Many-sources delay asymptotics with applications to priority queues

In this paper, we study discrete-time priority queueing systems fed by a la rge number of arrival streams. We first provide bounds on the actual delay asymptote in terms of the virtual delay asymptote. Then, under suitable ass umptions on the arrival process to the queue, we show that these asymptotes are the same. As an application of this result, we then consider a priorit y queueing system with two queues. Using the earlier result, we derive an u pper bound on the tail probability of the delay. Under certain assumptions on the rate function of the arrival process, we show that the upper bound i s tight. We then consider a system with Markovian arrivals and numerically evaluate the delay tail probability and validate these results with simulat ions.