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.