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Large sample inference from single server queues

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Abstract

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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Authors and Affiliations

  1. Department of Statistics, University of Georgia, 30602, Athens, GA, USA

    I. V. Basawa

  2. Mathematical Sciences Institute, Cornell University, Caldwell Hall, 14853, Ithaca, NY, USA

    N. U. Prabhu

Authors
  1. I. V. Basawa
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  2. N. U. Prabhu
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Additional information

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

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  • DOI: https://doi.org/10.1007/BF01157852

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