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Control of the service process in a queueing system. (English) Zbl 0583.60092
The emphasis of this review of the control of service processes in a queueing system is put on the model considered and the results obtained rather than on the methods used and the technics applied.
The first part of this paper is devoted to the vacation models, i.e. to the determination of the optimal operating rule for the behaviour of a removable server. The author first examines the case of an individual service process, in M/G/1 queues with N-policy, D-policy and T-policy, respectively; certain special cases are also examined. The problems with batch service are then described and two related applications are considered in details: the control of a shuttle and of a clearing system.
The variable service rate models are examined in the second part in which a main distinction is made between the cases of denumerable and non- denumerable sets of service rates. N-policy and D-policy are considered and the importance of connected policies and of hysteretic policies is pointed out, for models without or with switching costs, respectively.
In a last section, some concluding remarks are then presented and further directions of research are pointed out.

MSC:
60K25 Queueing theory (aspects of probability theory)
93E20 Optimal stochastic control
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