zbMATH — the first resource for mathematics

Homogeneous finite-source retrial queues with server subject to breakdowns and repairs. (English) Zbl 1090.90036
Summary: This paper deals with a single server retrial queue with a finite number of homogeneous sources of calls and a single nonreliable server, which means that the server is subject to random breakdowns depending on whether it is busy or idle. The failure of the server may block or unblock the systems’ operations and the service of the interrupted request may be resumed or the call can be transmitted to the orbit. All random variables involved in the model constructions are supposed to be exponentially distributed and independent of each other.
The novelty of the investigation is the variability of this nonreliability of the server which makes the system rather complicated. The MOSEL tool was used to formulate and solve the problem and the main performance and reliability measures were derived and graphically displayed. Several numerical calculations were performed to show the effect of the nonreliability of the server on the mean response times of the calls.

90B22 Queues and service in operations research
90B25 Reliability, availability, maintenance, inspection in operations research
PDF BibTeX Cite
Full Text: DOI
[1] Artalejo, J.R., Retrial queues with a finite number of sources, J. Korean math. soc., 35, 503-525, (1998) · Zbl 0930.60079
[2] Artalejo, J.R., Accessible bibliography on retrial queues, Mathl. comput. modeling, 30, 3/4, 1-6, (1999) · Zbl 1009.90001
[3] ()
[4] Falin, G.I., A survey of retrial queues, Queueing systems, 7, 127-168, (1990) · Zbl 0709.60097
[5] Falin, G.I.; Templeton, J.G.C., Retrial queues, (1997), Chapman and Hall Philadelphia, PA · Zbl 0944.60005
[6] Kovalenko, I.N.; Kuznetsov, N.Yu.; Pegg, P.A., Mathematical theory of reliability of time dependent systems with practical applications, (1997), John Wiley and Sons London · Zbl 0899.60074
[7] Ravichandran, N., Stochastic methods in reliability theory, (1990), John Wiley and Sons Chichester · Zbl 0722.60089
[8] Trivedi, K.S., Probability and statistics with reliability, queueing and computer science applications, (1982), Prentice Hall New York
[9] Artalejo, J.R., New results in retrial queueing systems with breakdown of the servers, Statistica neerlandica, 48, 23-36, (1994) · Zbl 0829.60087
[10] Aissani, A.; Artalejo, J.R., On the single server retrial queue subject to breakdowns, Queueing systems theory and applications, 30, 309-321, (1998) · Zbl 0918.90073
[11] Kulkarni, V.G.; Choi, B.D., Retrial queues with server subject to breakdowns and repairs, Queueing systems theory and applications, 7, 191-208, (1990) · Zbl 0727.60110
[12] Wang, J.; Cao, J.; Li, Q., Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing systems theory and applications, 38, 363-380, (2001) · Zbl 1028.90014
[13] Takagi, H., Queueing analysis, A foundation of performance evaluation, volume 2, finite systems, (1993), North-Holland Englewood Cliffs, NJ
[14] Kornyshev, Y.N., Design of a fully accessible switching system with repeated calls, Telecommunications, 23, 46-52, (1969)
[15] Falin, G.I.; Artalejo, J.R., A finite source retrial queue, European journal of operational research, 108, 409-424, (1998) · Zbl 0943.90012
[16] Falin, G.I., A multiserver retrial queue with a finite number of sources of primary calls, Mathl. comput. modelling, 30, 3/4, 33-49, (1999) · Zbl 1042.60537
[17] Artalejo, J.R.; Gomez-Corral, A., Information theoretic analysis for queueing systems with quasi-random input, Mathl. comput. modelling, 22, 3, 65-76, (1995) · Zbl 0831.60101
[18] Artalejo, J.R.; Rajagopalan, V.; Sivasamy, R., On finite Markovian queues with repeated attempts, Investigacion operativa, 9, 83-94, (2000)
[19] Dragieva, V.I., Single-line queue with finite source and repeated calls, Problems of information transmission, 30, 283-289, (1994) · Zbl 0916.90104
[20] Falin, G.I.; Gomez Corral, A., On a bivariate Markov process arising in the theory of single-server retrial queues, Statistica neerlandica, 54, 67-78, (2000) · Zbl 0974.60081
[21] Gomez-Corral, A., Analysis of a single-server retrial queue with quasi-random input and nonpreemptive priority, Computers math. applic., 43, 6/7, 767-782, (2002) · Zbl 1009.60083
[22] Kok, A.G., Algorithmic methods for single server systems with repeated attempts, Statistica neerlandica, 38, 23-32, (1984) · Zbl 0547.60098
[23] Li, H.; Yang, T., A single server retrial queue with server vacations and a finite number of input sources, European journal of operational research, 85, 149-160, (1995) · Zbl 0912.90139
[24] Stepanov, S.N., The analysis of the model with finite number of sources and taking into account the subscriber behaviour, Automation and remote control, 55, 100-113, (1994)
[25] Ohmura, H.; Takahashi, T., An analysis of repeated call model with a finite number of sources, Electronics and communications in Japan, 68, 112-121, (1985)
[26] Tran-Gia, P.; Mandjes, M., Modeling of customer retrial phenomenon in cellular mobile networks, IEEE journal of selected areas in communications, 15, 1406-1414, (1997)
[27] Houck, D.J.; Lai, W.S., Traffic modelling and analysis of hybrid fibercoax systems, Computer networks and ISDN systems, 30, 821-834, (1998)
[28] Janssens, G.K., The quasi-random input queueing system with repeated attempts as a model for collision-avoidance star local area network, IEEE transactions on communications, 45, 360-364, (1997)
[29] Mehmet-Ali, M.K.; Hayes, J.F.; Elhakeem, A.K., Traffic analysis of a local area network with star topology, IEEE transactions on communications, 36, 703-712, (1988)
[30] Kalmychkov, A.I.; Medvedev, G.A., Probability characteristics of Markov local-area networks with randomaccess protocols, Automatic control and computer science, 24, 38-45, (1990)
[31] Khomichkov, I.I., Study of models of local networks with multiple-access protocols, Automation and remote control, 54, 1801-1811, (1993)
[32] Begain, K.; Bolch, G.; Herold, H., Practical performance modeling, application of the MOSEL language, (2001), Kluwer Academic Amsterdam
[33] Sztrik, J.; Gál, T., A recursive solution of a queueing model for a multi-terminal system subject to breakdowns, Performance evaluation, 11, 1-7, (1990) · Zbl 0697.60092
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.