Some Heavy-Traffic Limit Theorems for a Priority Queue with General Arrivals

This paper considers a single-server queue with two priority classes of customers. Interarrival times and service times for the two classes of customers are assumed to form four mutually independent renewal processes determined by general distributions. In two cases for which a steady state does not exist, limit theorems are obtained for the low-priority waiting time and for the total uncompleted service time of all customers in the system at time t.