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As regards the ticket allotment issue of the intercity passenger corridor designed for different train grades, the matching relationship between the ticket allotment and the passenger flow demand is studied. The passenger flow conversion equation which is based on the collaborative optimization of the intercity train stop schedule plan and ticket allotment is established. Then the mathematical model aiming at the maximum revenue of intercity train system and the highest satisfaction from the passengers is established. The particle swarm harmony search algorithm is designed to solve the model. The example verifies the effectiveness of the model and algorithm, which indicates that, through the collaborative optimization of the stop schedule plan and ticket allotment for different grades intercity trains, the sectional utilization rate of the train can be improved; meanwhile, the optimum matching between the intercity train revenue and the passenger satisfaction can be realized.

Intercity train ticket allotment is the important content of railway revenue management, which, with the basis of the passenger travelling demand at all stations along the corridor and the comprehensive consideration on the influence of the operation plan of different grades intercity trains, aims at the optimum matching between sectional tickets and the passenger demand.

Revenue management [

In the traditional seat inventory control, the basic ticket plan in the train diagram phase [

The main mode of intercity railway is ordinary train and high-speed trains in parallel; based on this, the paper investigates the influence of the stop schedule plan and ticket allotment on the passenger flow demand from the perspective of the passenger behavior choice, establishes the passenger flow conversion equation to depict the dynamic relationship, and sets up a multiobjective model to collaboratively optimize the stop schedule plan and ticket allotment strategy so as to realize the optimum matching between the passenger flow demand and the system revenue.

Build an intercity passenger rail corridor as it is shown in Figure

Stop schedule plan of the intercity passenger rail corridor.

Suppose there are trains of two grades in the intercity passenger rail corridor. Take

In view of the two different stop schedule plans above, at first the passenger should consider if there is the direct train and ticket corresponding to its passenger flow type at the destination; if so, the passenger can make the choice accordingly. Take the high-speed passenger flow as an example to analyze the passenger behavior choice process when there is no direct train or no ticket corresponding to its own passenger flow type. As is shown in Figure

From the above analysis, the passenger’s choice of direct train depends on its own passenger flow type and sectional ticket allotment and the passenger’s choice of transfer scheme depends on the train ticket allotment at the transfer station. In the process of the passenger behavior choice, different stop schedule plans and ticket allotments will cause the ceaseless conversion of initial passenger flow and the dynamism of passenger flow which, in turn, will affect the stop schedule plan and ticket allotment. In this way, the linkage and collaboration between passenger flow demand and ticket allotment can be realized.

Assume that the station set of intercity passenger rail corridor is

Passengers give priority to the passenger train which is corresponding to their passenger flow type. If the direct arrival cannot be achieved, then the passengers will change the train grade or transfer. When there are multiple transfer stations, passengers will choose the transfer station which can maximize their travel utilities according to their passenger flow type. Passenger travel utility includes the discounted cost as per the passenger travel time and the train ticket cost. The calculation formula is shown as in

When plans of transfer and changing the train grade are both feasible, passengers will make a comparison according to the travel utility computational formula. When the transfer utility is greater than the utility of changing the train grade in the transfer station

For passengers between

When

When

When

When there is no transfer station

Relational graph of remaining passengers and remaining tickets at the transfer station.

Now, the remaining high-speed passengers between

When

When

When

When

When there is no transfer station

When there is a transfer station

When

When

When

Since intercity trains operating costs involve many aspects of vehicle operation and organization management, it is rather difficult to measure accurately; hence, this paper resolves the maximum revenue of intercity passenger rail corridor system into the maximum total passenger fares and minimum total train number, objectively describing the passengers satisfaction on travel with the minimum conversion of passenger flow demand.

Total passenger fares of Train

Maximum passenger fares of intercity trains are

The maximum section of passenger flow will be used to solve the number of Train

Stop and transfer of trains will affect the initial passenger flow. In order to quantitatively measure the passenger flow matrix change caused by the stop schedule plan, the Generalized Euclidean distance

To ensure the passengers can get on and off at all the stations, constraint will be set up to ensure at least one grade train to stop in each station:

Sectional ticket allotment will not exceed the train seating capacity:

This model is a complicated multiobjective model with the general objective function taken as

In order to improve the algorithm applicability, the particle swarm harmony search algorithm (

Harmony memory size is HMS; number of variables is

Initial solution

Construction of the initial particle.

Check constraint conditions as per formulas (

Take

Distribute passenger flow as per formulas (

Particle formula is updated as

The sigmiod function is used to change the trend of inertia weight

Inertia weight decreasing formula is

The first HMS optimal solutions of particle swarm algorithm from Step

Find out the best particle

Find out the adaptive bw and PAR according to the current iteration:

(1) From 1 dimension to

Using this formula, find out the current solution, record it as

(2) Compare

Determine whether the number of iterations reaches the maximum; if so, stop the iteration and output optimal solutions; otherwise, repeat Steps

The intercity passenger rail corridor as shown in Figure

throughput capacity: 50 trains/round-the-clock,

travel time value:

transfer time:

ticket fare = distance

basic parameters of train operation which are shown in Table

the matrix of the initial passenger flow:

Basic parameters of train operation.

Type | High-speed | Ordinary-speed |
---|---|---|

Average travel speed (km/h) | 250 | 120 |

Train seating capacity (people) | 610 | 1114 |

Fare rate (yuan/km) | 0.49 | 0.24 |

Station dwell time |
2 | 4 |

Stops and mileage chart of railway passenger transport corridor.

The example demonstrates that collaborative optimization of the stop schedule plan and ticket allotment of intercity trains of two grades can improve the sectional utilization rate of the train; thus, the vehicle operation costs can be reduced, and the revenue of inter-city railway system can be improved. The effectiveness of the proposed model and algorithm is verified; meanwhile, although the passenger flow conversion caused by the collaborative optimization scheme may reduce the passenger travelling satisfaction, the matching relationship between the revenue of the railway system and the passenger travelling satisfaction can be adjusted by setting the weight parameters between them.

Train grade of intercity passenger rail corridor, stop schedule plan, and ticket allotment constitute the three elements of the passenger travelling behavior choice. This paper depicts the influence mechanism of the collaborative optimization of the stop schedule plan and ticket allotment on passenger flow conversion in the intercity passenger rail corridor with trains of different grades, based on which, a passenger flow conversion equation is set up and a multiobjective model considering the revenue of the intercity railway system and the passenger travel satisfaction is built up. The model is solved by the particle swarm harmony search algorithm. This updated algorithm sets up a new comparative rule and improves the occurrence probability of the best solution.

The example verifies the effectiveness of the model and algorithm, and it proves that the collaborative optimization of the stop schedule plan and ticket allotment of trains of different grades can improve the sectional utilization rate of the train, increase the revenue of intercity railway system, and realize the optimum matching between system revenue and passenger travelling satisfaction.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is partly supported by the National Social Science Fund (14XGL011) and Natural Science Fund (1506RJZA062) of Gansu Province, China.