Estimating variance of output from cyclic exponential queueing systems
Queueing Systems: Theory and Applications
Manufacturing flow line systems: a review of models and analytical results
Queueing Systems: Theory and Applications - Special issue on queueing models of manufacturing systems
Mathematical and Computer Modelling: An International Journal
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In this study the variability properties of the output of transfer lines are investigated. The asymptotic variance rate of the output of an N-station synchronous transfer line with no interstation buffers and cycle-dependent failures is analytically determined. Unlike the other studies, the analytical method presented in this study yields a closed-form expression for the asymptotic variance rate of the output. The method is based on a general result derived for irreducible recurrent Markov chains. Namely, the limiting variance of the number of visits to a state of an irreducible recurrent Markov chain is obtained from the n-step transition probability function. Thus, the same method can be used in other applications where the limiting variance of the number of visits to a state of an irreducible recurrent Markov chain is of interest. Numerical results show that the asymptotic variance rate of the output does not monotonically increase as the number of stations in the transfer line increases. The asymptotic variance rate of the output may first increase and then decrease depending on the station parameters. This property of the production rate is investigated through numerical experiments and the results are presented.