Approximate Analysis of a Closed Fork/]oin Model

An approximation algorithm for analyzing a closed queueing systems with a K-sibling fork/join queue is presented. The procedure is based on decomposition and aggregation. The approximation procedure gives good results for the mean response time and the system throughput. However, it gives results which are an upper bound of the mean response time of the fork/ join operation and a lower bound of the system throughput, for both homogeneous and non-homogeneous cases. A modification of this procedure, applicable only to the homogeneous case, is also presented. This procedure was found to give very good results for the system throughput and the mean response time of the fork/join operation (the relative error is less than 3%).