Large sample Bayesian analysis for Geo / G / 1 discrete-time queueing models

Annals of Statistics

Volumn 27, Issue 6, 1999, Pages 1785-1807

  Conti, Pier Luigi ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Asymptotics; Bernstein von Mises theorem; Consistency; Queues; Teletraffic

Indexed keywords

EID: 0033234637     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1017939239     Document Type: Article

References (26)

1. ARMERO, C. (1985). Bayesian analysis of M/M/1/∞/FIFO queues. In Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 613-618. North-Holland, Amsterdam.
2. ARMERO, C. (1994). Bayesian Inference in Markovian queues. Queueing Systems 15 419-426.
3. ARMERO, C. and BAYARRI, M. J. (1994). Bayesian prediction in M/M/1 queues. Queueing Systems 15 401-417.
4. ARMERO, C. and BAYARRI, M. J. (1996). Bayesian questions and answers in queues. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 3-23. North-Holland, Amsterdam.
5. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
6. BRUNEEL, H. and KIM, B. G. (1993). Discrete-Time Models for Communications Systems Including ATM. Kluwer, Boston.
7. CIFARELLI, D. M. and REGAZZINI, E. (1990). Distribution functions of means of a Dirichlet process. Ann. Statist. 18 429-442.
8. CONTI, P. L. (1997). Some statistical problem for Geo/G/1 discrete-time queueing models. Technical Report A 26, Univ. Roma "La Sapienza," Dipartimento di Statistica, Probabilità e Statistiche Applicate.
9. Cox, D. (1993). An analysis of Bayesian inference for nonparametric regression. Ann. Statist. 21 903-923.
10. DIACONIS, P. and FREEDMAN, D. A. (1997). On the Bernstein-von Mises theorem with infinite-dimensional parameter. Technical Report 492, Dept. Statistics, Univ. California, Berkeley.
11. FRASER, D. A. S. and MCDUNNOUGH, P. (1984). Further remarks on asymptotic normality of likelihood and conditional analysis. Canad. Statist. 12 183-190.
12. FREEDMAN, D. A. (1963). On the behavior of Bayes' estimates in the discrete case. Ann. Math. Statist. 34 1386-1403.
13. GAVER, D. P. and JACOBS, P. A. (1988). Nonparametric estimation of the probability of a long delay in the M/G/1 queue. J. Ray. Statist. Soc. Ser. B 50 392-401.
14. GHOSAL, S., GHOSH, J. K. and RAMAMOORTHI, R. V. (1997). Consistency issues in Bayesian nonparametrics. Unpublished manuscript.
15. GNETTI, A. S. (1997). Characterizations and measurements of teletraffic generated by IP protocol on ATM networks. M.S. thesis, Università di Roma "La Sapienza," Facoltà di Ingegneria (in Italian).
16. GRAVEY, A., LOUVION, J. R. and BOYER, P. (1990). On the Geo/D/1 and Geo/D/n queues. Performance Evaluation 11 117-125.
17. GRÜBEL, R. (1989). Stochastic models as functionals: some remarks on the renewal case. J. Appl. Probab. 26 296-303.
18. GRÜBEL, R. and PITTS, S. M. (1992). A functional approach to the stationary waiting time and idle time period distributions of the GI/G/1 queue. Ann. Probab. 20 1754-1778.
19. GRÜBEL, R. and PITTS, S. M. (1993). Nonparametric estimation in renewal theory I: the empirical renewal function. Ann. Statistic. 21 1431-1451.
20. Lo, A. Y. (1983). Weak convergence for Dirichlet process. Sankhyā Ser. A 45 105-111.
21. LOUVION, J. R., BOYER, P. and GRAVEY, A. (1988). A discrete-time single server queue with Bernoulli arrivals and constant service time. In Proceedings of the 12th International Teletraffic Conference (ITC 12), Turin.
22. MCGRATH, M. F. and SINGPURAWALLA, N. D. (1987). A subjective Bayesian approach to the theory of queues II: J. R. Louvion, inference and information. Queueing Systems 1 335-353.
23. PITTS, S. M. (1994). Nonparametric estimation of the stationary waiting time distribution function for the GI/G/1 queue. Ann. Statist. 22 1428-1446.
24. ROBERTS, J., MOCCI, U. and VIRTAMO, J. (1996). Broadband Network Teletraffic. Springer, Berlin.
25. SCHERVISH, M. J. (1995). Theory of Statistics. Springer, New York.
26. WASSERMAN, L. (1998). Asymptotic properties of nonparametric Bayesian properties. Technical Report 2/98, Dept. Statistics, Carnegie Mellon Univ.