## Numerical study of the optimal control of a system with heterogeneous servers.(English. Russian original)Zbl 1071.60086

Autom. Remote Control 64, No. 2, 302-309 (2003); translation from Avtom. Telemekh. 2003, No. 2, 143-151 (2003).
Let be given a controllable $$M/M/K/N - K$$ $$(K \leqslant N < \infty )$$ queueing system with $$K$$ heterogeneous servers, $$N - K$$ waiting places, Poisson input flow of intensity $$\lambda$$, and servicing durations distributed exponentially with the parameters $$\mu _k$$, $$1 \leqslant k \leqslant K$$. The instants of customer arrivals and completion of servicing are the instants of control. At the instant of customer arrival, control lies in queueing it, provided that there are free waiting places, or in choosing a free server and sending the customer to it. At the instant of customer release, control lies in choosing a server and sending or declining to send the first customer in the queue, if nonempty, to it. A customer is lost only if all servers and all waiting places are occupied; otherwise, it must be sent to any of the servers or queued. The problem is to organize servicing to minimize the mean number of customers in the stationary system mode. The well-known Howard algorithm is used to study numerically whether the optimal servicing disciplines satisfy the criterion for minimum stationary number of customers in the system.

### MSC:

 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research
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