Deducing queueing from transactional data: the queue inference engine, revisited

R. Larson (1990) proposed a method to statistically infer the expected transient queue length during a busy period with Poisson arrival in O(n⁵) solely from the n starting and stopping times of each customer´s service during the busy period. Here, the authors develop a novel O(n³ ) algorithm which uses those data to deduce transient queue lengths as well as the waiting times of each customer in the busy period. In a manner analogous to the Kalman filter, they also develop an O(n) online algorithm to dynamically update the current estimates for queue lengths after each departure. Moreover, they generalize their algorithms for the case of a time-varying Poisson process and also for the case of i.i.d. interarrival times with an arbitrary distribution. Computational results that exhibit the speed and accuracy of these algorithms are reported