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

N. H. BINGHAM^{1} AND SUSAN M. PITTS^{2}

1Department of Mathematics and Statistics, Birkbeck College, University of London,

Malet Street, London, WC1E 7HX, U.K.

2Department 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/∞ 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 = (Q_{t}). 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 deltamethod, empirical process, Little’s formula, Reynolds’ formula.