×

Complete analysis of finite and infinite buffer \(GI/MSP/1\) queue-a computational approach. (English) Zbl 1149.90322

Summary: We consider a finite buffer single server queue with renewal input and Markovian service process. System length distribution at pre-arrival and arbitrary epochs have been obtained along with some important performance measures. The corresponding infinite buffer queue has also been analyzed.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adan, I.; Zhao, Y., Analyzing \(GI / E_r / 1\) queues, Oper. Res. Lett., 19, 183-190 (1996) · Zbl 0873.90035
[2] Albores-Velasco, F. J.; Tajonar-Sanabria, F. S., Analysis of the \(GI / MSP / c / r\) queueing system, Inf. Process., 4, 46-57 (2004)
[3] Alfa, A. S.; Xue, J.; Ye, Q., Perturbation theory for the asymptotic decay rates in the queues with Markovian arrival process and/or Markovian service process, Queueing Syst., 36, 287-301 (2000) · Zbl 0969.60096
[4] Bocharov, P. P., Stationary distribution of a finite queue with recurrent flow and Markovian service, Autom. Remote Control, 57, 66-78 (1996) · Zbl 0926.60077
[5] Bocharov, P. P.; D’Apice, C.; Pechinkin, A.; Salerno, S., The stationary characteristics of the \(G / MSP / 1 / r\) queueing system, Autom. Remote Control, 64, 288-301 (2003) · Zbl 1066.60077
[6] Grassmann, W. K.; Taksar, M. I.; Heyman, D. P., Regenerative analysis and steady state distributions for Markov chains, Oper. Res., 33, 1107-1116 (1985) · Zbl 0576.60083
[7] Gupta, U. C.; Vijaya Laxmi, P., Analysis of \(MAP / G^{a, b} / 1 / N\) queue, Queueing Syst. Theory Appl., 38, 109-124 (2001) · Zbl 0997.90010
[8] Lucantoni, D. M.; Ramaswami, V., Efficient algorithms for solving non-linear matrix equations arising in phase type queues, Stochast. Models, 1, 29-52 (1985) · Zbl 0554.60093
[9] Neuts, M. F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981), Johns Hopkins University Press: Johns Hopkins University Press Baltimore, MD · Zbl 0469.60002
[10] Ohsone, T., The \(GI / E_k / 1\) queue with finite waiting room, J. Oper. Res. Soc. Japan, 24, 375-391 (1981) · Zbl 0475.60084
[11] Ramaswami, V.; Latouche, G., An experimental evaluation of the matrix-geometric method for the \(GI / PH / 1\) queue, Stochast. Models, 5, 629-667 (1989) · Zbl 0702.60083
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.