The convex optimization method and its applications to queueing systems

Theoretically, for a strictly convex problem, there is a unique global solution; practically, when put in the right form, convex optimization can be globally solved by fast polynomial time algorithms. Therefore, intractable optimization problems of performance measures of queueing systems can be solved. Based on queueing theory, a nonlinear load optimal allocation model is proposed in this paper. A novel transformation of the optimization variables is also devised and the constraints are combined so as to make this model into a convex one. The interior-point method for convex optimization is presented here as a computationally efficient tool. Finally, this model is evaluated on a real example. The interior-point method needs fewer iterations with significant computational savings. Other performance measures of queueing systems can also be optimized in the similar way.