On The Optimal Open-Loop Control Policy For Deterministic And Exponential Polling Systems

Authors:
Bruno Gaujal;Arie Hordijk;Dinard Van Der Laan
Affiliations:
Lab. ID-IMAG (INRIA, CNRS, INPG, UJF), 38330 Montbonnot Saint Martin, France, E-mail: bruno.gaujal@imag.fr;Department of Mathematics, Leiden University, 2300 RA Leiden, The Netherlands, E-mail: hordijk@math.leidenuniv.nl;Faculty of Economics and Business Administration, Department of Econometrics, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands, E-mail: dalaan@feweb.vu.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2007

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Abstract

In this article, we consider deterministic (both fluid and discrete) polling systems with N queues with infinite buffers and we show how to compute the best polling sequence (minimizing the average total workload). With two queues, we show that the best polling sequence is always periodic when the system is stable and forms a regular sequence. The fraction of time spent by the server in the first queue is highly noncontinuous in the parameters of the system (arrival rate and service rate) and shows a fractal behavior. Moreover, convexity properties are shown and are used in a generalization of the computation of the optimal control policy (in open loop) for the stochastic exponential case.