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Discrete-time geo$^{[X]}$/G$_{H}$/1 retrial queue with Bernoulli feedback. (English) Zbl 1061.60092
Bathes of calls arrive according to a geometrical arrival process. At every arrival epoch a batch of $l$ calls arrives with probability $c_l $. If the server is busy at the arrival epoch, then all these calls join the orbit, whereas the server is free, then one of the arriving calls begins its service and the others form sources of repeated calls. Each call before being served chooses a service distribution of type $h$ with probability $q_h $. A call who has received service returns to the orbit for reservice with probability $\theta $ or departs the system with probability $1 - \theta $. The retrial time is distributed geometrically. The paper gives the generating function of the number of calls in the orbit and in the system. It is shown that the total number of calls in the system can be represented as the sum of two independent variables, one of which is the total number of calls in a queueing system with Bernoulli feedback and the other is the number of repeated calls given that the server is free.

60K25Queueing theory
90B22Queues and service (optimization)
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