Annals of the Institute of Statistical Mathematics

, Volume 51, Issue 1, pp 71–97

Non-parametric Estimation for the M/G/∞ Queue

  • N. H. Bingham
  • Susan M. Pitts

DOI: 10.1023/A:1003831118254

Cite this article as:
Bingham, N.H. & Pitts, S.M. Annals of the Institute of Statistical Mathematics (1999) 51: 71. doi:10.1023/A:1003831118254


Given an M/G/∞ queue with input rate λ and service-time distribution G, we consider the problem of estimating λ and G from data on the queue-length process Q = (Qt). Our motivation is to study departures of G from exponentiality, following recent work of Bingham and Dunham (1997, Ann. Inst. Statist. Math., 49, 667–679).

Infinite-server queueinfinite-dimensional delta-methodempirical processLittle's formulaReynolds' formula

Copyright information

© The Institute of Statistical Mathematics 1999

Authors and Affiliations

  • N. H. Bingham
    • 1
  • Susan M. Pitts
    • 2
  1. 1.Department of Mathematics and Statistics, Birkbeck CollegeUniversity of LondonLondonU.K.
  2. 2.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeU.K.