The Interior Point Method In Convex Optimization And Its Application On The Queuing Problem

The queuing theory is a branch of science,which is to study all kinds of queu-ing properties and study how to design and use a service system,which can not only meet the practical problem solved requirement,but also make the whole process cost less.If we explain the queuing theory by mathematics thoughts and methods,it can be come down to the operational research.The queuing problems exists in our life every-where.The key of solving the problem is how to optimize the main property indications in a queuing system,such as the load optimal allocation,the average waiting queue length of the customers,the average waiting time of the customers,the occupancy of the the buffer,a steady state probability and so on.But the objective functions of those optimization problems are all non-linear,so it is difficult for the usual optimiza-tion algorithm to get satisfactory results.This article mainly study how to turn the non-linear optimization problems of the main property indications in a queuing system into the convex optimization problems in the operational research.And it is solved by the mature and complete interior point method in the current theory of convex optimization.Now we mainly study the optimization problem of the average wait-ing queue length of the customers which is one of the main property indications in a queuing problem.Firstly we approximately look the primary problem as the geometric programming problem.Then we will turn it into the convex optimization problem by change of variables.At last we will start concretely designing the algorithm and analyzing the convergence by the interior point method in the theory of convex opti-mization.When we introduce the interior point method into the optimization problem of the main property indications in a queuing system,it turns out that it can fully show the strong points of the interior point algorithms,which has less iteration time and faster convergence rate,and by which the convergence result can meet the real need of the queuing system and it is normally productive to concretely improve the efficiency and the quality of service of the whole queuing system.