Sojourn Time Estimation in an M/G/∞ Queue with Partial Information

Abstract

We propose an estimator for the cumulative distribution functionGof the sojourn time in a steady-state M/G/∞ queueing system, when the available data consists of the arrival and departure epochs alone, without knowing which arrival corresponds to which departure. The estimator generalizes an estimator proposed in Brown (1970), and is based on a functional relationship betweenGand the distribution function of the time between a departure and therth latest arrival preceding it. The estimator is shown to outperform Brown's estimator, especially when the system is heavily loaded.

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