Queue inference from periodic reporting data

We introduce new algorithms for queue inference problems involving periodic reporting data. We assume that in each of several consecutive time periods, new customer arrivals follow a Poisson process with period-specific arrival rates, but only the number of departing customers during each period is observed. Rather than exploiting relations with order statistics, our algorithms rely on direct recursions involving Poisson probabilities. We illustrate with several examples, some of which are not typically viewed as queueing applications.