Efficient simulation of a tandem queue with server slow-down

D.I. Miretskiy, Willem R.W. Scheinhardt, M.R.H. Mandjes

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Abstract

Tandem Jackson networks, and more sophisticated variants, have found widespread application in various domains. One such a variant is the tandem queue with server slow-down, in which the server of the upstream queue reduces its service speed as soon as the downstream queue exceeds some prespecified threshold, to provide the downstream queue some sort of `protection'. This paper focuses on the overflow probabilities in the downstream queue. Owing to the Markov structure, these can be solved numerically, but the resulting system of linear equations is usually large. An attractive alternative could be to resort to simulation, but this approach is cumbersome due to the rarity of the event under consideration. A powerful remedy is to use importance sampling, i.e., simulation under an alternative measure, where unbiasedness of the estimator is retrieved by weighing the observations by appropriate likelihood ratios. To find a good alternative measure, we first identify the most likely path to overflow. For the normal tandem queue (i.e., no slow-down), this path was known, but we develop an appealing novel heuristic, which can also be applied to the model with slow-down. Then the knowledge of the most likely path is used to devise importance sampling algorithms, both for the normal tandem system and for the system with slow-down. Our experiments indicate that the corresponding new measure is sometimes asymptotically optimal, and sometimes not. We systematically analyze the cases that may occur.
Original languageUndefined
Title of host publicationProceedings of the 6th International Workshop on Rare Event Simulation
EditorsW. Sandmann
Place of PublicationBamberg
PublisherUniversität Bamberg
Pages132-143
Number of pages12
ISBN (Print)not assigned
Publication statusPublished - Oct 2006
Event6th International Workshop on Rare Event Simulation - Bamberg, Germany
Duration: 8 Oct 200610 Oct 2006

Publication series

Name
PublisherUniversität Bamberg
Number10

Workshop

Workshop6th International Workshop on Rare Event Simulation
Period8/10/0610/10/06
Other8-10 October 2006

Keywords

  • EWI-8366
  • Importance sampling
  • IR-66689
  • METIS-237678
  • asymptotic optimality

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