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01.06.2015 | Ausgabe 1-2/2015 Open Access

# Perfect sampling of a single-server queue with periodic Poisson arrivals

Zeitschrift:
Queueing Systems > Ausgabe 1-2/2015
Autoren:
Yaofei Xiong, Duncan J. Murdoch, David A. Stanford

## Abstract

In this paper we present algorithms for the perfect sampling of single-server time-varying queues with periodic Poisson arrivals under the first come first served (FCFS) discipline. The service durations have periodically time-dependent exponential ($$\mathrm M _t/\mathrm M _t/1$$) or homogeneous general ($$\mathrm M _t/\mathrm G /1$$) distributions. Assuming a cycle length of 1, we construct discrete dominating processes at the integer instants $$n \in \{0, \pm 1, \ldots \}$$. Perfect sampling of the $$\mathrm M _t/\mathrm M _t/1$$ queue is obtained using dominated CFTP (Kendall and Møller 2000) when the system is relatively lightly loaded or with the regenerative method (Sigman 2012) in the general case. For the $$\mathrm M _t/\mathrm G /1$$ queue, perfect sampling is achieved with dominated CFTP.
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