CLOSED NETWORKS OF QUEUES
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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A closed network of queues consists of a finite set of N customers, a finite set of M single-channel servers, and a set of arcs i,j which represent the allowed instantaneous movement from station i to station j. One also assumes that all customers are identical in their stochastic behavior, that movement is governed by a set of given transition probabilities such that they form an irreducible Markov chain, that service times are governed by an exponential distribution, and that the imbedded Markov chain defined on the instants of service completions is irreducible. Under these assumptions steady- state operating characteristics are derived through analyses of the time-average steady-state equations and of the underlying Markov chain. The general results are specialized to cyclic queues and to open networks of queues jobshop-like queuing systems the structure of the steady-state probabilities is the same as that of the cyclic queue. It is also shown that the results can be generalized to a multi-channel server problem and that the number of customers at a given service center has an IFR increasing failure rate distribution. Optimal allocation of labor servers from a fixed pool is considered and it is shown that, in a cyclic queue, maximum output is achieved from an equal allocation of labor to each service center. A discrete optimization problem is then considered for a more general network that represents the operation of an airlines maintenance base.
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- Operations Research