Skip to main content
SpringerLink
Log in

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

  • Published:
Statistics and Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allen A. 1990. Probability, Statistics and Queueing Theory with Computer Science Applications. Academic Press, Boston.

    Google Scholar 

  • Armero C. and Bayarri M.J. 1997. A Bayesian analysis of a queueing system with unlimited service. Journal of Statistical Inference and Planning 58: 241-261.

    Google Scholar 

  • Baum L.E., Petrie T., Soules G., and Weiss N. 1970. A maximisation technique occurring in the statistical analysis of probabilistic functions of Markov chains. The Annals of Mathematical Statistics 41: 164-171.

    Google Scholar 

  • Bhat U.N. and Rao S.S. 1987. Statistical analysis of queueing systems. Queueing Systems 1: 217-247.

    Google Scholar 

  • Fearnhead P. and Meligotsidou L. 2004. Filtering for partially-observed continuous-time Markov models. Journal of the Royal Statistical Society (to appear).

  • Gourieroux C., Monfort A., and Renault E. 1993. Indirect inference. Journal of Applied Econometrics 8: 85-118.

    Google Scholar 

  • Heggland K. and Frigessi A. 2004. Estimating functions in indirect inference. Journal of the Royal Statistical Society, 66: 447-462.

    Google Scholar 

  • Nelder J.A. and Mead R. 1965. A simplex algorithm for function minimization. Computer Journal 7: 308-313.

    Google Scholar 

  • Scott S.L. 2002. Bayesian methods for hidden Markov models: Recursive computing in the 21st century. Journal of the American Statistical Association 97: 337-351.

    Google Scholar 

  • Scott S.L. 2003. Hidden Markov processes and sequential pattern mining. In: Ye N. (Ed.), The Handbook of Data Mining, Lawrence Erlbaum Associates, pp. 133-157.

  • Wiper M.P. 1998. Bayesian analysis of Er/M/1 and Er/M/cqueues. Journal of Statistical Planning and Inference 69: 65-79.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Lancaster University, LA1 4YF

    Paul Fearnhead

Authors
  1. Paul Fearnhead
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fearnhead, P. Filtering recursions for calculating likelihoods for queues based on inter-departure time data. Statistics and Computing 14, 261–266 (2004). https://doi.org/10.1023/B:STCO.0000035305.92337.80

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:STCO.0000035305.92337.80

Search

Navigation