Simulation results on the performance of Albin and Whitt's estimation method for waiting times in integrated production–inventory systems

We investigate the estimation of the average and standard deviation of the waiting times in a multi-product, single-server ∑GI/G/1 queueing system. It is well known that in such a queueing system the aggregate arrival process at the server is autocorrelated, which complicates the estimation of waiting times. Albin and Whitt jointly developed an approximation method for the waiting times in ∑GI/G/1 queueing systems. In this paper, we consider a manufacturing context and apply the approximation method in an integrated multi-product single-machine production–inventory system. The estimates of Albin and Whitt's method are compared with the outcome of an extensive simulation study. It appears from our study that the approximation formulaes proposed by Albin and Whitt perform poorly in this specific context. Since Albin and Whitt's estimation method is an essential building block of many queueing network analysers, the use of these methods for performance evaluation and decision-making in integrated production–inventory systems may result in serious errors.