Optimization schemes for queueing networks with applications to flexible manufacturing systems.

Abstract

Product-form queueing networks have been useful for modeling complex systems such as flexible manufacturing systems and computer systems. While the literature is rich with queueing models, little attention has been paid to the use of these models in optimization schemes. This dissertation addresses the optimal design of complex systems in conjunction with closed queueing network theory. The overall plan is as follows: Product-form queueing network models are used to evaluate system "performance measures" for a given setting of system "decision parameters". The performance measures are useful in the computation of system cost functions and/or their sensitivities with respect to decision parameters. Optimization algorithms are applied in order to find the set of decision parameter values which optimize performance measures and/or minimize the cost of the system. Typical performance measures are the throughput (production rate) and average queue lengths at individual nodes of the system. Sensitivities of performance measures with respect to the decision parameters are derived in closed-form. These sensitivities are used to study the concavity (convexity) properties of performance measures. Both the concavity properties and the sensitivities of performance measures are then utilized in the formulation and solution procedures of the optimization models. Decision variables for the design and operation of queueing systems include service rates, routing of jobs, number of servers, and level of work-in-process. Models with a single decision variable type, such as service rates, are considered first. Hybrid models which include several types of decision variables such as service rates and work-in-process levels are then addressed. Constraints include meeting production goals, capital budgeting, and bounds on decision variables. The optimization models are discussed and solved to optimality. Numerical examples are provided and results are analysed.