Nonparametric inference from the M/G/1 workload

Bernoulli

Volumn 12, Issue 4, 2006, Pages 737-759

  Hansen, Martin B ^a   Pitts, Susan M ^b  

^a AALBORG UNIVERSITY   (Denmark)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Asymptotic normality; Empirical processes; Functional central limit theorem; Infinite dimensional delta method; M G 1 queue; Regenerative processes; Workload

Indexed keywords

EID: 33846180650     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1155735934     Document Type: Article

References (23)

1. Asmussen, S. (2003) Applied Probability and Queues (2nd edn). New York: Springer-Verlag.
2. Billingsley, P. (1968) Convergence of Probability Measures. New York: Wiley.
3. Bingham, N.H. and Pitts, S.M. (1999a) Nonparametric estimation for the M/ G/∞ queue. Ann. Inst. Statist. Math., 51, 71-97.
4. Bingham, N.H. and Pitts, S.M. (1999b) Nonparametric inference from M/G/1 busy periods. Comm. Statist. Stochastic Models, 15, 247-272.
5. Buchmann, B. and Grübel, R. (2003) Decompounding: An estimation problem for Poisson random sums. Ann. Statist., 31, 1054-1074.
6. Chiu, S.-T. (2000) Boundary adjusted density estimation and bandwidth selection. Statist. Sinica, 10, 1345-1367.
7. Feller, W. (1971) An Introduction to Probability Theory and Its Applications (2nd edn), Vol. II. New York: Wiley.
8. Gill, R. (1989) Non- and semi-parametric maximum likelihood estimators and the von Mises method (Part 1). Scand. J. Statist., 16, 97-128.
9. Groeneboom, P. (1989) Brownian motion with a parabolic drift and Airy functions. Probab. Theory Related Fields, 81, 79-109.
10. Grübel, R. and Pitts, S.M. (1993) Non-parametric estimation in renewal theory, I: The empirical renewal function. Ann. Statist., 21, 1431-1451.
11. Hall, P. and Park, J. (2004) Nonparametric inference about service time distribution from indirect measurements. J. Roy. Statist. Soc. Ser. B, 66, 861-875.
12. Hoffmann-Jørgensen, J. (1994a) Probability with a View Toward Statistics, Vol. I. New York: Chapman & Hall.
13. Hoffmann-Jørgensen, J. (1994b) Probability with a View Toward Statistics, Vol. II. New York: Chapman & Hall.
14. Levental, S. (1988) Uniform limit theorems for Harris recurrent Markov chains. Probab. Theory Related Fields, 80, 101-118.
15. Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bull., 12, 22-26.
16. Pollard, D. (1984) Convergence of Stochastic Processes. New York: Springer-Verlag.
17. Prakasa Rao, B. (1983) Nonparametric Functional Estimation. Orlando, FL: Academic Press.
18. Resnick, S. (1997) Heavy tail modeling and teletraffic data. Ann. Statist., 25, 1805-1869.
19. Sharma, V. (1999) Estimating traffic intensities at different nodes in networks via a probing stream. In GLOBECOM 1999: Seamless Interconnection for Universal Services, Vol. 1, pp. 374-380. Piscataway, NJ: IEEE Operations Center.
20. Sharma, V. and Mazumdar, R. (1998) Estimating traffic parameters in queueing systems with local information. Perform. Eval., 32, 217-230.
21. Tsai, T.H. (1998) The uniform CLT and LIL for Markov chains. PhD thesis, University of Wisconsin, Madison.
22. van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge: Cambridge University Press.
23. Wand, M.P. and Jones, M. (1995) Kernel Smoothing. London: Chapman & Hall.