Filtering recursions for calculating likelihoods for queues based on inter-departure time data

  • Authors:

  • Paul Fearnhead

  • Affiliations:

  • Department of Mathematics and Statistics, Lancaster University, LA1 4YF. p.fearnhead@lancaster.ac.uk

  • Venue:
  • Statistics and Computing
  • Year:
  • 2004

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Abstract

We consider inference for queues based on inter-departure time data. Calculating the likelihood for such models is difficult, as the likelihood involves summing up over the (exponentially-large) space of realisations of the arrival process. We demonstrate how a likelihood recursion can be used to calculate this likelihood efficiently for the specific cases of M/G/1 and Er/G/1 queues. We compare the sampling properties of the mles to the sampling properties of estimators, based on indirect inference, which have previously been suggested for this problem.