The Ph-t/Ph-t/infinity (k) 100 (K) queueing system: Part II - the multiclass network

We demonstrate a numerically exact method for evaluating the time-dependent mean, variance, and higher-order moments of the number of entities in the multiclass Ph-t/Ph-t/infinity queueing network system, as well as at the individual network nodes. We allow for multiple, independent, time-dependent entity classes and develop time-dependent performance measures by entity class at the nodal and network levels. We also demonstrate a numerically exact method for evaluating the distribution function and moments of virtual sojourn time through the network for virtual entities, by entity class, arriving to the system at time t. We include an example using software that we have developed and have put in downloadable form in the Online Supplement to this paper on the journal's website.