zbMATH — the first resource for mathematics

The M/G/1 retrial queue with Bernoulli schedule. (English) Zbl 0706.60089
Summary: We consider an M/G/1 retrial queue with infinite waiting space in which arriving customers who find the server busy join either (a) the retrial group with probability p in order to seek service again after a random amount of time, or (b) the infinite waiting space with probability \(q(=1- p)\) where they wait to be served.
The joint generating function of the numbers of customers in the two groups is derived by using the supplementary variable method. It is shown that our results are consistent with known results when \(p=0\) or \(p=1\).

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
Full Text: DOI
[1] A.M. Alexandrov, A queueing system with repeated orders, Eng. Cybernet. Rev. 12 (1974) 1.
[2] Q.H. Choo and B. Conolly, New results in the theory of repeated orders queueing system, J. Appl. Probab. 16 (1979) 631. · Zbl 0418.60088 · doi:10.2307/3213090
[3] G.I. Falin, A single-line system with secondary orders, Eng. Cybernet. Rev. 17, no. 2 (1979) 76. · Zbl 0437.60073
[4] G.I. Falin, Calculation of the load on a shared-use telephone instrument, Moscow Univ. Compt. Math Cybernet. 2 (1981) 59. · Zbl 0548.90028
[5] B.S. Greenberg,M/G/1 queueing system with returning customers, J. Appl. Probab. 26 (1989) 152. · Zbl 0672.60094 · doi:10.2307/3214325
[6] P. Hokstad, A supplementary variable technique applied to theM/G/1 queue, Scand. J. Stat. 2 (1975) 95. · Zbl 0312.60051
[7] V.G. Kulkarni, A game theoretic model for two types of customers competing for service, Oper. Res. Lett. 2 (1983) 119. · Zbl 0523.60095 · doi:10.1016/0167-6377(83)90019-6
[8] V.G. Kulkarni, Expected waiting times in a multi-class batch arrival retrial queue, J. Appl. Probab. 23 (1986) 144. · Zbl 0589.60073 · doi:10.2307/3214123
[9] T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987) 201. · Zbl 0658.60124 · doi:10.1007/BF01158899
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.