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

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Abstract

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).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Birkbeck College, University of London, Malet Street, London, WC1E 7HX, U.K.

    N. H. Bingham

  2. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, U.K.

    Susan M. Pitts

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  1. N. H. Bingham
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  2. Susan M. Pitts
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Bingham, N.H., Pitts, S.M. Non-parametric Estimation for the M/G/∞ Queue. Annals of the Institute of Statistical Mathematics 51, 71–97 (1999). https://doi.org/10.1023/A:1003831118254

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