Queuing System Modeling And Analysis Based On Change Point Test ——Taxi At Jinan Railway Station As An Example

In recent years,with the improvement of people's income level and the acceleration of work rhythm,passengers' standards and requirements for travel have also been relatively improved.People's expenditure on transportation is increasing."comfort" in the process of travel has become an important factor for passengers to consider,and fast and convenient high-speed railways have undoubtedly become many people the first choice of transportation for passengers.The flow of people at the railway station has increased significantly,and passengers waiting in line at the railway station are often congested.Most passengers arriving at the railway station will choose to take a taxi to leave.The number of taxis providing services is obviously insufficient,resulting in an increasingly obvious contradiction between the supply and demand of passengers and taxis.There are many reasons for the shortage of taxis.First of all,the passenger flow at the railway station has increased,and secondly,the passenger arrival rate is different,and the number of passengers at different times has changed greatly,which leads to the unstable demand of passengers for taxis,which is also the reason for the contradiction between passengers and the supply and demand of taxis.The number of passengers arriving at the railway station may vary greatly due to time.The number of passengers arriving is likely to exceed the capacity of taxis.If the number of taxis is insufficient at this time,the waiting time of passengers will exceed the maximum tolerance.However,when the number of passengers arrives at a certain time,excessive taxis may also cause unreasonable use of public resources.Therefore,it is very important to scientifically and effectively monitor the queuing situation and reasonably allocate public service resources.The classic queuing system assumes that the customer's arrival rate is stable,and divides the queuing system into n segments for processing,ignoring the randomness of the customer's arrival rate.In this paper,the control chart method based on variable point detection is applied to the queuing system,which is different from other variable point detection methods.The advantage of this method is that it can detect the change of arrival rate in real time,and then make statistical estimates of the arrival rate.Therefore,for the queuing model in real life,the variable point detection dynamic queuing model based on the control graph can find the changes in the customer arrival law in time,which is conducive to changing the service desk configuration in time when the customer arrival rate changes,and allocate limited resources more reasonably.In addition,in previous queuing theory studies,only the statistical nature of the system itself and the main indicators were considered,and the behavior of customers was not considered.However,in practice,customer behavior will also affect the performance of the queuing service system.With the development of queuing theory,based on game theory,the field of queuing economics has developed rapidly.Therefore,with the help of game theory,this article analyzes whether passengers enter the queuing system,makes decisions on whether passengers enter the queuing system,reduces passenger losses,and increases the overall benefits of society.This paper mainly includes the following aspects of queuing system modeling based on variable point detection: 1.The basic theoretical method for detecting the change points of the queuing system is introduced,and the real-time change of the queuing model is considered.2.The arrival rate in the queuing system is detected by the control chart method,and the position of the variable point is obtained.Based on the step-by-step stabilization method,the queuing performance index is calculated according to the classic queuing theory.3.Combining queuing theory with game theory,the decision-making behavior of passengers in the queuing system is analyzed to solve the optimal decision-making of passengers and the optimal social benefits.4.Collect the data of passengers and taxis at Jinan Railway Station and apply the actual problems to the model built.Based on the above content,the results of simulation and empirical analysis show that the queuing system model based on variable point detection can timely find the variable points of the queuing system,issue alarms,and provide decision-making basis for decision makers,so as to reasonably arrange the service desk and save public resources.At the same time,the game decision-making model provides passengers with the best decision to enter the queuing system and increases social benefits to a certain extent.