I have written some introductions to the theory of perfect simulation (also called Coupling from the Past: CFTP). Recently, working with Stephen Connor, I have produced a paper (Connor & Kendall, 2015) on perfect simulation for the M/G/c queue (here is Stephen giving a talk on a related topic), and we are now working on a follow-up concerning perfect simulation for SIR epidemics. Two natural questions arise: To what extent might one be able to develop perfect simulation for compartment models? and can one use perfect simulation to get a good handle on some questions (Gupta et al, 2009) concerning distributional behaviour for M/G/c queues?
- Connor, S. B., & Kendall, W. S. (2015). Perfect Simulation of M/G/c Queues. Advances in Applied Probability 47.4, 1039-1063.
- Gupta, V., Harchol-Balter, M., Dai, J. G., & Zwart, B. (2009). On the inapproximability of M/G/K: why two moments of job size distribution are not enough. Queueing Systems, 64(1), 5–48.