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01.06.2015 | Ausgabe 1-2/2015 Open Access

Queueing Systems 1-2/2015

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

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


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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