Prediction in Markovian bulk arrival queues

Queueing Systems

Volumn 34, Issue 1-4, 2000, Pages 327-350

  Armero, Carmen ^a   Conesa, David ^a  

^a UNIVERSITY OF VALENCIA   (Spain)

Author keywords

Bayesian inference; Empirical Bayes methods; Hierarchical Bayesian models; Measures of performance; Numerical inversion of transforms

Indexed keywords

BAYESIAN NETWORKS; INFERENCE ENGINES; LAPLACE TRANSFORMS; NUMERICAL METHODS; PROBABILITY DISTRIBUTIONS;

BAYESIAN INFERENCE; EMPIRICAL BAYES METHOD; HIERARCHICAL BAYESIAN MODELS; MEASURES OF PERFORMANCE; NUMERICAL INVERSION;

QUEUEING THEORY;

EID: 0034343617     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019121506451     Document Type: Article

References (46)

1. J. Abate and W. Whitt, The Fourier series method for inverting transforms of probability distributions, Queueing Systems 10 (1992) 5-87.
2. S.R. Adke and E.S. Murphee, Efficient sequential estimation for compound Poisson processes, Comm. Statist. Theory Methods 17(2) (1988) 443-460.
3. C. Armero, Bayesian inference in Markovian queues, Queueing Systems 15 (1994) 419-426.
4. C. Armero and M.J. Bayarri, Bayesian prediction in M/M/1 queues, Queueing Systems 15 (1994) 401-417.
5. C. Armero and M.J. Bayarri, Prior assessments for prediction in queues, The Statistician 43 (1994) 139-153.
6. C. Armero and M.J. Bayarri, Bayesian questions and answers in queues, in: Bayesian Statistics 5, eds. J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (Oxford Univ. Press, Oxford, 1996) pp. 3-23.
7. C. Armero and M.J. Bayarri, Dealing with uncertainties in queues and networks of queues: A Bayesian approach, in: Multivariate Analysis, Design of Experiments and Survey Sampling, ed. S. Ghosh (Marcel Dekker, New York, 1999) pp. 579-608
8. C. Armero and D. Conesa, Inference and prediction in bulk arrival queues and queues with service in stages, Appl. Stochastic Models Data Anal. 14 (1998) 35-46.
9. I.W. Basawa and N.U. Prabhu, Large sample inference from single server queues, Queueing Systems 3 (1988) 289-304.
10. J.O. Berger, Objective Bayesian analysis: Development of reference noninformative priors, in: Problemi di Recerca nella Statistica Bayesiana, ed. W. Racugno (Societa Italiana di Statistica, Cagliari, 1992).
11. U.N. Bhat, G.K. Miller and S.S. Rao, Statistical analysis of queueing systems, in: Frontiers in Queueing, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997) chapter 13.
12. M.L. Chaudhry and J.G.C. Templeton, A First Course in Bulk Queues (Wiley, New York, 1983).
13. A.B. Clarke, Maximum likelihood estimates in a simple queue, Ann. Math. Statist. 28 (1957) 1036-1040.
14. P.L. Conti, Large sample Bayesian analysis for Geo/G/1 discrete-time queueing models. Technical Report, Dipartamento di Statistica, Probabilit̀ e Statistiche Applicate, Universitá di Roma "La Sapienza" (1998).
15. D.R. Cox, Some problems of statistical analysis connected via congestion, in: Proc. Symp. on Congestion Theory, Chapel Hill (University of North Carolina Press, 1965) pp. 289-316.
16. S. Dalal, J. Lee and D. Sabavala, Empirical Bayes prediction for a compound Poisson-multinomial process, Statist. Probab. Lett. 9 (1990) 385-389.
17. A. Ganesh, P. Green, N. O'Connell and S. Pitts, Bayesian network management, Queueing Systems 28 (1998) 267-282.
18. A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin, Bayesian Data Analysis (Chapman and Hall, London, 1995).
19. W.R. Gilks, S. Richardson and D.J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman and Hall, London, 1996).
20. R.D. Gorsky, Modelling the effect of decreased food intake on the activity pattern of an individual, Managm. Sci 29 (1983) 378-381.
21. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, Boston).
22. J.D. Griffiths, Queueing at the Suez Canal, J. Oper. Res. Soc. 46 (1995) 1299-1309.
23. J. Lehoczky, Statistical methods, in: Handbooks in O.R. and M.S., eds. D.P. Heyman and M.J. Sobel (Elsevier Science/North-Holland, Amsterdam, 1990) chapter 6.
24. J.S. Maritz and T. Lwin, Empirical Bayes Methods, 2nd ed. (Chapman and Hall, London).
25. M.F. McGrath, D. Gross and N.D. Singpurwalla, A subjective Bayesian approach to the theory of queues: I - Modeling, Queueing Systems 1 (1987) 317-333.
26. M.F. McGrath and N.D. Singpurwalla, A subjective Bayesian approach to the theory of queues: II - Inference and information in M/M/1 queues, Queueing Systems 1 (1987) 335-353.
27. J. Medhi, Stochastic Models in Queueing Theory (Academic Press, Boston, 1991).
28. C.N. Morris, Parametric empirical Bayes inference: Theory and applications, J. Amer. Statist. Assoc. 78 (1983) 47-65.
29. M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models - An Algorithmic Approach (John Hopkins Univ. Press, Baltimore, MD, 1981).
30. M.F. Neuts and Y. Chaudramouli, Statistical group testing with queueing involved, Queueing Systems 2 (1987) 19-39.
31. k/1 queues, Queueing Systems 30 (1998) 289-308.
32. B.D. Ripley, Stochastic Simulation (Wiley, New York, 1987).
33. H. Robbins, An empirical Bayes approach to statistics, in: Proc. 3rd Berkeley Symp. on Mathematical Statistics and Probability (Univ. of California Press, Berkeley, CA, 1955) pp. 157-164.
34. H. Robbins, Prediction and estimation for the compound Poisson distribution, Proc. Nat. Acad. Sci. U.S.A. (1977) 2670-2671.
35. H. Robbins, Some thoughts on empirical Bayes estimation, Ann. Statist. (1983) 713-723.
36. F. Ruggeri, M. Wiper and D. Rios Insua, Bayesian analysis of dependence in M/M/1 models, Technical Report #8, IAMI (1996).
37. L. Schruben and R. Kulkarni, Some consequences of estimating parameters for the M/M/1 queue, Oper. Res. Lett. 1 (1982) 75-78.
38. B.W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman and Hall, London, 1986).
39. S.Y. Sohn, Empirical Bayesian analysis for traffic intensity: M/M/1 queues with covariates, Queueing Systems 22 (1996) 383-401.
40. C. Tebaldi and M. West, Bayesian inference on network traffic using link count data, Technical Report ISDS, Duke University (1997).
41. D. Thiruvaiyaru and I.V. Basawa, Empirical Bayes estimation for queueing systems and networks, Queueing Systems 11 (1992) 179-202.
42. H.C. Tijms, Stochastic Models: An Algorithmic Approach (Wiley, New York, 1994).
43. H.C. Tijms, Computational methods in queueing, in: Frontiers in Queueing, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997) chapter 12.
44. r/M/c queues, J. Statist. Plann. Inference 69 (1998) 65-79.
45. R.W. Wolf, Problems of statistical inference for birth and death queueing models, Oper. Res. 13 (1965) 343-357.
46. R. Yang and J.O. Berger, A catalog of noninformative priors, ISDS Discussion Paper 97-42.