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Setups in polling models: does it make sense to set up if no work is waiting?

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Robert B. Cooper ,
Shun-Chen Niu  and
Mandyam M. Srinivasan
Robert B. Cooper*
Affiliation:
Florida Atlantic University
Shun-Chen Niu*
Affiliation:
University of Texas at Dallas
Mandyam M. Srinivasan*
Affiliation:
University of Tennessee
*
∗Postal address: Department of Computer Science and Engineering, Florida Atlantic University, Boca Raton, FL 33431–0991, USA. Email address: [email protected].
∗∗Postal address: School of Management, The University of Texas at Dallas, P.O. Box 830688, Richardson, TX 75083–0688, USA.
∗∗∗Postal address: Management Science Program, College of Business Administration, The University of Tennessee, Knoxville, TN 37996–0562, USA.
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Abstract

We compare two versions of a symmetric two-queue polling model with switchover times and setup times. The SI version has State-Independent setups, according to which the server sets up at the polled queue whether or not work is waiting there; and the SD version has State-Dependent setups, according to which the server sets up only when work is waiting at the polled queue. Naive intuition would lead one to believe that the SD version should perform better than the SI version. We characterize the difference in the expected waiting times of these two versions, and we uncover some surprising facts. In particular, we show that, regardless of the server utilization or the service-time distribution, the SD version performs (i) the same as, (ii) worse than, or (iii) better than its SI counterpart if the switchover and setup times are, respectively, (i) both constants, (ii) variable (i.e. non-deterministic) and constant, or (iii) constant and variable. Only (iii) is consistent with naive intuition.

Keywords

Polling modelsstate-dependent setup timeswaiting timesswitchover timesvacation modelsdecomposition

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 585 - 592
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Research supported in part by the National Science Foundation under grants DMI-9500216, 9500040, 9500471.

Research also supported in part by a Summer Research Grant from the School of Management, The University of Texas at Dallas.

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