Perfect sampling for infinite server and loss systems. (September 2015)

• Record Type: Journal Article
• Authors: Blanchet, Jose; Dong, Jing
• Is Part Of: Advances in applied probability. Volume 47:Number 3(2015)
• Page Start: 761
• Page End: 786
• Publication Date: 2015-09
• Subjects: Perfect sampling, -- dominated coupling from the past, -- infinite server queue, -- loss queue, -- renewal point process, -- many-server asymptotics; 65C05, -- 68U20, -- 60K25; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1239/aap/1444308881
• Languages: English
• ISSNs: 0001-8678

Abstract

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.