Problems of large sample estimation and tests for the parameters in a single server queue are discussed. The service time and the interarrivai time densities are assumed to belong to (positive) exponential families. The queueing system is observed over a continuous time interval (0,T] whereT is determined by a suitable stopping rule. The limit distributions of the estimates are obtained in a unified setting, and without imposing the ergodicity condition on the queue length process. Generalized linear models, in particular, log-linear models are considered when several independent queues are observed. The mean service times and the mean interarrival times after appropriate transformations are assumed to satisfy a linear model involving unknown parameters of interest, and known covariates. These models enhance the scope and the usefulness of the standard queueing systems.
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I.V. Basawa and N.U. Prabhu, Estimation in single server queues. Nav. Res. logist. Quart. 28 (1981) 475–487.
U.N. Bhat and S.S. Rao, Statistical analysis of queueing systems, Queueing Systems Theory Appl. 1 (1987) 217–247.
P. Billingsley,Statistical Inference for Markov Processes (Chicago University Press, Chicago, 1961).
P. Billingsley,Convergence of Probability Measures (John Wiley, New York, 1968).
L. Fahrmeir and H. Kaufmann, Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models, Ann. Statist. 13 (1985) 342–368.
L. Fahrmeir and H. Kaufmann, Correction to consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models, Ann. Statist. 14 (1986) 1643.
P. McCullagh and J.A. Nelder,Generalized Linear Models (Chapman and Hall, London, 1983).
M.F. McGrath, D. Gross and N.D. Singpurwalla, A subjective approach to the theory of queues I-modeling, Queueing Systems Theory Appl. 1 (1987) 317–333.
M.F. McGrath and N.D. Singpurwalla, A subjective approach to the theory of queues II-inference and information in M/M/-queues. Queueing Systems Theory Appl. 1 (1987) 335–353.
C.R. Rao,Linear Statistical Inference and its Applications, 2nd ed. (John Wiley, New York, 1973).
R.W. Wolff, Problems of statistical inference for birth and death queueing models, Oper. Res. 13 (1965) 343–357.
Partially supported by the U. S. Army Research Office through the Mathematical Sciences Institute of Cornell University.
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Basawa, I.V., Prabhu, N.U. Large sample inference from single server queues. Queueing Syst 3, 289–304 (1988). https://doi.org/10.1007/BF01157852
- Single server queues
- maximum likelihood
- stopping times
- exponential families
- generalized linear models
- tests of fit
- asymptotic inference