A Relative Entropy Approach to Study Critical Fluid Model Solutions for Multiclass Processor Sharing Queues

A multiclass processor sharing queue consists of a single server and a buffer that contains jobs that require service. At each time, the server simultaneously processes the work associated with each job in the buffer at a rate equal to the reciprocal number of jobs in system. The processor sharing queue is meant to be a mathematical idealization of a computer server time sharing algorithm [10]. Unlike its single class counterpart, a multiclass processor queue works on inhomogeneous jobs; i.e., some jobs may take longer to serve than others. A critical fluid model of a multiclass processor sharing queue describes the average behavior of the queue. We propose a strategy for analyzing the long run behavior of critical fluid model solutions using a notion of relative entropy. This generalizes the work in [13] concerning single class processor sharing queues by incorporating a term that accounts for the equilibration of the distribution of work across job classes. The potential application of this relative entropy approach is substantiated via simulations.