Two Queues Under Preemptive Priority with Poisson Arrival and Service Rates

This paper extends the work of White and Christie, reported in Operations Research, vol 6, pp 79-95 (January-February, 1958), on preemptive priority queuing. A random walk procedure yields recursive relations between the state probabilities in the steady state. Recursive relations for the moments of the length of the lower priority queue follow. Combined with the use of moment generating functions, this approach provides moments of the waiting time for elements of the lower priority class that arrive when the system is in a given state, i.e., the two queues are of given lengths. The moments of waiting time and time in the system are also obtained recursively for the steady state. Routines for computing and checking are provided.