Simplification of des models of M/M/1 tandem queues by approximating WIP-dependent inter-departure times

This paper presents two algorithms to analytically approximate work in process (WIP)-dependent inter-departure times for tandem queues composed of a series of M/M/1 systems. The first algorithm is used for homogeneous tandem queues, the second for such with bottlenecks. Both algorithms are based on the possible combinations of distributing the WIP on the queues. For each combination the time to the next departure is estimated. A weighted average of all estimated times of each WIP level is calculated to get the expected mean inter-departure time. The generated inter-departure times are used in a simple model of the tandem queue. The inter-departure times, the average WIP and average cycle time of the tandem queue and the simple model are compared in several tandem queue parameterizations. Results show only a small error between the simple model and the tandem queue, rendering this approach applicable in many applications.