A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive

Robert B. Cooper, Shun-Chen Niu and Mandyam M. Srinivasan
Additional contact information
Robert B. Cooper: Florida Atlantic University, Boca Raton, Florida
Shun-Chen Niu: The University of Texas at Dallas, Richardson, Texas
Mandyam M. Srinivasan: The University of Tennessee, Knoxville, Tennessee

Operations Research, 1996, vol. 44, issue 4, 629-633

Abstract: We consider the classical polling model: queues served in cyclic order with either exhaustive or gated service, each with its own distinct Poisson arrival stream, service-time distribution, and switchover-time (the server's travel time from that queue to the next) distribution. Traditionally, models with zero switchover times (the server travels at infinite speed) and nonzero switchover times have been considered separately because of technical difficulties reflecting the fact that in the latter case the mean cycle time approaches zero as the travel speed approaches infinity. We argue that the zero-switchover-times model is the more fundamental model: the mean waiting times in the nonzero-switchover-times model decompose (reminiscent of vacation models) into a sum of two terms, one being a simple function of the sum of the mean switchover times, and the other the mean waiting time in a “corresponding” model obtained from the original by setting the switchover times to zero and modifying the service-time variances. This generalizes a recent result of S. W. Fuhrmann for the case of constant switchover times, where no variance modification is necessary. The effect of these studies is to reduce computation and to improve theoretical understanding of polling models.

Keywords: queues; polling models; cyclic-service queues; decomposition; waiting times; switchover times; server vacations (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.44.4.629 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:44:y:1996:i:4:p:629-633

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().