Heavy traffic analysis of the discriminatory randomorderofservice discipline

Abstract

We study the steady-state queue-length vector in a multiclass single-server queue with relative priorities. Upon service completion, the probability that the next customer to be served is from class k is controlled by class-dependent weights. Once a customer has started service, it is served without interruption until completion. This is a generalization of the random-order-of-service discipline. We investigate the system in a heavy-traffic regime. We first establish a state-space collapse for the scaled queue length vector, that is, the scaled queue length vector is in the limit the product of an exponentially distributed random variable and a deterministic vector. As a direct consequence, we obtain that the scaled number of customers in the system reduces as classes with smaller mean service requirement obtain relatively larger weights. In addition, we present the distribution of the scaled sojourn time of a customer given its class, in heavy traffic.