Importance sampling for non-Markovian tandem queues using subsolutions

Anne  Buijsrogge; Pieter-Tjerk  de Boer; Werner R.W. Scheinhardt

doi:10.1007/s11134-019-09623-0

Importance sampling for non-Markovian tandem queues using subsolutions

Anne Buijsrogge^*
, Pieter-Tjerk de Boer
, Werner R.W. Scheinhardt

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

20 Downloads (Pure)

Abstract

In this paper, we use importance sampling simulation to estimate the probability that the number of customers in a d-node GI|GI|1 tandem queue reaches some high level N in a busy cycle of the system. We present a state-dependent change of measure for a d-node GI|GI|1 tandem queue based on the subsolution approach, and we prove, under a mild conjecture, that this state-dependent change of measure gives an asymptotically efficient estimator for the probability of interest when all supports are bounded.

Original language	English
Pages (from-to)	31-65
Number of pages	35
Journal	Queueing systems
Volume	93
Issue number	1-2
Early online date	16 Jul 2019
DOIs	https://doi.org/10.1007/s11134-019-09623-0
Publication status	Published - 1 Oct 2019

Keywords

GI|GI|1 queues
Importance sampling
Rare event simulation
Tandem queues

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10.1007/s11134-019-09623-0Licence: CC BY

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keywords = "GI|GI|1 queues, Importance sampling, Rare event simulation, Tandem queues",

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N2 - In this paper, we use importance sampling simulation to estimate the probability that the number of customers in a d-node GI|GI|1 tandem queue reaches some high level N in a busy cycle of the system. We present a state-dependent change of measure for a d-node GI|GI|1 tandem queue based on the subsolution approach, and we prove, under a mild conjecture, that this state-dependent change of measure gives an asymptotically efficient estimator for the probability of interest when all supports are bounded.

AB - In this paper, we use importance sampling simulation to estimate the probability that the number of customers in a d-node GI|GI|1 tandem queue reaches some high level N in a busy cycle of the system. We present a state-dependent change of measure for a d-node GI|GI|1 tandem queue based on the subsolution approach, and we prove, under a mild conjecture, that this state-dependent change of measure gives an asymptotically efficient estimator for the probability of interest when all supports are bounded.

KW - GI|GI|1 queues

KW - Importance sampling

KW - Rare event simulation

KW - Tandem queues

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JF - Queueing systems

IS - 1-2

ER -

Importance sampling for non-Markovian tandem queues using subsolutions

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