Summary
Jobs generated by a single Poisson source can be routed through N alternative gateways, modelled as parallel M/M/1 queues. The servers are subject to random breakdowns which leave their corresponding queues intact, but may affect the routing of jobs during the subsequent repair periods.
The marginal equilibrium queue size distributions are determined by spectral expansion. This can be done, at least in principle, for any number of queues. Several routing strategies are evaluated and compared empirically. In the special case N = 2, it may also be possible to find the joint distribution of the numbers of jobs in the two queues.
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References
B. Avi-Itzhak and P. Naor, “Some Queueing Problems with the Service Station Subject to Breakdowns”, Operations Research, 11, pp. 303–320, 1963.
J.W.Cohen and O.J. Boxma, “Boundary Value Problems in Queueing System Analysis”, North-Holland (Elsevier), 1983.
G. Fayolle and R. Iasnogorodski, “Two Coupled Processors: The reduction to a Riemann-Hilbert Problem Z”, Wahrsheinlichkeitstheorie, 47, pp. 325–351, 1979.
F.D. Gakhov, “Boundary Value Problems”, Addison Wesley, 1966.
N. Mikou. “A Two-Node Jackson Network Subject to Breakdowns”, Stochastic Models, 4, pp. 523–552, 1988.
O. Idrissi-Kacemi, N. Mikou and S. Saadi, “Two Processors Only Interacting During Breakdown: The Case Where the Load is Not Lost”, submitted for publication.
I. Mitrani, “Networks of Unreliable Computers”, in Computer Architectures and Networks (ed. E. Gelenbe and R. Mahl), North-Holland, 1974.
I. Mitrani and B. Avi-Itzhak, “A Many-Server Queue with Service Interruptions”, Operations Research, 16(3), pp. 628–638, 1968.
I. Mitrani and R. Chakka, “Spectral Expansion Solution for a Class of Markov Models: Application and Comparison with the Matrix-Geometric Method”, Performance Evaluation, 23, 1995.
I. Mitrani and D. Mitra, “A Spectral Expansion Method for Random Walks on Semi-Infinite Strips”, in Iterative Methods in Linear Algebra (ed. R. Beauwens and P. de Groen), North-Holland, 1992.
I. Mitrani and P.E. Wright, “Routing in the Presence of Breakdowns”, Performance Evaluation, 20, pp. 151–164, 1994.
N.I. Muskhelishvili, “Singular Integral Equations”, P. Noordhoff, 1953.
B. Sengupta, “A Queue with Service Interruptions in an Alternating Markovian Environment”, Operations Research, 38, pp. 308–318, 1990.
H.C. White and L.S. Christie, “Queueing with Preemptive Priorities or with Breakdown”, Operations Research, 6, pp. 79–95, 1958.
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© 1995 ECSC-EC-EAEC, Brussels-Luxembourg
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Thomas, N., Mitrani, I. (1995). Routing Among Different Nodes Where Servers Break Down Without Losing Jobs. In: Baccelli, F., Jean-Marie, A., Mitrani, I. (eds) Quantitative Methods in Parallel Systems. Esprit Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79917-4_17
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DOI: https://doi.org/10.1007/978-3-642-79917-4_17
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