Solving Semi-Open Queuing Networks

Semi-open queueing networks (SOQNs) are a special type of queueing network systems consisting of two parts: an inner network with a population constraint and external queues to accommodate jobs whose entrance is delayed. We first study such systems with single class jobs in tandem configuration. We then extend our study to multi-class configurations. Multi-class SOQNs fall into two categories: general pallet scenario and dedicated pallet scenario. For the general pallet case, we aggregate all classes and solve the resulting single class SOQN. For the dedicated pallet case, we construct a method based on Baynat and Dallery's product-form approximation method for multi-class general closed networks. Our approximation method combines the use of the matrix-geometric method and the decomposition-aggregation approach. Numerical results show our approximations have desirable accuracy and efficiency.