Optimization of Polling Systems and Dynamic Vehicle Routing Problems on Networks
Name
OR-283-93.pdf
Size
1.52 MB
Format
Adobe PDF
Checksum (MD5)
04c36348917ce73ec15553d19cc65398
Author(s)
Bertsimas, Dimitris J.
Xu, Haiping
Date Issued
December 1993
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 283-93
Abstract
We consider the problem of optimizing a polling system, i.e., of optimally sequencing a server in a multi-class queueing system with switch-over times in order to minimize a linear objective function of the waiting times. The problem has important applications in computer, communication, production and transportation networks. We propose nonlinear programming relaxations that provide strong lower bounds to the optimal cost for all static policies. We also obtain lower bounds for dynamic policies as well, which are primarily useful under light traffic conditions and/or small switch-over times. We conjecture that the lower bounds developed in this paper for the class of static policies are also valid for dynamic policies under heavy traffic conditions. We use the information from the lower bound and integer programming techniques to construct static policies that are very close (0-3%) to the lower bounds. We compare numerically our proposed policies with static policies proposed in the literature as well as with dynamic policies and find that the policies we propose outperform all static policies proposed in the literature and at least in heavier traffic outperform dynamic policies as well.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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