A Priority Queue with Low-Priority Arrivals General

This paper considers a single-server queue with two priority classes of customers. High-priority arrivals are assumed to be Poisson, but interarrival times for low-priority customers are allowed to have a general distribution. Under either the head-of-the-line or preemptive-resume discipline, a formal solution is obtained for the Laplace-Stieltjes transform of the steady-state distribution of the low-priority waiting time. A limit theorem for the low-priority waiting time is also obtained under one heavy-traffic condition for which a steady state does not exist.