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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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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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Keywords

  • Single server queues
  • maximum likelihood
  • stopping times
  • exponential families
  • generalized linear models
  • tests of fit
  • asymptotic inference