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On a retrial single-server queueing system with finite buffer and Poisson flow. (English. Russian original) Zbl 1114.90332

Probl. Inf. Transm. 37, No. 3, 248-261 (2001); translation from Probl. Peredachi Inf. 37, No. 3, 67-81 (2001).
Summary: A retrial single-server queueing system with finite buffer is considered. The primary incoming flow is Poissonian. If the buffer is overflown, a call entering the system becomes a repeat call and joins the group of repeat calls referred to as an orbit. The maximum number of calls that can simultaneously be contained in the orbit is limited. A call from the orbit makes new attempts to enter the system until a vacancy occurs. Time between repeat attempts for each call is an exponentially distributed random variable. At the initial moment of service, a type of a call is defined: with probability \(a_i\) it becomes a call of type \(i\) and its service time in this case has distribution function \(B_i(x)\), \(i = 1,\dots, K\). For this system, the stationary joint distribution of queues in the buffer and orbit is found. Numerical examples are given.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
94C99 Circuits, networks
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