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Variance of the output as a function of time: Production line dynamics. (English) Zbl 0948.90056
Summary: We consider Markovian models of discrete materials flow production systems. The transient behavior of a production line is investigated. Namely, mean and variance of the number of parts produced in a given time period conditioned on an arbitrary initial condition is determined by using a Markov reward model. Closed-form expression for the variance of the output from a single unreliable station is derived to illustrate the procedure. Then variance of the output from a general two-station production line with a finite buffer is determined by using a set of recursive equations that exploits the special structure of the probability matrix. The relationship between the due-time performance and variability of the line is investigated by determining the probability of meeting a customer order on time and also the time to produce a given order approximately. Numerical experiments that investigate the relationships between the system parameters and production line dynamics are also included.

MSC:
90B30 Production models
90C40 Markov and semi-Markov decision processes
90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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