Statistical Inference Of Minimum Waiting Time In Queuing Model

In daily life,there are always many tangible or intangible queuing phenomena,such as queuing at the train station to buy tickets,or waiting for a taxi online.Queuing theory is a discipline based on probability theory and stochastic processes.It is created to solve the queuing problem.The knowledge of queuing theory can solve the queuing problem in daily life.Therefore,it plays a very important role in many fields,Such as hospitals,Banks,supermarkets,transportation systems,communications systems,etc.In the traditional queuing system,customers can only wait for services in one queue,which is only the difference between single service desk and multiple service desk.But in real life,if different queues provide the same type of service,people often queue multiple queues at the same time,thereby reducing their waiting time.This article aims at this situation,and analyzes the changes of customer waiting time and sojourn time when two GI/M/1 queuing models are queuing at the same time.The specific research content is as follows.(1)Based on the distribution function of waiting time and sojourn time of a single GI/M/1 queuing model,this paper derives the distribution function and mathematical expectation of customer waiting time and sojourn time when two independent GI/M/1queuing models are queued simultaneously.Later,this article simulated two independent GI/M/1 queuing models at the same time according to Monte Carlo ideas.By analyzing the simulation results,it is found that the simulation results are consistent with the theoretical values,and two independent GI/M/1 queuing models queuing at the same time will greatly reduce customer waiting time and sojourn time.(2)In this paper,we consider the case that two queues are dependent on each other.In this case,we introduce the Copula function to analyze the relationship between minimum distribution of wait time for two queues simultaneously and the Copula function.In response to this situation,this paper considers taxis as passengers,and obtains data of taxis waiting time for passengers at Jinan Railway Station.By fitting the binary Copula function,the Copula function with the best fitting effect is selected.And then based on therelationship between the Copula function and minimum distribution of wait time for two queues simultaneously,simulate data that meets the minimum distribution function for analysis.It is found that waiting for two queues at the same time can still reduce the waiting time,but the reduced wait time is not much.After that,this article analyzes the reasons for the difficulty of taking a taxi in Jinan Railway Station and proposes the optimization measures based on local conditions.Finally,this paper compares and analyzes the two independent queues with related ones,and finds that two independent queues queuing at the same time can reduce the waiting time more.