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- Title
Perfect sampling of a single-server queue with periodic Poisson arrivals.
- Authors
Xiong, Yaofei; Murdoch, Duncan; Stanford, David
- 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 ) when the system is relatively lightly loaded or with the regenerative method (Sigman ) in the general case. For the $$\mathrm M _t/\mathrm G /1$$ queue, perfect sampling is achieved with dominated CFTP.
- Subjects
POISSON algebras; ASSOCIATIVE algebras; QUEUING theory; MANAGEMENT science; ALGORITHMS
- Publication
Queueing Systems, 2015, Vol 80, Issue 1/2, p15
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-014-9431-9