Blanchet J, Pei Y, Sigman K. Exact sampling for some multi-dimensional queueing models with renewal input. Advances in Applied Probability. 2019;51(4):1179-1208. doi:10.1017/apr.2019.45

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Abstract

Using a result of Blanchet and Wallwater (2015) for exactly simulating the maximum of a negative drift random walk queue endowed with independent and identically distributed (i.i.d.) increments, we extend it to a multi-dimensional setting and then we give a new algorithm for simulating exactly the stationary distribution of a first-in–first-out (FIFO) multi-server queue in which the arrival process is a general renewal process and the service times are i.i.d.: the FIFO GI/GI/c queue with . Our method utilizes dominated coupling from the past (DCFP) as well as the random assignment (RA) discipline, and complements the earlier work in which Poisson arrivals were assumed, such as the recent work of Connor and Kendall (2015). We also consider the models in continuous time, and show that with mild further assumptions, the exact simulation of those stationary distributions can also be achieved. We also give, using our …

Authors
Jose Blanchet, Yanan Pei, Karl Sigman
Publication date
2019/12
Journal
Advances in Applied Probability
Volume
51
Issue
4
Pages
1179-1208
Publisher
Cambridge University Press