Approximate/perfect samplers for closed Jackson networks

Shuji Kijima; Tomomi Matsui

doi:10.1109/WSC.2005.1574333

Approximate/perfect samplers for closed Jackson networks

Shuji Kijima, Tomomi Matsui

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we propose two samplers for the product-form solution of basic queueing networks, closed Jackson networks with multiple servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose two of new ergodic Markov chains both of which have a unique stationary distribution that is the product form solution of closed Jackson networks. One of them is for approximate sampling, and we show it mixes rapidly. To our knowledge, this is the first approximate polynomial-time sampler for closed Jackson networks with multiple servers. The other is for perfect sampling based on monotone CFTP (coupling from the past) algorithm proposed by Propp and Wilson,and we show the monotonicity of the chain.

Original language	English
Title of host publication	Proceedings of the 2005 Winter Simulation Conference
Pages	862-868
Number of pages	7
DOIs	https://doi.org/10.1109/WSC.2005.1574333
Publication status	Published - Dec 1 2005
Externally published	Yes
Event	2005 Winter Simulation Conference - Orlando, FL, United States Duration: Dec 4 2005 → Dec 7 2005

Publication series

Name	Proceedings - Winter Simulation Conference
Volume	2005
ISSN (Print)	0891-7736

Other

Other	2005 Winter Simulation Conference
Country/Territory	United States
City	Orlando, FL
Period	12/4/05 → 12/7/05

All Science Journal Classification (ASJC) codes

Software
Modelling and Simulation
Computer Science Applications

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10.1109/WSC.2005.1574333

Cite this

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title = "Approximate/perfect samplers for closed Jackson networks",

abstract = "In this paper, we propose two samplers for the product-form solution of basic queueing networks, closed Jackson networks with multiple servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose two of new ergodic Markov chains both of which have a unique stationary distribution that is the product form solution of closed Jackson networks. One of them is for approximate sampling, and we show it mixes rapidly. To our knowledge, this is the first approximate polynomial-time sampler for closed Jackson networks with multiple servers. The other is for perfect sampling based on monotone CFTP (coupling from the past) algorithm proposed by Propp and Wilson,and we show the monotonicity of the chain.",

author = "Shuji Kijima and Tomomi Matsui",

year = "2005",

month = dec,

day = "1",

doi = "10.1109/WSC.2005.1574333",

language = "English",

isbn = "0780395204",

series = "Proceedings - Winter Simulation Conference",

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note = "2005 Winter Simulation Conference ; Conference date: 04-12-2005 Through 07-12-2005",

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AU - Kijima, Shuji

AU - Matsui, Tomomi

PY - 2005/12/1

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N2 - In this paper, we propose two samplers for the product-form solution of basic queueing networks, closed Jackson networks with multiple servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose two of new ergodic Markov chains both of which have a unique stationary distribution that is the product form solution of closed Jackson networks. One of them is for approximate sampling, and we show it mixes rapidly. To our knowledge, this is the first approximate polynomial-time sampler for closed Jackson networks with multiple servers. The other is for perfect sampling based on monotone CFTP (coupling from the past) algorithm proposed by Propp and Wilson,and we show the monotonicity of the chain.

AB - In this paper, we propose two samplers for the product-form solution of basic queueing networks, closed Jackson networks with multiple servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose two of new ergodic Markov chains both of which have a unique stationary distribution that is the product form solution of closed Jackson networks. One of them is for approximate sampling, and we show it mixes rapidly. To our knowledge, this is the first approximate polynomial-time sampler for closed Jackson networks with multiple servers. The other is for perfect sampling based on monotone CFTP (coupling from the past) algorithm proposed by Propp and Wilson,and we show the monotonicity of the chain.

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M3 - Conference contribution

AN - SCOPUS:33846704799

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BT - Proceedings of the 2005 Winter Simulation Conference

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ER -

Approximate/perfect samplers for closed Jackson networks

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