Server waiting times in infinite supply polling systems with preparation times

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

Research output: Book/ReportReportAcademic

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Abstract

We consider a system consisting of a single server serving a ¿xed number of stations. At each station there is an in¿nite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queueing networks, to an extension of polling systems, and surprisingly to random graphs. We are interested in the waiting time of the server. For the case where the server polls the stations cyclically, we give a suf¿cient condition for the existence of a limiting waiting-time distribution and we study the tail behavior of the stationary waiting time. Furthermore, assuming that preparation times are exponentially distributed, we describe in depth the resulting Markov chain. We also investigate a model variation where the server does not necessarily poll the stations in a cyclic order, but always serves the customer with the earliest completed preparation phase. We show that the mean waiting time under this dynamic allocation never exceeds that of the cyclic case, but that the waiting-time distributions corresponding to both cases are not necessarily stochastically ordered. Finally, we provide extensive numerical results investigating and comparing the effect of the system’s parameters to the performance of the server for both models.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages24
Publication statusPublished - 2013

Publication series

NameReport Eurandom
Volume2013018
ISSN (Print)1389-2355

Fingerprint

Polling Systems
Waiting Time
Preparation
Server
Waiting Time Distribution
Customers
Tail Behavior
Queueing Networks
Single Server
Limiting Distribution
Random Graphs
Queue
Markov chain
Exceed
Model
Numerical Results

Cite this

Dorsman, J. L., Perel, N., & Vlasiou, M. (2013). Server waiting times in infinite supply polling systems with preparation times. (Report Eurandom; Vol. 2013018). Eindhoven: Eurandom.
Dorsman, J.L. ; Perel, N. ; Vlasiou, M. / Server waiting times in infinite supply polling systems with preparation times. Eindhoven : Eurandom, 2013. 24 p. (Report Eurandom).
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Dorsman, JL, Perel, N & Vlasiou, M 2013, Server waiting times in infinite supply polling systems with preparation times. Report Eurandom, vol. 2013018, Eurandom, Eindhoven.

Server waiting times in infinite supply polling systems with preparation times. / Dorsman, J.L.; Perel, N.; Vlasiou, M.

Eindhoven : Eurandom, 2013. 24 p. (Report Eurandom; Vol. 2013018).

Research output: Book/ReportReportAcademic

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Dorsman JL, Perel N, Vlasiou M. Server waiting times in infinite supply polling systems with preparation times. Eindhoven: Eurandom, 2013. 24 p. (Report Eurandom).