Deducing Queueing from Transactional Data: The Queue Inference Engine, Revisited

R. Larson proposed a method to statistically infer the expected transient queue length during a busy period in On⁵ solely from the n starting and stopping times of each customer's service during the busy period and assuming the arrival distribution is Poisson. We develop a new On³ algorithm which uses these data to deduce transient queue lengths as well as the waiting times of each customer in the busy period. We also develop an On on-line algorithm to dynamically update the current estimates for queue lengths after each departure. Moreover, we generalize our 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. We report computational results that exhibit the speed and accuracy of our algorithms.