×

\(M/G/1/r\) retrial queueing systems with priority of primary customers. (English) Zbl 1042.60532

Summary: We analyze a single-server retrial queueing system with finite buffer, Poisson arrivals, and general distribution of service time. If an arriving customer finds the queue completely occupied he joins a retrial group (or orbit) in order to seek service again after an exponentially distributed amount of time. We obtain a stationary distribution of the primary queue size, a recurrent algorithm for the factorial moments of the number of retrial customers and an expression for the expected number of customers in the system.

MSC:

60K25 Queueing theory (aspects of probability theory)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Artalejo, J. R.; Falin, G. I., On the orbit characteristics of the M/G/1 retrial queue, Naval Research Logistics, 43, 1147-1161 (1996) · Zbl 0859.60088
[2] Artalejo, J. R., Explicit formulae for the characteristics of the M/\(H_2\)/1 retrial queue, Operation Research Society, 44, 3, 309-313 (1993) · Zbl 0771.60073
[3] Choi, B. D.; Rhee, K. H., The \(M/G/1\) retrial queue with retrial rate control policy, Probability in the Engineering and Informational Sciences, 7, 29-46 (1993)
[4] Farahmand, K.; Smith, N. H., Retrial queues with recurrent demand option, Journal of Applied Mathematics and Stochastic Analysis, 9, 2, 221-228 (1996) · Zbl 0858.60078
[5] Artalejo, J. R.; Gómez-Corral, A., Stochastic analysis of the departure and quasi-input processes in versatile single-server queue, Journal of Applied Mathematics and Stochastic Analysis, 9, 2, 171-183 (1996) · Zbl 0858.60083
[6] Artalejo, J. R., A queueing system with returning customers and waiting line, Operation Research Letters, 17, 191-199 (1993) · Zbl 0836.90072
[7] Falin, G. I.; Artalejo, J. R., Approximations for multiserver queues with balking/retrial discipline, OR Spektrum, 17, 239-244 (1995) · Zbl 0843.90046
[8] 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
[9] Bocharov, P. P.; Pechinkin, A. V., Queueing Theory (1995), Peoples’ Friendship University Press: Peoples’ Friendship University Press Moscow · Zbl 1061.60093
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.