Modeling a Class of Flexible Manufacturing Systems with Reversible Routing

We model a flexible manufacturing system FMS as a closed queueing network with a set of stations, each with a local buffer of limited capacity. Based on the theory of reversibility as well as some known approaches in the studies of queueing networks with finite buffers, we derive product-form solutions to a class of such FMS networks that have reversible parts routing a system with a centralized material handling station being one example. This class also includes a certain type of dynamic routing scheme. For systems with zero-buffer stations, we show that the solutions have product form even for nonexponential processing times.

[1]  Kathryn E. Stecke,et al.  The Optimality of Unbalancing Both Workloads and Machine Group Sizes in Closed Queueing Networks of Multiserver Queues , 1985, Oper. Res..

[2]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[3]  J. Keilson.  Markov Chain Models--Rarity And Exponentiality , 1979 .

[4]  Benjamin Melamed,et al.  On the reversibility of queueing networks , 1982 .

[5]  J. A. Buzacott,et al.  Models of automatic transfer lines with inventory banks a review and comparison , 1978 .

[6]  J. Buzacott.  "Optimal" operating rules for automated manufacturing systems , 1980 .

[7]  J. A. Buzacott,et al.  Models of flexible manufacturing systems with limited local buffers , 1986 .

[8]  Boris G. Pittel,et al.  Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis , 1979, Math. Oper. Res..

[9]  J. Kingman.  Markov population processes , 1969, Journal of Applied Probability.

[10]  Donald F. Towsley,et al.  Queuing Network Models with State-Dependent Routing , 1980, JACM.

[11]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[12]  Stanley B. Gershwin,et al.  Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers , 1983, Oper. Res..

[13]  A. Barbour.  Networks of queues and the method of stages , 1976, Advances in Applied Probability.

[14]  Harry G. Perros,et al.  Approximate analysis of arbitrary configurations of open queueing networks with blocking , 1987 .

[15]  J. A. Buzacott,et al.  Models for Understanding Flexible Manufacturing Systems , 1980 .

[16]  David D. Yao,et al.  On queueing network models of flexible manufacturing systems , 1986, Queueing Syst. Theory Appl..