An Analytic Congestion Model for Closed Production Systems with IFR Processing Times

We present an analytic model relating the mean cycle time or throughput as a function of the number of jobs in a closed production system composed of a tandem network of queues having exponential and/or IFR processing times. This model exhibits macroscopic behavior that is predicted by results from queueing theory and involves three meaningful parameters: the bottleneck rate and the "raw process" time that can be determined from first moment data; and a dimensionless congestion coefficient that is typically obtained from a single WIP/average cycle time observation (e.g., simulation). The derivation of the model is based on observations of the behavior of the relation between mean cycle time and WIP. This "engineering" approach is different from a purely "probabilistic" one in that we do not consider the distribution of processing times at individual station. We compare the accuracy of the model in predicting mean cycle times to other techniques such as mean value analysis and simulation.