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Heterogeneous multiprocessor systems with breakdowns: Performance and optimal repair strategies. (English) Zbl 0795.68017

Summary: A model of a system with \(N\) parallel processors subject to occasional interruptions of service, and a common unbounded queue fed by a Poisson arrival stream, is analyzed in the steady state. The service, breakdown and repair characteristics may vary from processor to processor. A solution method called spectral expansion is used to determine the joint distribution of the state of the processors and the number of jobs in the queue. The problem of optimizing the repair policy is addressed. The optimal policy is determined in the case when all breakdown rates are equal, and some heuristics for the general case are investigated.

MSC:

68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
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[1] Avi-Itzhak, B.; Noar, P., Some queueing problems with the service station subject to breakdowns, Oper. Res., 11, 303-320 (1963) · Zbl 0114.34202
[2] Chakka, R.; Mitrani, I., A numerical solution method for multiprocessor systems with general breakdowns and repairs, Proc. 6th Internat. Conf. Modelling Techniques and Tools (1992), Edinburgh
[3] Gaver, D. P., A waiting line with interrupted service including priorities, J. Roy. Statist. Soc. Ser. B, 24, 73-90 (1962) · Zbl 0108.31403
[4] Gohberg, I.; Lancaster, P.; Rodman, L., Matrix Polynomials (1982), Academic Press: Academic Press New York
[5] Jennings, A., Matrix Computations for Engineers and Scientists (1977), Wiley: Wiley New York · Zbl 0355.65018
[6] Kameda, H., A finite-source queue with different customers, J. ACM, 29, 478-491 (1982) · Zbl 0499.68016
[7] Kameda, H., Realizable performance vectors of a finite source queue, Oper. Res., 32, 1358-1367 (1984) · Zbl 0555.90048
[8] Mitrani, I.; Avi-Itzhak, B., A many-server queue with service interruptions, Oper. Res., 16, 628-638 (1968) · Zbl 0239.60094
[9] Mitrani, I.; King, P. J.B., Multiserver systems subject to breakdowns: an empirical study, IEEE Trans. Comput., C-32, 96-99 (1983)
[10] Mitrani, I.; Mitra, D., A spectral expansion method for random walks on semi-infinite strips, IMACS Symp. Iterative Methods in Linear Algebra (1991), Brussels
[11] Neuts, M. F., Matrix Geometric Solutions in Stochastic Models (1981), John Hopkins Univ. Press: John Hopkins Univ. Press Baltimore, MD · Zbl 0469.60002
[12] Neuts, M. F.; Lucantoni, D. M., A Markovian queue with \(N\) servers subject to breakdowns and repairs, Management Sci., 25, 849-861 (1979)
[13] Prabhu, N. U.; Zhu, Y., Markov-modulated queueing systems, Queueing Systems Theory Appl., 5, 215-246 (1989) · Zbl 0694.60087
[14] Sengupta, B., A queue with service interruptions in an alternating Markovian environment, Oper. Res., 38, 308-318 (1990) · Zbl 0706.60094
[15] Thiruvengadam, K., Queueing with breakdowns, Oper. Res., 11, 62-71 (1963) · Zbl 0109.36701
[16] White, H. C.; Christie, L. S., Queueing with preemptive priorities or with breakdown, Oper. Res., 6, 79-95 (1958) · Zbl 1414.90126
[17] Yechiali, U., A queueing-type birth-and-death process defined on a continuous time Markov chain, Oper. Res., 21, 604-609 (1973) · Zbl 0288.60090
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