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A polling model with smart customers


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 at the server’s 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 customer’s 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.


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Correspondence to M. A. A. Boon.

Additional information

The research was done in the framework of the BSIK/BRICKS project, and of the European Network of Excellence Euro-NF.

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Boon, M.A.A., van Wijk, A.C.C., Adan, I.J.B.F. et al. A polling model with smart customers. Queueing Syst 66, 239–274 (2010).

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  • Polling
  • Smart customers
  • Varying arrival rates
  • Queue lengths
  • Waiting times
  • Pseudo-conservation law

Mathematics Subject Classification (2000)

  • 60K25
  • 90B22