In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this model we study the joint queue length distribution at polling epochs and departure epochs. We also study the marginal queue length distribution at arrival epochs, as well as at arbitrary epochs (which is not the same in general, since we cannot use the PASTA property). A generalised version of the distributional form of Little's law is applied to the joint queue length distribution at departure epochs in order to find the waiting time distribution for each customer type. We also provide an alternative, more efficient way to determine the mean queue lengths and mean waiting times, using Mean Value Analysis. Furthermore, we show that under certain conditions a Pseudo-Conservation Law for the total amount of work in the system holds. Finally, typical features of the model under consideration are demonstrated in several numerical examples.
Originele taal-2Engels
Plaats van productieEindhoven
Aantal pagina's30
StatusGepubliceerd - 2009

Publicatie series

NaamReport Eurandom
ISSN van geprinte versie1389-2355

Vingerafdruk Duik in de onderzoeksthema's van 'A polling model with smart customers'. Samen vormen ze een unieke vingerafdruk.

Citeer dit