Efficient simulation of a tandem Jackson network

Dirk P. Kroese; Victor F. Nicola

doi:10.1109/WSC.1999.823103

Efficient simulation of a tandem Jackson network

Dirk P. Kroese, Victor F. Nicola

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

7 Citations (Scopus)

Abstract

We consider a two-node tandem Jackson network. Starting from a given state, we are interested in estimating the probability that the content of the second buffer exceeds some high level L before it becomes empty. The theory of Markov additive processes is used to determine the asymptotic decay rate of this probability, for large L. Moreover, the optimal exponential change of measure to be used in importance sampling is derived and used for efficient estimation of the rare event probability of interest. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer, and yields asymptotically efficient simulation for any set of arrival and service rates. The relative error is bounded independent of the level L, except when the first server is the bottleneck and its buffer is infinite, in which case the relative error is bounded linearly in L.

Original language	English
Title of host publication	Proceedings 1999 Winter Simulation Conference (WSC'99)
Subtitle of host publication	'Simulation - A Bridge to the Future'
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	411-419
Number of pages	8
ISBN (Print)	0-7803-5780-9
DOIs	https://doi.org/10.1109/WSC.1999.823103
Publication status	Published - 6 Dec 1999
Event	1999 Winter Simulation Conference: Simulation - A Bridge to the Future - Phoenix, United States Duration: 5 Dec 1999 → 8 Dec 1999

Conference

Conference	1999 Winter Simulation Conference
Abbreviated title	WSC
Country	United States
City	Phoenix
Period	5/12/99 → 8/12/99

Keywords

Buffer overflow
Monte Carlo methods
Australia
Feedforward systems
State estimation
Network servers
Testing
Analytical models
Discrete event simulation
State-space methods

Access to Document

10.1109/WSC.1999.823103

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title = "Efficient simulation of a tandem Jackson network",

abstract = "We consider a two-node tandem Jackson network. Starting from a given state, we are interested in estimating the probability that the content of the second buffer exceeds some high level L before it becomes empty. The theory of Markov additive processes is used to determine the asymptotic decay rate of this probability, for large L. Moreover, the optimal exponential change of measure to be used in importance sampling is derived and used for efficient estimation of the rare event probability of interest. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer, and yields asymptotically efficient simulation for any set of arrival and service rates. The relative error is bounded independent of the level L, except when the first server is the bottleneck and its buffer is infinite, in which case the relative error is bounded linearly in L.",

keywords = "Buffer overflow, Monte Carlo methods, Australia, Feedforward systems, State estimation, Network servers, Testing, Analytical models, Discrete event simulation, State-space methods",

author = "Kroese, {Dirk P.} and Nicola, {Victor F.}",

year = "1999",

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booktitle = "Proceedings 1999 Winter Simulation Conference (WSC'99)",

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address = "United States",

note = "1999 Winter Simulation Conference : Simulation - A Bridge to the Future, WSC ; Conference date: 05-12-1999 Through 08-12-1999",

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T1 - Efficient simulation of a tandem Jackson network

AU - Kroese, Dirk P.

AU - Nicola, Victor F.

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N2 - We consider a two-node tandem Jackson network. Starting from a given state, we are interested in estimating the probability that the content of the second buffer exceeds some high level L before it becomes empty. The theory of Markov additive processes is used to determine the asymptotic decay rate of this probability, for large L. Moreover, the optimal exponential change of measure to be used in importance sampling is derived and used for efficient estimation of the rare event probability of interest. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer, and yields asymptotically efficient simulation for any set of arrival and service rates. The relative error is bounded independent of the level L, except when the first server is the bottleneck and its buffer is infinite, in which case the relative error is bounded linearly in L.

AB - We consider a two-node tandem Jackson network. Starting from a given state, we are interested in estimating the probability that the content of the second buffer exceeds some high level L before it becomes empty. The theory of Markov additive processes is used to determine the asymptotic decay rate of this probability, for large L. Moreover, the optimal exponential change of measure to be used in importance sampling is derived and used for efficient estimation of the rare event probability of interest. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer, and yields asymptotically efficient simulation for any set of arrival and service rates. The relative error is bounded independent of the level L, except when the first server is the bottleneck and its buffer is infinite, in which case the relative error is bounded linearly in L.

KW - Buffer overflow

KW - Monte Carlo methods

KW - Australia

KW - Feedforward systems

KW - State estimation

KW - Network servers

KW - Testing

KW - Analytical models

KW - Discrete event simulation

KW - State-space methods

U2 - 10.1109/WSC.1999.823103

DO - 10.1109/WSC.1999.823103

M3 - Conference contribution

SN - 0-7803-5780-9

SP - 411

EP - 419

BT - Proceedings 1999 Winter Simulation Conference (WSC'99)

PB - IEEE

CY - Piscataway, NJ

T2 - 1999 Winter Simulation Conference

Y2 - 5 December 1999 through 8 December 1999

ER -