Performance analysis of service systems with priority upgrades

Abstract

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare service, perishable inventory and project management. We give a comprehensive study on the system stationary distribution, computational algorithm design and sensitivity analysis. We observe that when queue 2 is large, the conditional distribution of queue 1 approximates a Poisson distribution. The tail probability of queue 2 decays geometrically, while the tail probability of queue 1 decays much faster than queue 2's. This helps us to design an algorithm to compute the stationary distribution. Finally, by using the algorithm, we do sensitivity analysis on various system parameters, i.e., the arrival rates, service rates and the upgrading rate. The numerical study provides helpful insights on designing such service systems.

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

“…When the number of servers occupied in the second stage reaches the threshold, non-priority customers cannot enter the system upon arrival. On the other side, Atencia [22] analyzed a discrete-time queuing model with general distributed service time and preemptive priority service, while Xie et al [23] investigated an M/M/1 queuing system where preemptive service allows low-priority customers to be upgraded to high-priority. More recently, Xu, Liu, and Wu [24] considered an M/G/1 retrial queue with preemptive priority operating on a Bernoulli schedule, where a new arrival either immediately displaces the current customer being served with a probability α or joins the retrial orbit with a probability 1 − α. Chamberlain and Starobinski [25] studied a single server queue with preemptive-resume service and general distributed service time, customer equilibrium joining strategies, and social welfare under the unobservable scenario are presented.…”

Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities

“…The short surveys of the literature devoted to the queueing systems with changing the priority of customers are given, e.g., in [1][2][3][4][5][6][7][8][9][10][11]. In [5][6][7][8], the change of the priority occurs deterministically as a function of the elapsed sojourn time.…”