Cyclic-type polling models with preparation times

N. Perel, J.L. Dorsman, M. Vlasiou

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
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Abstract

We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are interested in the waiting time of the server. The waiting time of the server satisfies a Lindley-type equation of a non-standard form. We give a sufficient condition for the existence of a limiting waiting time distribution in the general case, and assuming preparation times are exponentially distributed, we describe in depth the resulting Markov chain. We provide detailed computations for a special case and extensive numerical results investigating the effect of the system's parameters to the performance of the server.
Original languageEnglish
Title of host publicationProceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013)
PublisherINSTICC Press
Pages14-23
ISBN (Print)978-989856540-2
Publication statusPublished - 2013

Fingerprint

Polling
Preparation
Server
Waiting Time
Polling Systems
Queuing Networks
Waiting Time Distribution
Limiting Distribution
Random Graphs
Model
Queue
Markov chain
Customers
Numerical Results
Sufficient Conditions

Cite this

Perel, N., Dorsman, J. L., & Vlasiou, M. (2013). Cyclic-type polling models with preparation times. In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013) (pp. 14-23). INSTICC Press.
Perel, N. ; Dorsman, J.L. ; Vlasiou, M. / Cyclic-type polling models with preparation times. Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013). INSTICC Press, 2013. pp. 14-23
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Perel, N, Dorsman, JL & Vlasiou, M 2013, Cyclic-type polling models with preparation times. in Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013). INSTICC Press, pp. 14-23.

Cyclic-type polling models with preparation times. / Perel, N.; Dorsman, J.L.; Vlasiou, M.

Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013). INSTICC Press, 2013. p. 14-23.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AU - Dorsman, J.L.

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AB - We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are interested in the waiting time of the server. The waiting time of the server satisfies a Lindley-type equation of a non-standard form. We give a sufficient condition for the existence of a limiting waiting time distribution in the general case, and assuming preparation times are exponentially distributed, we describe in depth the resulting Markov chain. We provide detailed computations for a special case and extensive numerical results investigating the effect of the system's parameters to the performance of the server.

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BT - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013)

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Perel N, Dorsman JL, Vlasiou M. Cyclic-type polling models with preparation times. In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013). INSTICC Press. 2013. p. 14-23