A fluid model for closed queueing networks with PS stations

Abstract

This technical report introduces a closed multi-class queueing network (QN) model with class-switching, where the service rates are de ned to represent multi-processor stations with a processor-sharing (PS) allocation policy. These transition rates are also able to consider traditional delay nodes, and therefore a QN model with these transition rates is well-suited for multi-threaded software applications. In this report, we de ne the QN model and use the results in [1] to show that the transient sample paths of the QN model converge to the solution of a system of ordinary di erential equations (ODEs). As the size of the ODE system grows linearly with the number of stations and job classes in the QN model, solving the ODE system becomes a scalable alternative to Markov chain representations.