×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: DOI
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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.