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Optimal design and control of queues. (English) Zbl 1102.60076

The paper is an extensive and detailed review containing two main parts: optimal design of queueing systems and optimal control of queues. (The latter has the lion’s share of the review.) The second part focuses mainly on the modelling aspects and analyses of different threshold (control) policy models, in particular, \(N\), \(T\), and \(D\) policies.
Under stationary \(N\)-policy, the server is turned on when the total number of units in the queue reaches the value \(N\) and turned off when the system becomes empty. A stationary \(T\)-policy is defined as follows. The server scans the queue \(T\) times units after the end of the last busy period. If customers are found, a busy period begins and the server is active until the system is empty (otherwise, zero length period begins). In either case, the next scan is made \(T\) units after the end of a busy period. Finally, the stationary \(D\)-policy switches a server on when the workload reaches or exceeds the level \(D\) and switches the server off when the system becomes empty. The review contains an extensive bibliography.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
90B22 Queues and service in operations research
90B25 Reliability, availability, maintenance, inspection in operations research
60K25 Queueing theory (aspects of probability theory)
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References:

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