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November, 1993 The QNET Method for Two-Moment Analysis of Closed Manufacturing Systems
J. G. Dai, J. M. Harrison
Ann. Appl. Probab. 3(4): 968-1012 (November, 1993). DOI: 10.1214/aoap/1177005269


Consider a job-shop or batch-flow manufacturing system in which new jobs are introduced only as old ones depart, either because of physical constraints or as a matter of management policy. Assuming that there is never a shortage of new work to be done, the number of active jobs remains constant over time, and the system can be modeled as a kind of closed queueing network. With manufacturing applications in mind, we formulate a general closed network model and develop a mathematical method to estimate its steady-state performance characteristics. A restrictive feature of our network model is that all the job classes that are served at any given node or station share a common service time distribution. Our analytical method, which is based on an algorithm for computing the stationary distribution of an approximating Brownian model, is motivated by heavy traffic theory; it is precisely analogous to a method developed earlier for analysis of open queueing networks. The required inputs include not only first-moment information, such as average product mix and average processing rates, but also second-moment data that serve as quantitative measures of variability in the processing environment. We present numerical examples that show that system performance is very much affected by changes in second-moment data. In these few numerical examples, our estimates of average throughput rates and average throughput times for different product families are generally accurate when compared against simulation results.


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J. G. Dai. J. M. Harrison. "The QNET Method for Two-Moment Analysis of Closed Manufacturing Systems." Ann. Appl. Probab. 3 (4) 968 - 1012, November, 1993.


Published: November, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0798.60080
MathSciNet: MR1241031
Digital Object Identifier: 10.1214/aoap/1177005269

Primary: 60K25
Secondary: 60J70 , 90B22 , 90B30

Keywords: Brownian approximation , closed multiclass , heavy traffic , performance analysis , Queueing network

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 4 • November, 1993
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