Minimize aggregate measure of waiting times and queue lengths in M/G/1 queue

Abstract

The classic optimization techniques are helpful to find the optimum resolution or free maxima or minima of continuous and differentiable functions. The target of this study is to develop a replacement formula to solve the pedestrian congestion problem based on queuing theory and optimization that will lead to an efficient algorithm for pedestrian flow in optimizing allocation of pedestrian and service capacity subject to limited buffer space by show a mathematical model that minimizes an aggregate measure of waiting times and queue lengaths for a group of arrivals by using Lagrange multiplayer. Ls (expected variety of consumers within the i th system, Ws (expected time employment spends within the i th system), Lq(expected variety of consumers within the queue in the i th system),Wq(Expected time employment spends in the queue in the i th system) decreased compared with the naïve value of λi. A queuing model calculator used to calculate the optimal values.