Asymptotics of waiting time distributions in the accumulating priority queue

Abstract

We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by Kleinrock in the 60s -he coined it time-dependent priority -to diversify waiting time objectives of different classes in a paramaterized way. It also avoids the typical starvation problem of regular priority queues. All customers build up priority linearly while waiting in the queue but at a class-dependent rate. At a service opportunity epoch, the customer with highest priority present is served. Stanford and colleagues recently calculated the Laplace-Stieltjes Transform (LST) of the waiting time distributions of the different classes, but only invert these LSTs numerically. In this paper, we analytically calculate the asymptotics of the corresponding distributions from these LSTs. We show that different singularities of the LST can play a role in the asymptotics, depending on the magnitude of service differentiation between both classes.

Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time

“…The problem of optimal management in such systems is much more complicated than in single-server systems due to the larger dimensionality of the stochastic process that describes the dynamics of the system. However, the importance of consideration of such priority queueing systems made them a popular subject of research; see, e.g., the papers [6][7][8][9][10][11][12][13][14][15][16] published within the last two years.…”