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Inference and prediction in bulk arrival queues and queues with service in stages

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  • C. Armero
  • D. Conesa

Abstract

This paper deals with the statistical analysis from a Bayesian point of view, of bulk arrival queues where the batch size is considered as a fixed constant. The focus is on prediction of the usual measures of performance of the system in the steady state. The probability generating function of the posterior predictive distribution of the number of customers in the system and the Laplace transform of the posterior predictive distribution of the waiting time in the system are obtained. Numerical inversion of these transforms is considered. Inference and prediction of its equivalent single queue with service in stages is also discussed. © 1998 John Wiley & Sons, Ltd.

Suggested Citation

  • C. Armero & D. Conesa, 1998. "Inference and prediction in bulk arrival queues and queues with service in stages," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 35-46, March.
    • Handle: RePEc:wly:apsmda:v:14:y:1998:i:1:p:35-46
    DOI: 10.1002/(SICI)1099-0747(199803)14:13.0.CO;2-O
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    Cited by:

    1. Armero, Carmen & Conesa, David, 2004. "Statistical performance of a multiclass bulk production queueing system," European Journal of Operational Research, Elsevier, vol. 158(3), pages 649-661, November.
    2. Ausín Olivera, María Concepción & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2001. "Bayesian inference and prediction for the GI/M/1 queueing system," DES - Working Papers. Statistics and Econometrics. WS ws014126, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. M. A. C. Almeida & F. R. B. Cruz & F. L. P. Oliveira & G. Souza, 2020. "Bias correction for estimation of performance measures of a Markovian queue," Operational Research, Springer, vol. 20(2), pages 943-958, June.
    4. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, F.R.B. & Cançado, André L.F., 2023. "Change point estimation in an M/M/2 queue with heterogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 182-194.
    5. Ausín Olivera, María Concepción & Wiper, Michael Peter & Lillo Rodríguez, Rosa Elvira, 2001. "Bayesian estimation for the M/G/1 queue using a phase type approximation," DES - Working Papers. Statistics and Econometrics. WS ws013019, Universidad Carlos III de Madrid. Departamento de Estadística.

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