Efficient estimation of overflow probabilities in queues with breakdowns

Dirk Kroese, V.F. Nicola

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)

Abstract

Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources and generally distributed service time when the server is operational. We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.
Original languageUndefined
Pages (from-to)471-484
JournalPerformance evaluation
Volume36-37
DOIs
Publication statusPublished - 1999

Keywords

  • METIS-111782
  • IR-74030
  • Importance sampling
  • Markov-modulated rate processes
  • Effective bandwidth
  • Rare event simulation
  • Queues with breakdowns

Cite this

Kroese, Dirk ; Nicola, V.F. / Efficient estimation of overflow probabilities in queues with breakdowns. In: Performance evaluation. 1999 ; Vol. 36-37. pp. 471-484.
@article{e51aed1056954811ad124f4866f687b5,
title = "Efficient estimation of overflow probabilities in queues with breakdowns",
abstract = "Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources and generally distributed service time when the server is operational. We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.",
keywords = "METIS-111782, IR-74030, Importance sampling, Markov-modulated rate processes, Effective bandwidth, Rare event simulation, Queues with breakdowns",
author = "Dirk Kroese and V.F. Nicola",
year = "1999",
doi = "10.1016/S0166-5316(99)00036-X",
language = "Undefined",
volume = "36-37",
pages = "471--484",
journal = "Performance evaluation",
issn = "0166-5316",
publisher = "Elsevier",

}

Efficient estimation of overflow probabilities in queues with breakdowns. / Kroese, Dirk; Nicola, V.F.

In: Performance evaluation, Vol. 36-37, 1999, p. 471-484.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Efficient estimation of overflow probabilities in queues with breakdowns

AU - Kroese, Dirk

AU - Nicola, V.F.

PY - 1999

Y1 - 1999

N2 - Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources and generally distributed service time when the server is operational. We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.

AB - Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources and generally distributed service time when the server is operational. We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.

KW - METIS-111782

KW - IR-74030

KW - Importance sampling

KW - Markov-modulated rate processes

KW - Effective bandwidth

KW - Rare event simulation

KW - Queues with breakdowns

U2 - 10.1016/S0166-5316(99)00036-X

DO - 10.1016/S0166-5316(99)00036-X

M3 - Article

VL - 36-37

SP - 471

EP - 484

JO - Performance evaluation

JF - Performance evaluation

SN - 0166-5316

ER -