Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2005-06-21
Number: 05-066/4
Author-Name: Bruno Gaujal
Author-Email: bruno.gaujal@imag.fr
Author-Workplace-Name: INRIA Rhône-Alpes, Montbonnot Saint Martin, France
Author-Name: Arie Hordijk
Author-Email: hordijk@math.leidenuniv.nl
Author-Workplace-Name: Dept of Mathematics, Leiden University, Leiden
Author-Name: Dinard van der Laan
Author-Email: dalaan@feweb.vu.nl
Author-Workplace-Name: Dept of Econometrics & Operations Research, Vrije Universiteit Amsterdam
Title: On the Optimal Policy for Deterministic and Exponential Polling Systems
Abstract: In this paper, 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, 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 non continuous in the parameters of the system (arrival rate and service rate) and shows a fractal behavior. Convexity properties are shown in Appendix as well as a generalization of the computations to the stochastic exponential case.
Classification-JEL: C60; C63; C65
Keywords: Polling systems; regular sequences; multimodularity; optimal control
File-Url: https://papers.tinbergen.nl/05066.pdf
File-Format: application/pdf
File-Size: 564418 bytes
Handle: RePEc:tin:wpaper:20050066