Application of Convex Optimization to Queuing Systems

On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so as to make this model convex. The interior-point method for convex optimization is presented as an efficient computational tool. Finally, this model is evaluated by a real example,from which the following conclusions are drawn： the optimum result can ensure the full utilization of machines and the smallest amount of WIP （work-in-progress） in queuing systems; the interior-point method needs a few iterations with significant computational savings; other performance measures of queuing systems can also be optimized in a similar way.     

Application of PI Control Algorithm to Discrete Manufacturing Systems

PI （proportional-integral） control algorithm is applied to control WlP （work-in-progress） in a discrete manufacturing system, where the cascade control of PI controllers is presented. It is in the frequency domain that the PI controller is designed with constraints on sensitivity options to ensure the stability and robustness of its parameters. A case is evaluated on a motorcycle engine crankcase production system, whose simulation results confirm that demand fluctuations can be compensated by PI controllers under a normal demand. PI controllers also possess low sensitivity to the distribution of production times.