DiffServ router the capacity for high-priority traffic is often small to prevent this traffic from monopolizing the output link and hence causing starvation of other traffic. The presented model takes the exact (finite) high-priority queue capacity into account. Analytical formulas for system contents and packet delay of each traffic class are determined. This requires extensive use of the spectral decomposition theorem as the service time of a high-priority packet takes a general distribution, which complicates the analysis. Numerical examples indicate the considerable impact of the finite capacity on the system performance