Transient flows in queueing systems via closure approximations

The authors present a method for obtaining approximations to the distribution of flow times of customers in arbitrary queueing systems. They first propose approximations for uni-variate and multi-variate distributions of non-negative random variables. Then using a closure approximation, the authors show that the distribution of flow time can be calculated recursively. Computational results for the single server, multi-server and tandem queues are encouraging, with less than 5% average error in the mean flow time in most cases. The average error in the variance of flow times is found to be less than 10% for the more regular distributions.