Publication:
Inference in ergodic queues using occupation cycles

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1994
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Facultad de Ciencias Económicas y Empresariales. Decanato
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We deal with inference problems on traffic intensity and on the mean number of customers in the system in steady state (q). We define the slopping time in terms of occupation cycles and apply the resulting estimators to a large class of stationary queues comparing it with alternative methods and with the integral estimator obtained directly from the sample in the Markovian case. Our method is quite effocient to estimate q. Also the asymptotic problems posed by Schruben and Kulkarni [7] do not appear. We observe that reductions in the sample information do not necessarily give worse estimations. We also give some numerical examples by simulating known models.
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S. Asmusen. "Applied probability and queues", Wiley, New York, 1987. I.V. Basawa and N.U.Prabhu. "Large sample inference from simple server queues". Queueing Systems. 1, 289-304, 1988. P. Billingsley. "Statistical inference for Markov processess, The University of Chicago Press, Chicago, 1961. G. Falin, A. Rodrigo and H. Vazquez. "A new model for the M/G/1 retrial queue", Preprint, 1993. L. Kleinrock. "Queueing Systems", Vol. I. Wiley, New York, 1914. J. F. Reynolds. "Asymptotic properties of mean length estimators for finite Markov queue". Oper. Res. 20, 1, 52-57, 1972. L. Schruben and R.Kulkarni. "Some consecuences of estimating parameters for the M/M/1 queue", Oper. Res. Letters, 1. 2, 75-78, 1982.