Finite closed queueing networks with multiple servers and multiple chains
In this dissertation, closed queueing networks with limited capacities are studied. Systems with the service centers have exponential service times, first-come-first-served queueing discipline and blocked after service mechanism are considered. The properties and the behaviors of such networks are analyzed, and algorithms are proposed to be used for performance evaluation.
First, finite cyclic queues, which are a special form of closed networks, are studied. A new property of finite cyclic queues, defined as the customer threshold property (CTP), is identified. Using this property, the throughput of these queues are shown to be insensitive to the allocation of buffers and the order of the stations.
Further, an algorithm is developed for single class closed queueing networks with configurations likely to occur in real-world manufacturing systems, i.e. split-merge topologies and stations with multiple servers. The proposed method is an approximate Mean Value Analysis (MVA) which uses insights from the Expansion Method, and thus, regarded as the Expanded Mean Value Analysis (EMVA). The approach has been tested by several numerical experiments to evaluate its robustness under different conditions. The algorithm is shown to be accurate, efficient and very consistent with balanced and unbalanced service rates, the number of customers in the system and the system size.
An optimal buffer allocation procedure for closed queueing networks with finite buffers is also presented. The performance measures are evaluated using the Expanded Mean Value Analysis, and the solution is incorporated into nonlinear optimization scheme to arrive at the sub-optimal buffer space vector. The effectiveness of the method is demonstrated through several numerical experiments.
Finally, closed queueing networks with multiple customer classes are studied. An approximate MVA algorithm is developed for the performance analysis of these systems. The effects of limited capacities on the performance of the system are also investigated.