Queue decomposition & finite closed queueing network models

Closed, finite queueing networks are applicable to many different manufacturing and service system settings. The incorporation of material handling and transportation networks in finite buffer closed queueing networks is studied. A novel queue decomposition approach using state dependent queues to capture the buffer of finite M/M/1/K   queues is shown to be a viable approach for modelling these systems. Each M/M/1/KM/M/1/K queue is replaced with a coupled state dependent queue plus an M/M/1 queue. An extended mean value analysis (MVA) algorithm is employed to demonstrate the integration of the state dependent queues for the buffers in the approach. Under certain restrictions concerning the network population, finite queueing networks with the state dependent queues acting as buffers should have a product form distribution. This paper focuses on M/M/1/K queues and their transformation while future papers will treat the multi-server case. Several different closed series (i.e. cyclic), merge, and split topological systems of finite queues are analyzed and presented.