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Discrete-time $$Geo_ 1$$, $$Geo_ 2/G/1$$ retrial queueing systems with two types of calls. (English) Zbl 0878.90041
Summary: We consider a discrete-time $$Geo_1, Geo_2/G/1$$ retrial queue with two types of calls. When arriving calls are blocked due to the server being busy, Type I calls are queued in the priority queue with infinite capacity whereas, Type II calls enter the retrial group in order to try service again after a random amount of time. We find the joint generating function of the number of calls in the priority queue and the number of calls in the retrial group in a closed form. It is shown that our results are consistent with those already known for special cases.

##### MSC:
 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory)
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##### References:
 [1] Yang, T.; Templeton, J.G.C., A survey of retrial queues, Queueing systems, 2, 203-233, (1987) · Zbl 0658.60124 [2] Falin, G.I., A survey of retrial queues, Queueing systems, 7, 127-168, (1990) · Zbl 0709.60097 [3] Yang, T.; Li, H., On the steady-state queue size distribution of the discrete-time geo/G/1 queue with repeated customers, Queueing systems, 21, 199-215, (1995) · Zbl 0840.60085 [4] Choi, B.D.; Park, K.K., The M/G/1 retrial queue for Bernoulli schedule, Queueing system, 7, 219-228, (1990) · Zbl 0706.60089 [5] Foster, F.G, On the stochastic matrices associated with certain queuing processes, Ann. math. stat., 24, 355-360, (1953) · Zbl 0051.10601 [6] Falin, G.I., On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls, Adv. appl. prob., 16, 447-448, (1984) · Zbl 0535.60087 [7] Takagi, H., Queueing analysis: A foundation of performance evaluation, () [8] Takahashi, Y.; Hashida, O., Delay analysis of discrete-time priority queue with structured inputs, Queueing systems, 8, 149-163, (1991) · Zbl 0727.60111 [9] Choo, Q.H.; Conolly, B., New results in the theory of repeated orders queueing systems, J. appl. prob., 16, 631-640, (1979) · Zbl 0418.60088 [10] Falin, G.I.; Artalejo, J.R.; Martin, M., On the single server retrial queue with priority customers, Queueing systems, 14, 439-455, (1993) · Zbl 0790.60076 [11] Rajeswari, A.R., Nonpreemptive priority queue with binomial input, Operations research, 16, 2, 416-421, (1968)
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