Closed two node priority queueing networks

Analytical results for priority queueing networks are extremely rare. Morris gave the exact solution for closed two node preemptive priority networks with negative exponential service time distributions which were independent of state. In this paper these results are extended to the case of state dependent service rates. Morris also gave an approximate solution to the system with non-preemptive priority at one node. The exact solution is presented and a comparison given between the exact and approximate solution. Also obtained are the exact solutions for two node systems with priorities reversed, state dependent service parameters and generalised service time distributions. Finally, a matrix geometric solution is obtained for two node systems with pre-emptive priority discipline at one node and any non-batching servicing queue discipline at the other.