Journal of Applied Probability

Matchmaking and testing for exponentiality in the M/G/∞ queue

Rudolf Grübel and Hendrik Wegener

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Customers arrive sequentially at times x1 < x2 < · · · < xn and stay for independent random times Z1, ..., Zn > 0. The Z-variables all have the same distribution Q. We are interested in situations where the data are incomplete in the sense that only the order statistics associated with the departure times xi + Zi are known, or that the only available information is the order in which the customers arrive and depart. In the former case we explore possibilities for the reconstruction of the correct matching of arrival and departure times. In the latter case we propose a test for exponentiality.

Article information

Source
J. Appl. Probab., Volume 48, Number 1 (2011), 131-144.

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1300198140

Digital Object Identifier
doi:10.1239/jap/1300198140

Mathematical Reviews number (MathSciNet)
MR2809891

Zentralblatt MATH identifier
1217.60081

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 62M07: Non-Markovian processes: hypothesis testing 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Asymptotics Kendall's tau log-concave density log-convex density queue prediction permutation

Citation

Grübel, Rudolf; Wegener, Hendrik. Matchmaking and testing for exponentiality in the M/G/∞ queue. J. Appl. Probab. 48 (2011), no. 1, 131--144. doi:10.1239/jap/1300198140. https://projecteuclid.org/euclid.jap/1300198140


Export citation

References

  • An, M. Y. (1998). Logconcavity versus logconvexity: a complete characterization. J. Econom. Theory 80, 350–369.
  • Asmussen, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.
  • Bagnoli, M. and Bergstrom, T. (2005). Log-concave probability and its applications. Econom. Theory 26, 445–469.
  • Bai, Z. and Hsing, T. (2005). The broken sample problem. Prob. Theory Relat. Fields 131, 528–552.
  • Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
  • Bäuerle, N. and Grübel, R. (2005). Multivariate counting processes: copulas and beyond. ASTIN Bull. 35, 379–408.
  • Billingsley, P. (1986). Probability and Measure, 2nd edn. John Wiley, New York.
  • Bingham, N. H. and Pitts, S. M. (1999). Non-parametric estimation for the M/G/$\infty$ queue. Ann. Inst. Statist. Math. 51, 71–97.
  • Buchmann, B. and Grübel, R. (2003). Decompounding: an estimation problem for Poisson random sums. Ann. Statist. 31, 1054–1074.
  • Chung, K. L. (1967). Markov Chains With Stationary Transition Probabilities. Springer, New York.
  • DeGroot, M. H. and Goel, P. K. (1980). Estimation of the correlation coefficient from a broken random sample. Ann. Statist. 8, 264–278.
  • DeGroot, M. H., Feder, P. L. and Goel, P. K. (1971). Matchmaking. Ann. Math. Statist. 42, 578–593.
  • Diaconis, P. (1988). Group Representations in Probability and Statistics (IMS Lecture Notes Monogr. Ser. 11). Institute of Mathematical Statistics, Hayward, CA.
  • Hall, P. and Park, J. (2004). Nonparametric inference about service time distribution from indirect measurements. J. R. Statist. Soc. B 66, 861–875.
  • Jungnickel, D. (1999). Graphs, Networks and Algorithms. Springer, Berlin.
  • Lehmann, E. L. (1959). Testing Statistical Hypotheses. John Wiley, New York.
  • Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, Chichester.
  • Takács, L. (1962). Introduction to the Theory of Queues. Oxford University Press, New York.