Advances in Applied Probability

Perfect sampling for infinite server and loss systems

Jose Blanchet and Jing Dong

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 3 (2015), 761-786.

Dates
First available in Project Euclid: 8 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1444308881

Digital Object Identifier
doi:10.1239/aap/1444308881

Mathematical Reviews number (MathSciNet)
MR3406607

Zentralblatt MATH identifier
1331.65025

Subjects
Primary: 65C05: Monte Carlo methods 68U20: Simulation [See also 65Cxx]
Secondary: 60K25: Queueing theory [See also 68M20, 90B22]

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

Citation

Blanchet, Jose; Dong, Jing. Perfect sampling for infinite server and loss systems. Adv. in Appl. Probab. 47 (2015), no. 3, 761--786. doi:10.1239/aap/1444308881. https://projecteuclid.org/euclid.aap/1444308881


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