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Importance sampling algorithms for first passage time probabilities in the infinite server queue

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  • Ridder, Ad

Abstract

This paper applies importance sampling simulation for estimating rare event probabilities of the first passage time in the infinite server queue with renewal arrivals and general service time distributions. We consider importance sampling algorithms which are based on large deviations results of the infinite server queue, and we consider an algorithm based on the cross-entropy method, where we allow light-tailed and heavy-tailed distributions for the interarrival times and the service times. Efficiency of the algorithms is discussed by simulation experiments.

Suggested Citation

  • Ridder, Ad, 2009. "Importance sampling algorithms for first passage time probabilities in the infinite server queue," European Journal of Operational Research, Elsevier, vol. 199(1), pages 176-186, November.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:176-186
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    Cited by:

    1. Cheung, Eric C.K. & Rabehasaina, Landy & Woo, Jae-Kyung & Xu, Ran, 2019. "Asymptotic correlation structure of discounted Incurred But Not Reported claims under fractional Poisson arrival process," European Journal of Operational Research, Elsevier, vol. 276(2), pages 582-601.
    2. Fatma Başoğlu Kabran & Ali Devin Sezer, 2022. "Approximation of the exit probability of a stable Markov modulated constrained random walk," Annals of Operations Research, Springer, vol. 310(2), pages 431-475, March.
    3. Jose Blanchet & Henry Lam, 2014. "Rare-Event Simulation for Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1142-1178, November.
    4. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.

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