NON-PARAMETRIC ESTIMATION FOR THE M/G/infinity QUEUE

N. H. BINGHAM1 AND SUSAN M. PITTS2

1 Department of Mathematics and Statistics, Birkbeck College, University of London,
Malet Street, London, WC1E 7HX, U.K.
2 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge,
16 Mill Lane, Cambridge, CB2 1SB, U.K.

(Received November 7, 1996; revised October 17, 1997)

Abstract.    Given an M/G/infinity queue with input rate lambda and service-time distribution G, we consider the problem of estimating lambda 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).

Key words and phrases:    Infinite-server queue, infinite-dimensional delta- method, empirical process, Little's formula, Reynolds' formula.

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