When Does Forced Idle Time Improve Performance in Polling Models?

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...

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Bibliographic Details
Published in:Management science 1998-08, Vol.44 (8), p.1079-1086
Main Authors: Cooper, Robert B, Niu, Shun-Chen, Srinivasan, Mandyam M
Format: Article
Language:English
Subjects:
Applied sciences
Critical values
Customer services
Cyclic Production Systems
Decomposition
Exact sciences and technology
Inventory control, production control. Distribution
Management science
Mathematical constants
Mathematical expressions
Mathematical models
Operational research and scientific management
Operational research. Management science
Paradoxes
Polling Models
Process engineering
Production technology
Queuing theory. Traffic theory
Recursion
Research grants
Setup Times
Studies
Switchover Times
Vacation Models
Vacations
Variance Paradox
Waiting Times
Work in process
Working papers
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Summary: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.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.44.8.1079