The Annals of Applied Probability

The QNET Method for Two-Moment Analysis of Closed Manufacturing Systems

J. G. Dai and J. M. Harrison

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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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Ann. Appl. Probab., Volume 3, Number 4 (1993), 968-1012.

First available in Project Euclid: 19 April 2007

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Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 90B22: Queues and service [See also 60K25, 68M20] 90B30: Production models

Performance analysis closed multiclass queueing network Brownian approximation heavy traffic


Dai, J. G.; Harrison, J. M. The QNET Method for Two-Moment Analysis of Closed Manufacturing Systems. Ann. Appl. Probab. 3 (1993), no. 4, 968--1012. doi:10.1214/aoap/1177005269.

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