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A new model for the M/G/1 retrial queve

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1994
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Facultad de Ciencias Económicas y Empresariales. Decanato
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This article deals with a new model for the M/G/1 retrial queue. We consider the process (M(t),N(t)) where M(t) is the total number of arrivals from the last departure until time t and N(t) is the number of customers in orbit at time t. We obtain the generating function together with a recurrent formula for factorial moments in the steady state. Limit behavior under heavy traffic is also studied. We use this process to get an estimator of the parameter of retrial and obtain its accuracy by solving some linear differential equations. We also give some numerical examples.
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Falin, G. "A single-line system with secondary orders", Eng. Cybernet. Rev. 17 (2), (1978) 76-83. Falin, G. "Asymptotic propertles of the number of demands distribution in a M/G/1/oo., queueing system with repeated calls", Paper 5418-83, All-Union Institute for Scientific and Technical Information, Moscow, (1983). (in Russian). Falin, G. "Traffic measurements in M/G/1 retrial queues", preprint (1993). Kellson J., Cozzolino J. and Young H. "A service system with unfilled request repeated", Opero Res. 16, (1968) 1126-1137. Martin, M. and Falin, G. "Inference for M/M/1/., retrial queues", preprint (1994).