Using the M/G/1 queue under processor sharing for exact simulation of queues

In Sigman (J. Appl. Probab. 48A:209–216, 2011b), a first exact simulation algorithm was presented for the stationary distribution of customer delay for FIFO M/G/c queues in which ρ=λ/μ<1 (super stable case). The key idea involves dominated coupling from the past while using the M/G/1 queue under the processor sharing (PS) discipline as a sample-path upper bound, taking advantage of its time-reversibility properties so as to be able to simulate it backwards in time. Here, we expand upon this method and give several examples of other queueing models for which this method can be used to exactly simulate from their stationary distributions. Examples include sojourn times for single-server queues under various service disciplines, tandem queues, and multi-class networks with general routing.