Monotonicity of Performance Measures in a Processor Sharing Queue

Abstract In this paper we study the monotonicity of performance measures in a processor sharing queue with two types of customers. The access control law is such that when a new customer arrives he is admitted only if the number of customers of the same type that is already present in the queue does not exceed a predefined threshold. We show that performance measures such as throughput, mean queue length and mean sojourn time are monotonic functions of the threshold for one type if the threshold for the other type is held constant. Monotonicity of throughput and mean queue length is proven by comparing policies for discrete time Markov processes. Monotonicity of the mean sojourn time is proven directly with the closed form formula for this measure using the existence of a product-form equilibrium distribution for the queuing system.

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