Decomposition and aggregation by class in closed queueing networks

摘要

A method is described whereby a multiple class closed network of first-come first-served (FCFS) queues can be analyzed exactly by a decomposition and aggregation procedure that proceeds class by class, rather than node by node. The preliminary step of the method is to transform the FCFS network into an equivalent network of processor sharing queues in which a hierarchy of subsystems associated with subsets of the classes may be identified. This decomposition and aggregation procedure reduces the problem of analyzing a multiple class queueing network into a hierarchy of single-class queueing network problems. A useful consequence of adopting this procedure is that a reduced system is constructed which contains one particular class of customers. A parametric analysis of this class, with respect to the routing, may then be made without having to repetitively analyze the entire multiple class queueing network. The time and space requirements of this parametric analysis technique are derived and compared to the requirements of a straightforward repetitive analysis of the network using the convolution algorithm. An example parametric analysis of a store-and-forward communication network model is given.