Research Article  Open Access
Method for Determining the Valid Travel Route of Railways Based on Generalised Cost under the Syncretic Railway Network
Abstract
Travel route options for passengers can provide data support for railway line planning, passenger flow organisation, and train operation establishment. A critical review of the literature indicates that previous studies mainly focused on choices offered by a single railway network path without much consideration of China’s normalspeed and highspeed integrated railway network and the effect of train timetable on passengers’ travel choice. In this study, a method based on generalised cost is proposed to discover the valid routes of passenger travel in the integrated network of China’s normalspeed and highspeed railways. After quantifying the effects of train fare, travel time, transfer, travel convenience, comfort, and other factors on the generalised expenses of passengers, this study presents a generalised cost determination method when individuals select an option from different seats of different trains of specific railway transport products. Theoretically, the valid routes considering the train schedule is defined, and a valid route search algorithm is designed using the deep traversal idea in a new valid route searching network. Considering the LanzhouBeijing passenger travel routes as an example, this study verifies the practicability of the generalised cost calculation method, as well as that of the valid routes search method.
1. Introduction
Highspeed railway, as a land transportation mode with high speed, large capacity, low energy consumption, and environmental protection, is setting off a wave of development all over the world. As the country with the longest operating mileage of normalspeed and highspeed railways worldwide, China’s normalspeed railway and highspeed railway operation mileages reached 132,000 and 30,000 kilometres, respectively, by the end of 2018 [1]. Therefore, railway networks formed by highspeed and normalspeed railways have begun to expand. Under this network condition, ways of making the passenger decisionmaking service more demandresponsive have stood under the spotlight. Therefore, as a base of the railway passenger decisionmaking service, it is essential to study the railway passenger path choice.
Scholars have studied passenger travel route selection, including the physical route selection of passengers and passenger trains. Based on the behaviour of passenger path selection, Xu et al. [2] proposed a method of random delay path selection of trains based on reliability and established a model of travel choice of road network passengers, considering heterogeneous passengers. van Loon et al. [3] studied the effect of travel time reliability on railway passenger travel and established six travel time reliability indexes for analysing the preference of passenger travel route selection. Lim et al. [4] analysed a postdisaster evacuation route selection using three binary logit route selection models. Two models were found to be useful in providing relevant suggestions on evacuation time, route, and destination for postdisaster route selection. Moghaddam et al. [5] investigated a travel purpose based on a simulated driver experiment. The travel time reliability and income were found to be important factors that affect the route selection of road traffic passengers.
For passengers who choose rail as their primary means of transport, the physical path only determines whether the passengers can get to their respective destination stations from the departure station. However, in the railway network, a physical route usually runs multiple trains with varying grades, speeds, and costs. Consequently, the travel path based on the physical network cannot reflect the transfer behaviour of longdistance passengers. Several scholars have studied the route selection of passengers in the case of train schedules. Shi et al. [6] proposed a traffictype assignment algorithm based on route choice by defining the transfer reliability using passengers’ expected reliability threshold to choose the lowest cost path. When calculating the passenger travel expenses, they found that the generalised cost function mainly depends on the cost of travel time, ticket prices, and discomfort. Dou et al. [7] built a railway passenger travel network based on a train timetable, taking the generalised cost function and remaining train capacity as the basis of passenger travel path search. They proposed an optimal path search algorithm for railway passenger transport network based on the residual train capacity. By analysing the main factors that affect the route choice behaviour of passengers, Yang et al. [8] established an optimisation model for optimising the route selection for railway passengers by minimising the total travel time, total price cost, transfer time, transfer distance, and fatigue recovery time.
Some studies of passenger travel paths also considered the train timetable. For example, by using the smart card data of an urban rail transit, Wu et al. [9] proposed a method considering the uncertainty of walking time and transfer time simultaneously and estimated the travel time of all possible travel paths from the origin to destination. More accurate studies of passenger path matching and passenger flow distribution have been carried out. Similarly, based on passenger travel data, Zhang et al. [10] proposed a set of novel methods for predicting the passenger travel path selection in urban rail transits. Furthermore, Xu et al. [11] investigated the route selection behaviour of urban rail transit passengers using ticket price, train schedule, and train passenger flow data by combining Bayesian reasoning and urban congestion sampling.
When the train timetable is used for selecting passengers’ travel routes, travel cost is usually the most critical factor in choosing a route, followed by ticket cost and time cost. Earnhart [12] chose channel cost, transportation cost, and time cost as the components of generalised cost in a constructed generalised cost model, and by detailed analyses, he concluded that time cost is the most crucial factor. De Borger and Fosgerau [13] divided the conversion methods of travel time and cost into four categories: willingness to pay (WTP), willingness to accept compensation (WTA), equivalent gain (EG), and equivalent loss (EL). Other researchers have further studied time cost. Deserpa [14] refined the concept of time cost and defined it in three kinds, namely, time cost as a resource, as a commodity, and time spent on an activity being less than a given time. Hess et al. [15] applied the hybrid logit algorithm to estimate the cost of saved travel time using the strategy of WTP and provided an estimation model with income and travel distance as independent variables for calculating the cost of saved travel time. Although many scholars have studied passenger travel behaviours, only a few studies considered the transfer, comfort, convenience, and other costs in the passenger travel process.
When considering travel costs in route selection, it is theoretically possible to use the exhaustive method of searching all the paths in the network to select the best path. However, the massive travel paths generated in either the railway network or urban traffic network will reduce the operating efficiency of this method. Therefore, many scholars proposed search algorithms for different paths in networks [16, 17]. Modesti and Sciomachen [18] proposed a multicriterion shortest path search method for urban traffic networks to minimise the total path cost. Samà et al. Sama et al. [19] studied the realtime train route choice problem in the railway system, where the core problem was converted into an integer linear programming problem and solved using the ant colony algorithm.
Most researchers have studied the passenger travel routes generation of normalspeed railway network and highspeed railway network separately, whereas the influence of the integration of the tworailway network is rarely taken into account. However, in the syncretic railway network, the possibilities for creating transfer between different lines have expanded, which makes it more difficult to calculate the generalised cost of passenger travel route. In this study, when searching the valid routes based on the train timetable, the adoption of ellipse method and angle method may increase the number of invalid nodes and missing valid partial routes. This study integrates the highspeed and normalspeed railway networks and then presents a detailed study of all the components (including fare, time, convenience, and comfort) of the generalised cost of efficient travel routes. Finally, considering the current train timetable, the generalised cost is used to design a searching algorithm for the effective transfer routes search based on the nodes of each direct route. A deep traversal search technique is applied to determine all the reasonable passenger travel routes.
The significant contributions of this study are as follows: (1) the calculation method of the generalised cost is proposed, including the calculation methods of comfort cost, convenience cost, and transfer cost, and (2) A method of passenger travel routes search between the OriginDestination (OD) considering the train schedule under the dualnetwork integration is proposed.
This paper is organised as follows. The calculation method of the generalised cost of railway passenger travel is discussed in Section 2. The valid routes search based on the generalised cost is analysed and discussed in Section 3, considering the actual train timetable. Section 4 presents a summary of the results and recommends suggestions for future research.
2. Generalised Cost Function
In this study, the generalised cost of each OD travel includes the following five parts: fare, time, convenience, transfer, and comfort values.
2.1. Fare
The passengers travelling fares between OD stations consists of three parts, namely, the travel cost from the origin to departure station, railway specific product cost, and cost taken from the terminal railway station to the destination, as presented in Figure 1 and equation (1):where is the total fare during the trip; is the fare of a particular train service; is the fare from origin O to departure railway station; is the fare from the terminal railway station to the destination D.
2.2. Travel Time Cost
Professionally, the passenger’s travel time cost is calculated by the production method, which is defined as the cost that can be created if the time expended by the passenger during the journey is spent on productive activities. The travel time that determines the corresponding cost [20] varies from passenger to passenger. The calculation formula of travel time value per unit is listed as follows:where refers to the gross national product and and are the average working hours and population, respectively.
The total travel time for passengers is the sum of the travel time from the origin to departure station, from the departure to the terminal station (including transfer), and from the terminal station to the destination:where is the time cost of passengers; is the travel time cost parameter; is the travel time from the origin to the departure station; is travel time between the tworailway stations; and is the travel time from the terminal station to the destination.
2.3. Convenience Cost
The travel convenience cost of passengers mainly deals with the issue of whether the departure and arrival times match the service time of the urban public transport system (bus or subway). If the departure or arrival time is within the operational range of the urban public transport, the time is considered to be relatively convenient, and the corresponding convenience cost is comparatively lower. Otherwise, the time will be considered inconvenient and increases the convenience cost.
The urban public transport operation time considering the remarkable volatility of passenger flow can be divided into peak hours and offpeak hours. Specifically, it is quite convenient to travel with a little cost during the nonpeak periods. However, the convenience cost increases rapidly during rush hours because of the massive passenger flow and traffic congestion.
To sum up, the convenience cost can be categorised as hours with no public transport service, peak hours, and offpeak hours, whose respective costs reduce gradually. For urban residents, set the convenience cost during offpeak hours as assuming the service period of the bus is equal to that of the urban rail transit. Consequently, the convenience cost of the passenger departure time for each period can be designed as follows:where and are the convenience cost coefficients of peak hours and the hours when no public transport is available, respectively.
During the travel, the convenience value of arrival is designed similar to that of departure. Thus, the total convenience value can be calculated as follows:
2.4. Transfer Cost
During the travelling process, the costs of the railway transfer value have three parts, namely, the transfer cost from the urban transportation to railway products, the internal transfer cost in the railway terminals, and the transfer cost from the railway products to urban traffic, as illustrated in Figure 2. The total transfer cost from the origin to destination can be formulated as follows:where is the cost of the transfer value from the urban traffic to railway departure stations; is the transfer cost generated in the railway network; is the transfer cost from railway arrival stations to urban traffic. The three indicators can be quantitatively calculated as follows.
2.5. Calculation of and
For passengers travelling by train, the transfer value between the urban traffic and railway service is principally determined by the transfer time. Hence, the value is the product of the transfer time and time value coefficient.(1)Transfer cost from urban traffic to railway is Here, is the total transfer time from the urban traffic to the railway station, which is mainly composed of the transfer travel time and the waiting time as follows: Here, is the walking time from the urban traffic platform to the railway station (or the waiting room at the railway station). is the average waiting time for connecting two different transportation systems.(2)Similarly, the transfer cost from the railway system to the urban traffic can be designed as follows:where is the total transfer time from the railway network to the urban traffic; is the walking time from the railway station platform to the urban traffic; and is the waiting time connecting the transfer.
2.6. Calculation of
An extended period may be taken to transfer from one train to another at the railway station due to transfer failure. This case is different from the transfer between the urban traffic and railway transportation. Therefore, the accommodation and transportation costs in the city where the transfer station is located should be considered.
Here, is the cost generated in the entire transfer process at the railway terminal (transfer taking place at the different stations in a city) or railway station (transfer taking place at the same station), is the transfer time between the arriving and departing trains, and is the accommodation cost in the city where the transfer node is located. The equation for calculating is expressed as follows:where is the cost of the accommodation and transportation supposing that the transfer is unsuccessful on the day in the node city.
The transfer time from the arrival train to the departure train is composed of the transfer walking time and transfer waiting time, that is,where is the travel time at the transfer station (city) and is the waiting time for the following train.
2.7. Comfort Cost
Along the journey, the comfort level depends typically on factors such as the train class, seat type, travel time, and travel conditions, among which the seat type and travel time are the top prioritised factors. For passengers travelling during the day at a short travel time, the comfort level of the firstclass seat (ZY) and secondclass seat (ZE) of the running trainset on the highspeed lines is usually more preferable to that of hard seat and hard sleeper. When highspeed railways undergo maintenance at night during 0 : 00–6 : 00 hours (the skylight period), travellers can only choose the normalrailway train services with only the hard seat (YZ), hard sleeper (YW), and soft berth (RW) being available. When considering the comfort value cost during travels, a more comfortable journey generates lower comfort cost. The comfort level order is RW, YW, and YZ. In this study, assuming the highest comfort score is 10 and defining the comfort value coefficient as constant A, the passenger comfort value can be determined by the following function:where is the comfort value of the seat type corresponding to the travel time. For the firstclass seats, secondclass seats, and hard seats, the comfort level is relatively acceptable within a specified time range. However, the comfort level will decline sharply when the travel time increases and exceeds a particular critical value. For hard and soft sleepers, the comfort level varies linearly with an increase in travel time.
Depending on whether the passengers can have a good rest during the journey, the seat types can be roughly divided into two categories. The seats, including ZY, ZE, and YZ, belong to one category, whereas the other category includes YW and RW. The passenger comfort value of the different seat types during various travel times can be obtained after processing the data from a questionnaire survey, as listed in Table 1.

In this study, the efficiency and convenience are directly measured by the price simultaneously. The time value cost, transfer value cost, and comfort value cost are quantified by the time cost together with the normalisation by time value coefficient. A unified dimension can be adopted for these five generalised costs. Therefore, the total generalised costs can be defined as follows:
For example, an individual travels through the LanzhouBeijing section. Assuming that the fare and travel cost from origin (O, home or office) to the railway station equals that of the railway station to destination (D, home or office), the fare is ¥20, and the travel time is 0.75 h. If the other parameters are set as follows: = ¥3, , , , A = 50, GDP = 90.0309 trillion, T = 8 h, P = 1.390 billion, then the generalised cost of all seat types on different trains in the syncretic railway network can be determined, as presented in Table 2.

As can be seen in Table 2, the generalised cost components of seat types of the normalspeed railway vary with those of the highspeed railway. The price of the normalspeed railway is much lower than that of the highspeed railway, and its time value cost is much higher than that of highspeed railway. In terms of comfort value cost, the transfer between normalspeed railway and highspeed railway is more friendly than that of the normalspeed railway or highspeed railway only. During the transferring process, the generalised cost is usually higher than that of the route travel.
3. Valid Route Search in the Syncretic Railway Network
3.1. Valid Route in the Syncretic Railway Network
The valid routes concept has been theoretically studied and obtained mature works [21], deriving from traffic allocation issues. Under the doublenetwork integration condition, the valid route is defined as follows. When travellers choose a railway travel product, the train number and different seats constitute the travel routes. Meanwhile, it is assumed that the route impedance e is within the period of shortest routes, namely, the valid route threshold , where is a nonnegative constant representing the route stretching coefficient. To determine the valid routes between specific ODs in the railway network, it is first required to find the shortest routes between the ODs, as well as all other possible routes. If the possible routes meet certain conditions, in practice, they can be regarded as valid routes.
In the valid route definition above, the value of the extension coefficient directly determines the number of valid routes. When , only a few routes based on the shortest routes can be found. The smaller the value of , the smaller the number of valid routes. With an increase in , the number of valid routes increases. In this study, the value of influences the operation mileage. The values of coefficient for different travel mileages are listed in Table 3.

3.2. Construction of Route Searching Network
When passengers choose railway products for travelling, they rely on operational railway lines and trains. Under the fixed conditions of line facilities, the train operation charts directly guide the selection of passenger travel routes. When passengers select a railway from OD, they can choose a through route or transfer route. The route should be the shortest route based on generalised cost. When they choose the through route, there are two options: the through route of normalspeed railway or highspeed railway. If the transfer route is selected, there are three options: the transfer between normalspeed railway lines, between highspeed railways lines, or between both highspeed railway lines and normalspeed railway lines. The railway network for selecting the OD passenger travel route is depicted in Figure 3. From the perspectives of S_{S}S_{e} and physical routes, passengers can choose multiple routes, such as S_{S}123S_{e}, S_{S}47S_{e}, and S_{S}547S_{e}. However, from the perspective of the railway service department, a farther physical route increases the travel ticket price, time cost, and generalised cost. Consequently, few passengers will likely select these unreasonable routes.
In the physical travel route, assuming that S_{S}123S_{e} is the shortest physical route and this route runs through normalspeed and highspeed railways, passengers can choose the normalspeed railway route S_{S}123S_{e} or highspeed railway route S_{S}123S_{e}. When considering the timetable of normalspeed and highspeed railways, in addition to the through route, the OD route selection scheme will become more complex. Passengers can follow the normalspeed train from S_{s} to city node 1 and then transfer to another normalspeed train or highspeed train to S_{e}. Passengers can choose the highspeed railway train from S_{s} to city node 2 and then transfer to the subsequent highspeed train or the subsequent normalspeed train to arrive at S_{e}. The partial train timetable considering the syncretic railway network between S_{s}S_{e} is displayed in Figure 4.
Based on a train timetable, this study investigated the passenger travel route. On the physical network formed by the syncretic normalspeed and highspeed railways, considering that there will be multiple railway stations at different city nodes under the syncretic networks, it will expand the space and establish the timespace service network of passenger travel route. For passengers travelling through the physical network integrated by the normalspeed and highspeed railway lines, assuming that the route choices between OD pairs, including the normalspeed and highspeed railways are built, the physical network can be constructed, as shown in Figure 5(a). The physical routes from the origin station (with normalspeed railway and highspeed railway) to the destination station (also with normalspeed railway and highspeed railway) can be represented as S_{S}12/2′3/3′S_{e}. It can be noticed that the number of passenger travel routes based on the physical network is quite small.
(a)
(b)
On the contrary, for the integrated doublenetwork mentioned above, the passenger travel constructed network based on the train timetable is largescale and complex. In addition to the direct travel schemes, the transfer plans between the highspeed trains, normalspeed trains, or both become available, as illustrated in Figure 5(b).
In this study, it is assumed that only one transfer is possible for the passengers in the course of the journey. All the routes between S_{s} and S_{e} in the syncretic railway network, including the direct routes and transfer routes, are shown in Figure 6. Figure 6 also presents the routing network based on the train timetable of each S_{s}–S_{e}; accordingly, all the routes can be found between OD in the syncretic railway network.
The parameters of the network for the railway passenger travel service are defined as follows: : the passenger travel service network and simultaneously a directed graph composed of the train service nodes and train service arcs between the nodes. : the set of all nodes in the travel service network. : the set of all service routes in the travel service network, . : the set of serving arc, , where is the head node of arc , is the tail node, and represents the arc of the train routes . : the set of generalised cost of train serving arc a between the start node and end node . : the set of all valid routes from node to .
3.3. Valid Route Search Algorithm
In the syncretic railway network, the transfer routing search results in difficulty for searching the valid routes based on generalised cost, and the number of transfer schemes is primarily affected by the transfer time and number of stations. A higher number of transfer stations passing through the travel routes results in a more complicated transfer route search. Generally, the success of the transfer depends on the transfer connection time, which should be set within a realistic range. Otherwise, the number of valid routes will increase sharply when the transfer connection time is prolonged.
Practically, all valid routes are searched by the depthfirst traversal algorithm. The idea behind this algorithm is as follows. First, examine all the valid routes using the ergodic method and determine whether the routes meet the discriminant criterion. If yes, the routes are recorded and put in the set of valid routes; otherwise, the searching process is repeated in the previous layer of nodes. The method is applied repeatedly until all valid routes are discovered.
In previous studies on the valid route of railway passenger travel, if the network fusion is neglected, the number of trains running on the existing line or highspeed railway line is limited. To obtain the feasible route within the shortest route time of the distance, researchers obtained more kshort routes using angle search or ellipse search techniques. However, for dual network convergence, the passenger train service (train number) between a specific OD is usually distributed on the shortest route. To obtain a lower ticket price and shorter travel time (two significant factors in the generalised cost), passengers do not usually choose the route outside the existing train service between specific OD. Although the threshold determination method of is also used in this study, this method is used for searching the feasible transfer route (or trip train number chain) based on the specific operation line, rather than when searching the physical route. In detail, the algorithm is designed as follows: Step 1 (initialisation): initialise the value of the extension coefficient of the valid routes. Set the transfer time between the maximum and minimum limit reasonably, that is, . Step 2: search all the through routes. After calculating the generalised cost of all the through routes between specific OD pairs based on the train timetable, set the generalised cost of the first route as the minimum cost. Replace the minimum route with a smaller route after a repeated calculation during the loop (if any). Check and update the strategy and obtain the minimum generalised cost for the normalspeed railway and highspeed railway . Put all direct routes into set and select all the valid routes to set , according to the judgement criterion. Step 3: search all the transfer routes. In the syncretic railway network, there are two kinds of transfer, namely, the internal transfer within the normalspeed railway network, that of the highspeed railway network, and the external transfer between the normalspeed and highspeed railway networks. Therefore, find all the transfer routes of four specific transfer patterns: the route from normalspeed railway to normalspeed railway, or highspeed railway, or the route from highspeed railway to normalspeed railway, or highspeed railway. For all of these transfers, the judgement criteria for valid routes are the constraint of transfer time. Step 3.1: search the internal transfer routes. According to the train timetable, if the number of transfers and the transfer time meet the specified standard ranges, then all the transfer routes of the node where the routes stop between the OD will be searched. It will then be analysed whether the routes can be regarded as valid routes. Repeatedly, all transferable nodes where the through routes pass will be obtained and added to set at the end. Step 3.2: search the external transfer routes. Unlike internal transfer, the external transfer requires further consideration of transfer plan occurring at different stations within the same city. Based on the train timetable, search the common stations (unique type of stations where both normalspeed and highspeed trains stop, which can also be called mixed stations) or the cities where both the normalspeed through train and highspeed through train pass. Then, locate all possible transfer connections in the mixed station (or each transfer city) restricted by the transfer time and put all found routes in set . Step 3.3: analyse the valid routes in set . For a given , the internal transfer route validity in the normalspeed railway network by and highspeed railway network, respectively, will be analysed. In terms of the external transfer routes in set , will be taken as the judging criteria to determine whether the routes are valid. Subsequently, all the valid routes can be put in set . Step 4: obtain all the feasible route set and valid route set for the particular OD pair.
4. Computational Experiments
To verify the accuracy of the proposed valid route search algorithm, the syncretic railway network from Lanzhou to Beijing was determined in this study, using the train timetable of March 2019. Figure 7 illustrates a simplified LanzhouBeijing railway network for both normalspeed and highspeed railway lines.
From the search results, 7,218 travel routes were available for passengers from Lanzhou to Beijing, among which 2,195 were valid routes, including 18 direct routes and 2,177 transfer routes. For a simpler representation, the head and tail nodes of the valid routes are omitted, and the nodes are represented by train numbers. The travel through routes (corresponding to the direct train services) of both normalspeed and highspeed railways from Lanzhou to Beijing are shown in Table 4.

From Table 4, the minimum generalised cost of the through route on normalspeed railway obtained by the searching algorithm is (less than ¥1645.34, the criteria for valid route determination). Thus, it can be identified as a valid route. Different from the actual timetable, neither of through train K886 and K4238 is a valid route. The reason is that both trains take a roundabout route, which depart from Lanzhou, stop at Yinchuan, Baotou, Huhehaote, and Datong during the journey and finally arrive at Beijing. Therefore, their travel time cost (28 hours) is much larger, compared with that of through train Z22 and Z56 (16.5 hours).
To further verify the accuracy of the method, a questionnaire survey was carried out, and the results indicate that among all the passengers, 98.6% prefer not to choose train K886 and K4238. When the tickets of the other through trains (with shorter travel time if possible) on normalspeed railway lines are sold out, 57.5% prefer to stop and transfer at Xi’an, Zhengzhou, and other city nodes, whereas 41.1% prefer to follow highspeed trains. A survey of the passengers taking trains K886 and K4238 reveals that the destinations of the trains departing from Lanzhou are mainly Yinchuan, Baotou, or Huhehaote, and the destination of the trains departing from Baotou and Huhehaote is usually Beijing. Therefore, K886 and K4238 trains are not in the valid route set from Lanzhou to Beijing. As for the highspeed railway lines from Lanzhou to Beijing, the minimal generalised cost of a through train service . The through travel routes for any seat type on train G428 and G430 are valid routes.
With a traversal of all the transfer stations (cities), a total of 2,183 transfer routes were found. Some of the routes are listed in Table 5.

By analysing the valid transfer route from Lanzhou to Beijing, it is clear that none of the transfer routes passing through Baotou or Huhehaote are in the valid route set. Moreover, the travel costs are high compared with those of other through trains and transfers at other nodes. The reason for this high cost is because the transfer cost at Baotou station where the Baolan and Jingbao rail lines intersect is relatively high owing to the long travel distances, prolonged travel time, and absence of highspeed railway available for transfer. In other words, as both K886 and K4238 through train services are invalid routes, transfer routes along K886 and K4238 are invalid.
An analysis of the search results reveals that under dualnetwork integration conditions, no valid transfer routes exist from normalspeed railway to highspeed railway at the following city (station) nodes: Tianshui, Xi’an, and Luoyang. The major reason is that the generalised cost from Lanzhou to the city (station) nodes mentioned above by a normalspeed railway (Longhai line) is much higher than that by highspeed railway. Taking Xi’an as an example, it takes 8 hours to travel from Lanzhou to Xi’an along the Longhai line (normalspeed railway line) having a distance of 676 km, and 3 hours from Lanzhou West Station to Xi’an North Station along Xulan highspeed railway line having a distance of 568 km. The generalised travel cost from Lanzhou to Xi’an by normalspeed railway is much higher than that by highspeed railway due to the effect of travel time value and comfort on passengers.
The number of valid transfer routes at each transfer node obtained using the searching algorithm is shown in Table 6.

From Table 6, Xi’an, Zhengzhou, and Shijiazhuang have the most valid transfer routes, whereas Yinchuan has the least valid routes. From the perspective of China’s railway network structure, first, the three cities (stations) connect more railway lines (both by normalspeed railway and highspeed railway) and have several passenger trains passing through the stations. Second, the Xi’an node has almost all transfer options for individuals travelling from Lanzhou to Beijing; this also applies to the Zhengzhou and Shijiazhuang nodes. Third, a passenger can select a preferable transfer plan from several options at the three city (station) nodes with a low generalised cost when no through train service is available from the timetable.
In terms of the valid routes shown in Table 7 (from various means of transport), the number of valid routes by normalspeed railway is 14, and its minimum generalised travel cost is ¥1175.24. Similarly, the number of valid routes by highspeed railway is 4, and its minimum generalised travel cost is ¥1358.96. There are 262 and 965 valid internal transfer routes by normalspeed railway and highspeed railway, respectively. The number of valid mixed transfer routes between normalspeed railway and highspeed railway is 950.

It should be noted that there are a few through travel routes from Lanzhou to Beijing, as well as a few valid transfer routes by normalspeed railway. The travel cost (especially that of transfer route) increases rapidly because of the low speed and long travel time. On one hand, due to the initially networked highspeed railway, there are several transfer schemes among the highspeed railways. On the other hand, passengers tend to take transfer routes in case that through trains are unavailable owing to the mixed transfer plans at the nodes (such as Xi’an, Zhengzhou, and Shijiazhuang) where the normalspeed and highspeed railways intersect.
Figure 8 compares the number of valid routes among normalspeed railway network, highspeed railway network, and syncretic railway network. Considering only normalspeed or highspeed railway, the valid routes from Lanzhou to Beijing reached 1230, including 276 produced by the normalspeed railway and 954 by highspeed railway. In the syncretic railway network, there were 2195 valid routes, which widens the travel plan choices of passengers and significantly improves travel convenience.
5. Conclusions
Through the analysis of each component of a generalised cost, such as fare, time, convenience, and transfer, this study presented a method to calculate the generalised cost in a syncretic railway network. Based on the minimum generalised cost calculated for different conditions and the preset cost of H, the valid routes with or without transfer from Lanzhou to Beijing were determined. The results show that in the syncretic railway network, the transfer plan between the normalspeed railway and highspeed railway significantly increases the number of valid routes.
Our study demonstrates that by integration of China’s normalspeed and highspeed railway networks, better synergy should be considered in preparing the train timetabling process of the two networks.
In addition, the findings of this study can be applied to many aspects as follows:(1)The calculated generalised cost can provide a favourable basis for passenger flow distribution and ticket allocation for the syncretic railway network.(2)The calculated generalised cost can be used to evaluate the transportation efficiency of the railway network and provide a reference for railway network planning.(3)According to the number of searched valid routes, the accessibility evaluation of railway network cities (stations) can be carried out.(4)The conclusion of this study does not only provide a theoretical reference for China’s railway operation but can also be extended to other countries with highspeed railway.
Data Availability
All data included in this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this article.
Acknowledgments
This study was jointly supported by grants from the National Natural Science Foundation of China (grant no. 71761023) and Natural Science Foundation of Gansu Province, China (grant no. 18JR3RA110).
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