September 2015 Perfect sampling for infinite server and loss systems
Jose Blanchet, Jing Dong
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Adv. in Appl. Probab. 47(3): 761-786 (September 2015). DOI: 10.1239/aap/1444308881


We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.


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Jose Blanchet. Jing Dong. "Perfect sampling for infinite server and loss systems." Adv. in Appl. Probab. 47 (3) 761 - 786, September 2015.


Published: September 2015
First available in Project Euclid: 8 October 2015

zbMATH: 1331.65025
MathSciNet: MR3406607
Digital Object Identifier: 10.1239/aap/1444308881

Primary: 65C05 , 68U20
Secondary: 60K25

Keywords: dominated coupling from the past , infinite server queue , loss queue , many-server asymptotics , perfect sampling , renewal point process

Rights: Copyright © 2015 Applied Probability Trust


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Vol.47 • No. 3 • September 2015
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