On a generalization of a queuing system \(M_ k/G/1\). (Russian) Zbl 0577.60090

Prizva, G. I.

Teor. Veroyatn. Mat. Stat. 29, 109-114 (1983).

A generalization of the system \(M_ k/G/1\) with n regimes is considered. Here a device may work in a different regime for every customer and the serving time may depend on the present regime of the device and its last one. Let \(\gamma_ n\) be the index of the regime of the device serving the n-th customer and \(x_ n\) the duration of serving. It is shown that the homogeneous Markov chain \((\gamma_ n,x_ n)\) is a (J,x)-process. Derived are the transition probabilities of the process (\(\xi\) (t),\(\gamma\) (t)), where \(\xi\) (t) is the number of customers which stay in the system at time t and \(\gamma\) (t) the index of the last regime of a device until t.

Reviewer: C.Baldauf

MSC:

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

Keywords:

different regime for every customer