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

We propose an estimator for the CDF G of 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 is a generalization of an estimator proposed by Brown (1970), and is based on a functional relationship between G and the distribution of the time between a departure and the rth latest arrival preceding it. The estimator is shown to outperform Brown’s estimator, especially when the system is heavily loaded.