Deducing Queue Statistics from Transactional Data
Author(s)Larson, Richard C., 1943-
The transactional data of a queueing system are the recorded times of service commencement and service completion for each customer served. With increasing use of computers to aid or even perform service one often has machine readable transactional data, but virtually no information about the queue itself. In this paper we propose a way to deduce the queueing behavior of Poisson arrival queueing systems from only the transactional data and the Poisson assumption. For each congestion period in which queues may form, the key quantities obtained are mean wait in queue, time-dependent mean number in queue, and probability distribution of the number in queue observed by a randomly arriving customer. The methodology builds on arguments of order statistics and usually requires a computer to evaluate a recursive function. The paper concludes with a proposed procedure for estimating the extent of balking and/or reneging present in a queueing system.
Revised May 1988
Massachusetts Institute of Technology, Operations Research Center
Operations Research Center Working Paper;OR 167-87