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

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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).