Bayesian prediction of the transient behaviour and busy period in short- and long-tailed GI / G / 1 queueing systems

Computational Statistics and Data Analysis

Volumn 52, Issue 3, 2008, Pages 1615-1635

  Ausín, M Concepción ^a   Wiper, Michael P ^b   Lillo, Rosa E ^b  

^a UNIVERSITY OF A CORUÑA   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Bayesian inference; Coxian distribution; Heavy tails; Queueing systems; Reversible jump; Semiparametric modelling; Transient analysis

Indexed keywords

APPROXIMATION ALGORITHMS; MARKOV PROCESSES; MONTE CARLO METHODS; PARAMETERIZATION; PARETO PRINCIPLE; QUEUEING NETWORKS; TRANSIENT ANALYSIS;

BAYESIAN INFERENCE; COXIAN DISTRIBUTION; HEAVY TAILS; QUEUEING SYSTEMS; REVERSIBLE JUMP; SEMIPARAMETRIC MODELLING;

BAYESIAN NETWORKS;

EID: 35548954212     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.05.009     Document Type: Article

References (30)

1. Abate J., Choudhury G.L., and Whitt W. Waiting-time tail probabilities in queues with long-tail service-time distributions. Queueing Systems 16 (1994) 311-338
2. Armero C., and Bayarri M.J. Bayesian prediction in M / M / 1 queues. Queueing Systems 15 (1994) 401-417
3. Armero C., and Bayarri M.J. Bayesian analysis of a queueing system with unlimited service. J. Statist. Plann. Inference 58 (1997) 241-261
4. Armero C., and Conesa D. Prediction in Markovian bulk arrival queues. Queueing Systems 34 (2000) 327-350
5. Asmussen S., and Moller J.R. Calculation of the steady-state waiting time distribution in GI / PH / c and MAP / PH / c queues. Queueing Systems 37 (2001) 9-29
6. Ausín M.C., Lillo R.E., Ruggeri F., and Wiper M.P. Bayesian modelling of hospital bed occupancy times using a mixed generalized Erlang distribution. In: Bernardo J.M., Bayarri M.J., Berger J.O., Dawid A.P., Heckerman D., Smith A.F.M., and West M. (Eds). Bayesian Statistics 7 (2003), Oxford University Press, Oxford 443-452
7. Ausín M.C., Wiper M.P., and Lillo R.E. Bayesian estimation for the M / G / 1 queue using a phase type approximation. J. Statist. Plann. Inference 118 (2004) 83-101
8. Bertsimas D. An analytic approach to a general class of G / G / c queueing systems. Oper. Res. 38 (1990) 139-155
9. Bertsimas D., and Nakazato D. Transient and busy period analysis of the G / G / 1 queue: the method of stages. Queueing Systems 10 (1992) 153-184
10. Cox D.R. A use of complex probabilities in the theory of stochastic processes. Proc. Cam. Phil. Soc. 51 (1955) 313-319
11. Crovella M.E., Taqqu M.S., and Bestavros A. Heavy-tailed probability distributions in the World Wide Web. In: Adler R.J., Feldman R.E., and Taqqu M.S. (Eds). A Practical Guide to Heavy Tails (1998), Chapman & Hall, New York 3-26
12. Cumani A. On the canonical representation of homogenous Markov processes modelling failure-time distributions. Microelectron. Reliability 22 (1982) 583-602
13. Diebolt J., and Robert C.P. Estimation of finite mixture distributions through Bayesian sampling. J. Roy. Statist. Soc. B 56 (1994) 363-375
14. Feldmann A., and Whitt W. Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. Performance Evaluation 31 (1998) 245-279
15. Green P. Reversible jump MCMC computation and Bayesian model determination. Biometrika 82 (1995) 711-732
16. Gross D., and Harris C.M. Fundamentals of Queueing Theory (1985), Wiley, New York
17. Gruet M.A., Philippe A., and Robert C.P. MCMC control spreadsheets for exponential mixture estimation. J. Comput. Graph. Statist. 8 (1999) 298-317
18. Hosono T. Numerical inversion of Laplace transform and some applications to wave optics. Radio Science 16 (1981) 1015-1019
19. Johnson N.L., and Kotz S. Distributions in Statistics. Continuous Univariate Distributions (1970), Wiley, New York
20. Lillo R. On the optimal control of M / G / 1 systems under the cycle criterion. Systems Control Lett. 41 (2000) 29-39
21. McGill W.J., and Gibbon J. The general-gamma distribution and reaction time. J. Math. Psych. 2 (1965) 1-18
22. Neuts M.F. Matrix Geometric Solutions in Stochastic Models (1981), Johns Hopkins University Press, Baltimore
23. Paxson V., and Floyd S. Wide-area traffic: the failure of Poisson modeling. IEEE Trans. Networking 3 (1995) 226-244
24. Prabhu N.U. Stochastic Storage Processes (1998), Springer, New York
25. Ralston A., and Rabinowitz P. A First Course in Numerical Analysis (1978), McGraw-Hill, New York
26. Richardson S., and Green P. On Bayesian analysis of mixtures with an unknown number of components. J. Roy. Statist. Soc. B 59 (1997) 731-792
27. k / 1 queues. Queueing Systems 30 (1998) 289-308
28. Riska A., Diev V., and Smirni E. An EM-based technique for approximating long-tailed data sets with PH distributions. Performance Evaluation 55 (2004) 147-164
29. Robert C.P., and Mengersen K.L. Reparameterisation issues in mixture modelling and their bearing on MCMC algorithms. Comput. Statist. Data Anal. 29 (1999) 325-343
30. Wiper M.P. Bayesian analysis of Er / M / 1 and Er / M / c queues. J. Statist. Plann. Inference 69 (1998) 65-79