Optimal resource allocation in closed finite queueing networks with blocking after service
Research on the area of queueing networks has been extensive over the last decades. This is largely due to their ability to model many complex systems which are receiving growing attention such as flexible manufacturing systems, assembly lines, facility planning problems, computer and communication networks, transportation systems and so on. The focus of prior research has been on queueing networks with unrestricted storage or buffer capacities and queueing networks with restricted buffer capacities where external arrivals and departures are allowed, that is, open finite queueing networks. In contrast, the field of closed finite queueing networks, where no arrival to or departures from the system are allowed, has been relatively neglected due in part to their more difficult mathematical tractability. This dissertation represents a contribution to narrow this gap by concentrating on the important field of closed finite queueing networks and their optimization problems.
First, an efficient numerical approximation is developed to evaluate the performance measures of this type of network where blocking can occur after service. Secondly, the optimal resource allocation problem is addressed by combining mostly elements of queueing theory and nonlinear optimization.
The proposed approximation method is based on expanding and decomposing the closed network to account for the blocking phenomenon for which an adapted version of the Expansion Method is used in conjunction with a especially developed Equalization Phase and the well known Mean Value Analysis. This approximation is applicable to network topologies with tandem nodes or combinations of split and merge sequences that have exponential service times and one-server stations. The resulting numerical evaluations are computational efficient and render excellent results as compared to simulation results under a variety of testing conditions.
This method is then embedded in an optimization scheme to study the resource allocation problem with the objective of optimizing a nonlinear cost function that integrates system throughput, cycle time, and the number of buffer spaces in the network. The flexibility of this objective function provides for a potentially great number of applications. The emphasis here is however on manufacturing and communication systems.
The optimization procedure solves for the suboptimal buffer allocation at each node or station, and for the suboptimal number of customers or entities circulating in the closed queueing network. The solution to the buffer allocation problem is achieved via Powell's nonlinear unconstrained optimization, where necessary tests are provided to ensure deadlock-free solutions. Then, building upon this scheme, a search with backward and forward sweeps is applied to find the best setting for the number of customers. This problem is highly complex, since no known closed form expression exists for the objective function and because the problem is nonlinear and integral in nature. Discussions on the applicability, convergence, and computational analysis of the procedure are presented, as well as comparisons against pertinent simulation results.
0796: Operations research
0548: Mechanical engineering