Processor Sharing Queues With Impatient Customers and State-Dependent Rates

Abstract

We study queues with impatient customers and Processor Sharing (PS) discipline as well as other variants of PS discipline, namely, Discriminatory Processor Sharing (DPS) and Generalized Processor Sharing (GPS) disciplines, where customers have deadlines until the end of service (DES). Customers arrive according to a state-dependent Poisson process and have general impatience. Customers have exponential service times with state-dependent service rates. Analytical methods based on simple Markov chains are given for the performance analysis of such queues. The principal measures of performance are the steady-state probability of missing deadline and the steady-state probability of blocking. Similar results are obtained for related queues with Random Order Service (ROS) discipline where customers have deadlines until the beginning of service (DBS). In view of a lack of exact analytical results for First Come First Served (FCFS) queues with state-dependent rates, a highly accurate approximation method is also given for these latter queues. The efficacy and accuracy of the approach are illustrated by some numerical examples and simulation experiments.