Research on Railway Passenger Transfer Selection Model Based on Generalized Cost

From the perspective of passenger demand, according to the characteristics of different types of passengers, based on the generalized cost optimization, a passenger transfer selection model is constructed. According to the actual needs of passengers during the transfer process, the definition and calculation method of the generalized cost of passenger transportation products in the model of economy, fastness, comfort, convenience and reliability are proposed, and the critical value of passenger transfer time is studied. Finally, the calculation is carried out by taking the passengers transferred from Harbin to Changsha at the Beijing as the research object. The results show that the calculation results of this model can meet the transfer needs of different types of passengers.


INTRODUCTION
At present, 12306 can provide passengers with transfer plans, but only complete the displacement of passenger space. With the rapid development of the national economy, service characteristics such as economy, speed, comfort, convenience, and reliability have become the focus of people's attention and have formed a huge market demand. Based on this, domestic scholars consider time, cost, and comfort to construct relevant mathematical models [1,2]. This type of model ignores some practical factors and cannot fully meet the passengers' travel needs. This paper considers the effects of transfer connection time, train arrival and departure times, train delays and service levels on passenger transfers, and establishes a mathematical model to define the critical value of the transfer time to provide passengers with good transfer program.

ANALYSIS OF THE TRANSFER PROCESS IN PASSENGERS
In this paper, the number of transfers on the passenger journey is 1, for the convenience of research, there are the following definitions: When a passenger chooses train to realize a full transfer, the train on the first journey is the transfer train, and the train on the second journey is the continuous train. The arrival station of the transfer train is the transfer station, and the departure station of the continuous train is the continuous station.  Figure 1. Passenger transfer process The passenger transfer process is shown in Fig.1. It is a decision-making process that takes into account the constraints of travel purpose, transportation service quality, and travel life needs. This paper aims at the decision-making process of railway transportation products in passenger selection, and solves the problem of passengers selecting trains in the first and the second journeys.

Influencing factors of passenger travel behavior
Passenger travel behavior is affected by subjective and objective factors. Subjective factors refer to the passenger's own characteristics, which determine the passenger's consumption characteristics and concepts. Objective factors refer to the economy, speed, comfort, convenience, reliability. According to passengers' consumption concept, passengers are classified into three categories: high, medium and low consumption. High-consumption passengers pay more attention to the speed and comfort of travel. Medium-consumption passengers have higher requirements for comfort and convenience. Lowconsumption passengers are more sensitive to economy. The consumption concept of passengers and the characteristics of railway transportation products have a great influence on travel behavior.

Construction of passenger transfer selection model
According to the theory of economic management, generalized cost refer to the total outflow of all economic benefits incurred by an enterprise due to production and operation activities and other activities. The generalized cost of passenger travel refers to the monetary value that is finally expressed by economy, speed, comfort, convenience and reliability through a certain conversion relationship. The calculation formula is: 5 C refer to the generalized cost of economy, speed, comfort, convenience and reliability. Different types of passengers have different degrees of sensitivity to economy, speed, comfort, convenience and reliability. Therefore, the parameter β is introduced to modify the generalized cost of travel, and a passenger transfer selection model based on generalized cost is obtained: Where n is the number of sections of the transfer plan, which is 2 in this study. j is the j train that passengers take. L is the initial set of passenger transfer plan. k i  is the sensitivity of the k passenger to the i influencing factor, namely the weight. ji C is the generalized cost of the i influencing factor of passengers taking the j train.

Parameter calibration of generalized cost (1) Economy
The generalized cost of economy refers to the fare, and the calculation formula is: Where E is fare,  is discount factor, and when the passenger is a student and chooses to travel by high-speed rail, it is 0.75, when it is a regular-speed railway, it is 0.5, and the rest is 1.
(2) Speed Train running time is a measure of speed, and speed is converted into speed generalized cost through time value. The opportunity cost method calculates the time value of passengers, the calculation formula is [1]: Where Y is the average annual salary of passengers, V is the time value. The formula for calculating the rapid generalized cost is: Where t is the train running time.
(3) Comfort Based on fatigue recovery time, this paper considers the effect of service level on passenger's psychological comfort. The service level is positively related to the fare [8], and negatively related to the generalized cost of comfort. The formula for calculating the generalized cost of comfort is: Where  is the correlation coefficient between service level and fare, take 8% [8]. g(t) is the fatigue recovery time of passengers, the calculation formula is [2]: Convenience includes the convenience of train arrival and departure and the convenience of transfer connection. The convenience of train arrival and departure time is inversely related to the time interval between the ideal and actual arrival and departure time of the train [1], and the convenience of transfer connection is indicated by the transfer time. The formula for calculating the generalized cost of convenience is: Where h t is transfer time. c t is the absolute value of the difference between the ideal and actual departure time of the train. d t is the absolute value of the difference between the ideal and actual arrival time of the train.
Literature [3] research shows that the ideal departure time for passengers is 7 o'clock, 11 o'clock, 16 o'clock, and 21 o'clock. For the convenience of research, it may be considered that the ideal arrival time is also the above four points. Reliability refers to the impact of train delays on passenger transfers. The late arrival of the transfer train is likely to cause passengers to fail to transfer. This paper expresses the reliability by the delay time of transfer train. The formula for calculating the generalized cost of reliability is: Where w t is the delay time of transfer train.  is the influence coefficient of train delay on passenger transfer.
 can be calculated by the following formula: The delay time can be calculated with the probability density function of train delay. Normally, the probability density function of train delay follows a single parameter negative exponential distribution [4]: The above formula shows that, regardless of the impact of major natural disasters, the train delay time does not exceed the transfer time. Calculating the mathematical expectation of the probability density function ( ) z w f t corresponding to the random variable w t within this range as the reference value of the train delay time: The solution is: Therefore, the formula for calculating the generalized cost of reliability is:

EXAMPLES
Take the passengers who transfer from Harbin to Changsha in Beijing as the research object. There are a total of 17 trains from Harbin to Beijing. The final stations are Beijing Railway Station and Beijing South Railway Station. There are 34 trains from Beijing to Changsha.

Weight calculation
Literature [7] research shows that the income of passengers on the Beijing-Shanghai line is mostly distributed between 5001-10000 yuan, 3001-5000 yuan and 3000 yuan, accounting for 34.67%, 35.81% and 18.29% respectively. This income range is used as the basis for dividing high, medium and lowconsumption passengers. The travel preference scores of different types of passengers are obtained through questionnaire surveys and used as the original data for model weight calculation, as shown in Fig.3: The weight is calculated by the improved analytic hierarchy process [6], and the results are shown in Tab.3:  (2) to (9), the optimal transfer plan for passengers is calculated as shown in Tab.5: It is known from the calculation results that the transfer train for high and medium-consumption passengers is Z18, the continuous train is G79, the transfer train for low-consumption passengers is Z18, and the continuous train is K967. Z18 is the evening train, which has high convenience, economy and comfort, and meets the travel needs of various passengers. G79 has fast running speed, high convenience, high reliability and comfort, and is suitable for high and medium-consumption passengers. The running time of K967 is longer, but the fare is relatively low, which matches the consumption capacity and philosophy of low-consumption passengers. In summary, the passenger transfer selection model can meet the transfer needs of different types of passengers.

CONCLUSION
From the perspective of passenger demand, the passenger transfer selection model is constructed based on the generalized cost optimization, and the calculation method of the generalized cost of passenger transportation products in the process of passenger transfer is studied. According to different transfer modes, the critical value of transfer time is studied to solve the problem of train selection for passenger transfer. Finally, a case study of passengers who transfer from Harbin to Changsha in Beijing shows that the passenger transfer selection model considers more comprehensive factors and the research results are more reliable, which can meet the transfer needs of different types of passengers and provide technical support for the decision-making of the transportation department.