The impact of reneging in processor sharing queues

We investigate an overloaded processor sharing queue with renewal arrivals and generally distributed service times. Impatient customers may abandon the queue, or renege, before completing service. The random time representing a customer’s patience has a general distribution and may be dependent on his initial service time requirement. We propose a scaling procedure that gives rise to a fluid model, with nontrivial yet tractable steady state behavior. This fluid model captures many essential features of the underlying stochastic model, and we use it to analyze the impact of impatience in processor sharing queues. We show that this impact can be substantial compared with FCFS, and we propose a simple admission control policy to overcome these negative impacts.