Server waiting times in infinite supply polling systems with preparation times

J.-P.L. Dorsman, N. Perel, Maria Vlasiou

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


We consider a system consisting of a single server serving 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 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 sufficient 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
Pages (from-to)153-184
Number of pages32
JournalProbability in the engineering and informational sciences
Issue number2
Publication statusPublished - Apr 2016
Externally publishedYes


Dive into the research topics of 'Server waiting times in infinite supply polling systems with preparation times'. Together they form a unique fingerprint.

Cite this