Larson [1] proposed a method to statistically infer the expected transient queue length during a busy period in 0(n 5 ) 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 O(n3 ) algorithm which uses this data to deduce transient queue lengths as well as the waiting times of each customer in the busy period. We also develop an O(n) on line algorithm to dynamically update the current estimates for queue lengths after each departure. Moreover we generalize our algorithms for the case of time-varying Poisson process and also for the case of iid interarrival times with an arbitrary distribution. We report computational results that exhibit the speed and accuracy of our algorithms.