R. Larson proposed a method to statistically infer the expected transient queue length during a busy period in O(n5) solely from the n starting and stopping times of each customer’s service during the busy period and assuming the arrival distribution is Poisson. The authors develop a new O(n3) algorithm which uses these data to deduce transient queue lengths as well as the waiting times of each customer in the busy period. They also develop an O(n) on-line algorithm to dynamically update the current estimates for queue lengths after each departure. Moreover, the authors generalize the present 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. They report computational results that exhibit the speed and accuracy of the algorithms.
