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An optimal multithreshold control for the input flow of the $$GI/PH/1$$ queueing system with a BMAP flow of negative customers. (English. Russian original) Zbl 1094.90008
Autom. Remote Control 65, No. 9, 1417-1428 (2004); translation from Avtom. Telemekh. 2004, No. 9, 71-84 (2004).
Summary: A $$GI/PH/1$$ queueing system with an additional flow of negative customers is studied. The system has many operation modes differing in the distribution of inter-arrival lengths. Mode control depends on the queue length at arrival instants defined by a multithreshold strategy. The stationary state probability distribution of the system for fixed thresholds is studied. Numerical examples are given to illustrate the determination of the optimal threshold set in a fixed search domain.

##### MSC:
 90B22 Queues and service in operations research
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