Abstract
Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. However, so far the repairable retrial queues are analyzed only by queueing theory. In this paper we give a detailed analysis for reliability of retrial queues. By using the supplementary variables method, we obtain the explicit expressions of some main reliability indexes such as the availability, failure frequency and reliability function of the server. In addition, some special queues, for instance, the repairable M/G/1 queue and repairable retrial queue can be derived from our results. These results may be generalized to the repairable multi-server retrial models.
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References
A. Aissani, Unreliable queueing with repeated orders, Microelectron. Reliab. 33 (1993) 2093-2106.
A. Aissani, A retrial queue with redundancy and unreliable server, Queueing Systems 17 (1995) 431-449.
A.M. Aleksandrov, A queueing system with repeated orders, Engrg. Cybernet. Rev. 12(3) (1974) 1-4.
J.R. Artalejo, New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandica 48 (1) (1994) 23-36.
B. Avi-Itzhak and P. Naor, Some queueing problems with the service station subject to breakdown, Oper. Res. 10 (1962) 303-320.
J. Cao and K. Cheng, Analysis of M/G/1 queueing system with repairable service station, ActaMath. Appl. Sinica 5 (1982) 113-127.
B.D. Choi and K.K. Park, The M/G/1 retrial queue for Bernoulli schedule, Queueing Systems 7 (1990) 219-228.
E. Çinlar, Introduction to Stochastic Processes (Prentice-Hall, Englewood Cliffs, NJ, 1975).
G.I. Falin, Multi-phase servicing in a single-channel system for automation of experiments with repeated calls, in: Problems of Automation of Scientific Investigations in Radio Engineering and Electronics (USSR Academy of Science, Moscow, 1975).
G.I. Falin, Aggregate arrival of customers in one-line system with repeated calls, Ukr. Math. J. 28 (1976) 437-440.
G.I. Falin, On the waiting-time process in a single-line queue with repeated calls, J. Appl. Probab. 23 (1986) 185-192.
G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990) 127-167.
G.I. Falin and C. Fricker, On the virtual waiting time in an M/G/1 retrial queue, J. Appl. Probab. 28 (1991) 446-460.
G.I. Falin and J.G.C. Templeton, Retrial Queues (Chapman & Hall, London, 1997).
K. Farahmand, Single line queue with repeated demands, Queueing Systems 6 (1990) 223-228.
J. Keilson, J. Cozzolino and H. Young, A service system with unfilled requests repeated, Oper. Res. 16 (1968) 1126-1137.
V.G. Kulkarni, On queueing systems with retrials, J. Appl. Probab. 20 (1983) 380-389.
V.G. Kulkarni and B.D. Choi, Retrial queues with server subject to breakdowns and repairs, Queueing Systems 7 (1990) 191-208.
V.G. Kulkarni and H.M. Liang, Retrial queues revisited, in: Frontiers in Queueing, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997).
I.L. Mitrany and B. Avi-Itzhak, A many server queue with service interruptions, Oper. Res. 16 (1968) 628-638.
M.F. Neuts and D.M. Lucantoni, A Markovian queue with N servers subject to breakdowns and repairs, Managm. Sci. 25 (1979) 849-861.
M.F. Neuts and M.F. Ramalhoto, A service model in which the server is required to search for customers, J. Appl. Probab. 21 (1984) 157-166.
A.G. Pakes, Some conditions for ergodicity and recurrence of Markov chains, Oper. Res. 17 (1969) 1058-1061.
K. Thiruvenydan, Queueing with breakdown, Oper. Res. 11 (1963) 62-71.
T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987) 201-233.
T. Yang and H. Li, The M/G/1 retrial queue with the server subject to starting failures, Queueing Systems 16 (1994) 83-96.
T. Yang and H. Li, On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated customers, Queueing Systems 21 (1995) 199-215.
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Wang, J., Cao, J. & Li, Q. Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs. Queueing Systems 38, 363–380 (2001). https://doi.org/10.1023/A:1010918926884
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DOI: https://doi.org/10.1023/A:1010918926884