When Does Forced Idle Time Improve Performance in Polling Models?

Robert B. Cooper, Shun-Chen Niu and Mandyam M. Srinivasan
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Robert B. Cooper: Department of Computer Science and Engineering, Florida Atlantic University, Boca Raton, Florida 33431-0991
Shun-Chen Niu: School of Management, The University of Texas at Dallas, Richardson, Texas 75083-0688
Mandyam M. Srinivasan: Management Science Program, College of Business Administration, The University of Tennessee, Knoxville, Tennessee 37996-0562

Management Science, 1998, vol. 44, issue 8, 1079-1086

Abstract: Sarkar and Zangwill (1991) showed by numerical examples that reduction in setup times can, surprisingly, actually increase work in process in some cyclic production systems (that is, reduction in switchover times can increase waiting times in some polling models). We present, for polling models with exhaustive and gated service disciplines, some explicit formulas that provide additional insight and characterization of this anomaly. More specifically, we show that, for both of these models, there exist simple formulas that define for each queue a critical value z* of the mean total setup time z per cycle such that, if z z*, then the expected waiting time at that queue will be minimized if the server is forced to idle for a constant length of time z* - z every cycle; also, for the symmetric polling model, we give a simple explicit formula for the expected waiting time and the critical value z* that minimizes it.

Keywords: Polling Models; Cyclic Production Systems; Setup Times; Switchover Times; Waiting Times; Variance Paradox; Vacation Models; Decomposition (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (5)

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