Minimize Aggregate Measure of Waiting Times and Queue Lengths in M/M/1 queue

摘要

In mathematical optimization, the method of Lagrange multipliers is a strategy to find the local maxima and minima of a function subject to equality constraints. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied.The objective of this study is to displays a mathematical model that minimizes an aggregate measure of waiting times and queue lengths for a collection of arrivals by using Lagrange multiplayer. Ls(= Expected number of customers in the ith system,Ws,Lq,Wq decreased compared with the na?ve value of ?i. A computer program used to calculate optimal values.