Impact of high-speed railway construction on freight capacity on sections of existing railways- A case on the Yangtze River Delta

doi:10.1016/j.cstp.2024.101301

Case Studies on Transport Policy
交通政策案例研究

Volume 18, December 2024, 101301
第 18 卷，2024 年 12 月，101301

https://doi.org/10.1016/j.cstp.2024.101301 Get rights and content 获取权利和内容

Highlights 突出

•
The passenger flow split rate after the construction of HSR is predicted.
预测高铁建设后的客流分流率。
•
FW algorithm is improved with One-OD-at-a-time strategy and the linear search.
FW 算法采用 One-OD-at-a-a a 策略和线性搜索进行改进。
•
The freight capacity release of existing railway section due to the construction of HSR routes is measured.
测量了由于高铁路线建设而释放的现有铁路段的货运能力。
•
Policy implications are provided for the freight capacity release.
提供了货运能力释放的政策影响。

Abstract 抽象

The construction of high-speed railway (HSR) can effectively release the freight capacity of existing railways. By analyzing the influencing factors of passengers’ travel choices, the Utility Function and Logit model are adopted to calculate the utility and passenger flow split rate, and get the passenger flow of the existing railways after the diversion of the newly-built HSR. The passenger flow allocation model is established based on User Equilibrium, and improved Frank-Wolfe (FW) algorithm is applied to solve it, and obtain the passenger capacity of the sections on existing railways. Based on the deduction coefficient method, the passenger capacity is deducted from total capacity to get the freight capacity of each section on existing railways after release. Finally, take the railway channel in the Yangtze River Delta as a case, the results show that after the construction of the HSR, the freight capacity of sections on existing railways in the Yangtze River Delta is released to varying degrees. The freight capacity of Hefei-Wuhu section will be released the most, which is 19.5 pairs of trains, while that of Shanghai-Jiaxing section is the least, which is only 3.5 pairs, following by Wenzhou-Jinhua and Hangzhou-Ningbo sections, which are 4 pairs. Therefore, the construction of HSR should be accompanied by focusing on sections with less released freight capacity to enhance the overall capacity of the regional railway network.
高速铁路（HSR）的建设可以有效释放现有铁路的货运能力。通过分析乘客出行选择的影响因素，采用效用函数和 Logit 模型计算效用和客流分流率，得到新建高铁改道后既有铁路的客流情况。基于用户均衡建立客流分配模型，并采用改进的 Frank-Wolfe （FW）算法求解，得到现有铁路各区段的客运能力。根据扣除系数法，从总运力中扣除载客运量，得到现有铁路释放后各区段的运力。最后，以长三角铁路航道为例，结果表明，高铁建设后，长三角既有铁路各段的货运能力得到不同程度的释放。合肥至芜湖段的运力释放最多，为 19.5 对，而沪嘉段的运力最少，仅为 3.5 对，其次是温金和杭甬段，均为 4 对。因此，高铁建设应同时关注货运能力释放较少的路段，以提升区域铁路网的整体运力。

Keywords 关键字

Railway transportation

Freight capacity

Logit model

User equilibrium

HSR

铁路运输

运力

Logit 模型

用户均衡

HSR

1. Introduction 1. 引言

According to the development requirements of China’s modern comprehensive transportation system, in the construction of modernized railway networks, emphasis should be placed on strengthening the capacity of the strained sections of the railroad capacity and promoting the construction of the main HSR corridor. Moreover, it is expected that China will have a HSR network of about 175,000 km, with 38,000 km of HSR by 2025. According to the development requirements, the HSR network will comprises eight vertical and eight horizontal main corridors, including the corridor along Yangtze River Delta.
根据我国现代综合交通系统的发展要求，在建设现代化铁路网方面，应重点加强铁路运力紧张路段的通力度，推进高铁干线干线建设。此外，预计到 2025 年，中国将拥有约 175,000 公里的高铁网络，其中高铁将达到 38,000 公里。根据发展要求，高铁网络将包括 8 条垂直和 8 条水平主走廊，包括长三角走廊。

In July 2018, the China State Council proposed to enhance the proportion of railway freight transport, for the construction of China’s freight railway is relatively slow, and the expansion of existing railways is the priority of railway construction. As the HSR has expanded, railway passenger and freight transport in China have gradually bifurcated, allowing railway freight capacity to continue increasing. The existing railways tend to be dedicated to freight transport, with the structure of co-located with passengers and goods currently though. In one of the most prominent illustration, after the construction of the HSR from Shanghai-Nanjing, the annual freight capacities of corresponding corridors has increased by over 83 million tons (Yang et al., 2022), which suffice it to say that the construction of HSR can effectively diverse the passenger flow and alleviate the problem of tight freight capacity, so as to shift freight flows transfer from roads to rails (Yin et al., 2020), promote energy conservation and emissions reduction in the transportation industry (Yin et al., 2023).
2018 年 7 月，中国国务院提出提高铁路货运比重，针对我国货运铁路建设相对缓慢，扩建现有铁路是铁路建设的优先方向。随着高铁的扩张，中国的铁路客运和货运逐渐分叉，使铁路货运能力继续增加。现有的铁路往往专门用于货运，但目前的结构是客货同地。其中一个最突出的例子是，沪宁高铁建设后，相应走廊的年货运能力增加了 8300 多万吨（Yang et al.， 2022），这足以说明高铁的建设可以有效地分散客流，缓解货运能力紧张的问题，从而将货物流转移从公路转向铁路（Yin et al.， 2020），促进交通运输行业的节能减排（Yin et al.， 2023）。

Passenger transportation is the priority in railway transportation, and the freight capacity is the residual capacity under the premise of passenger transportation, thus freight capacity can be obtained by deducting the capacity occupied by passenger trains from total railway capacity. The construction of HSR will share the demand of passenger flow on existing railways, the number of passenger trains running on the existing railways will be reduced, and the freight capacity will be released (Yin et al., 2024), enhancing the competitiveness of railway freight transport market.
客运是铁路运输中的优先项，货运能力是在客运的前提下产生的剩余运力，因此可以从铁路总运力中减去客运列车占用的运力来获得货运能力。高铁的建设将分享现有铁路的客流需求，减少在现有铁路上运行的客运列车数量，释放货运能力（Yin et al.， 2024），增强铁路货运市场的竞争力。

Due to the different passenger flow density, the freight capacity released in different sections of the corridor varies greatly. Therefore, it is essential to calculate the released freight capacity from the perspective of microscopic sections, rather than the macro channel as a whole. Aiming at the release of freight capacity in sections, the passenger flow sharing rate should be calculated first to obtain the passenger demand of each section on existing railways after the diversion by HSR, and passenger allocation in railway network should be carried out to obtain the realistic passenger flow of each section on lines, which will be deducted from the total capacity to calculated freight capacity after release of the existing railways.
由于客流密度不同，走廊不同路段释放的货运能力差异很大。因此，必须从微观截面的角度计算释放的货运能力，而不是从整个宏观通道的角度来计算。针对分段货运能力的释放，应首先计算客流共享率，得到高铁分流后现存铁路各路段的客运需求，并进行铁路网络内的客流分配，得到各路段在线路上的实际客流，从既有铁路释放后计算的货运能力的总运力中扣除。

2. Literature review 2. 文献综述

When the traffic assignment involves multiple travel modes, the mode split is inevitable, and many scholars have focused on the CMSTA problem in the multimodal network. A mathematical programming model that combines the mode split and traffic assignment problem are constructed (Florian and Nguyen, 1978), and it has been successively extended to problems such as Combined mode split and traffic assignment (CMSTA) model with stochastic user equilibrium (Nielsen et al., 2002), combined models with multi-class users (Liu and Nie, 2012), and multimodal network design problems (Liu et al., 2018a, Liu et al., 2021).
当交通分配涉及多种出行模式时，模式分裂是不可避免的，许多学者都专注于多模式网络中的 CMSTA 问题。构建了一个结合了模式分割和交通分配问题的数学规划模型（Florian 和 Nguyen，1978），并陆续扩展到诸如具有随机用户均衡的组合模式分割和交通分配（CMSTA）模型（Nielsen et al.， 2002）、具有多类用户的组合模型（Liu 和 Nie，2012）和多模态网络设计问题（Liu et al.， 2018a， Liu et al.， 2021）。

Existing researches on travel mode choices and passenger flow split rate mainly adopt the Utility function (He et al., 2006, Feng et al., 2022), Logit model (Sun et al., 2013, Ma et al., 2022a, Wu, 2011, Yao et al., 2020), Discrete Choice model (Zhu et al., 2018, Wang and Zhao, 2009), Competitive Game model (Adler et al., 2010, Zhu, 2003) and other methods. Xu et al. (2020) constructed a distance transfer curve model and multivariate Logit model to calculate the regional intercity multi-modal passenger flow split rate. Feng et al. (2022) proposed a two-stage Path-Size Weibit model which is decomposed into two-layer Path-Size Weibit model by the Two-Stage estimation method to calculate the split rate of multi-mode between cities respectively. Different traveler groups do perceive certain aspects of the transport service quality differently, and thus, Structural Equation Modeling is used to identify the most effective attributes in each traveler group (Mesbah et al., 2022). Li et al. (2009) established combined modal split and assignment model to simulated travelers’ choices of intercity bus and railway, and proposed the streamlined diagonalization algorithm for solving.
现有关于出行方式选择和客流分流率的研究主要采用效用函数（He et al.， 2006， Feng et al.， 2022）、Logit 模型（Sun et al.， 2013，马 et al.， 2022a， Wu， 2011， Yao et al.， 2020）、离散选择模型（Zhu et al.， 2018， Wang 和 Zhao，2009 年）、竞争博弈模型（Adler 等人，2010 年，Zhu，2003 年）和其他方法。Xu et al. （2020）构建了距离换乘曲线模型和多变量 Logit 模型来计算区域城际多模式客流分流率。Feng et al. （2022）提出了一个两阶段的 Path-Size Weibit 模型，该模型通过两阶段估计方法分解为两层 Path-Size Weibit 模型，分别计算城市间多模态的分裂率。不同的旅行者群体对交通服务质量的某些方面的看法确实不同，因此，结构方程模型用于识别每个旅行者群体中最有效的属性（Mesbah et al.， 2022）。Li et al. （2009）建立了模态拆分和分配相结合模型，以模拟旅行者对城际公交和铁路的选择，并提出了用于求解的流线化算法。

The capacity release of transportation network has been mostly studied through the CMSTA model (Jiang et al., 2022, Zhou et al., 2022) which can be solved by two-phase gradient projection algorithm (Ryu et al., 2021, Zhang et al., 2023). The researches on freight capacity release mainly focus on the macro level, and the integer linear programming model is proposed to calculate the overall release of the channel generally (Li et al., 2014, Chen et al., 2016). Tian and Lin (2015) set the virtual volume growth coefficient to simulate the trend of traffic volume after capacity release of existing railways, and constructed the optimization model for the resorting capacity for marshalling station which is solved to accurately obtain the capacity allocation demand. Hao (2014) constructed a passenger flow split rate model and quantified the capacity release of the Wuhan-Guangzhou corridor. While the limitation of these studies is that they focus on the capacity release of the macro channel, instead of a more microscopic perspective, i.e., the capacity release on each section of the realistic railway network.
交通网络的容量释放主要通过 CMSTA 模型（江 et al.， 2022，周 et al.， 2022）进行研究，该模型可以通过两阶段梯度投影算法来解决（Ryu et al.， 2021， Zhang et al.， 2023）。运力释放的研究主要集中在宏观层面，提出了整数线性规划模型来计算通道的整体释放（Li et al.， 2014， Chen et al.， 2016）。Tian 和 Lin （2015）设置虚拟容量增长系数来模拟现有铁路运力释放后的交通量趋势，并构建了编组站重新分配容量的优化模型，并求解了该模型，以准确获取容量分配需求。Hao （2014）构建了客流分流率模型，量化了武广走廊的容量释放。虽然这些研究的局限性在于它们侧重于宏观通道的容量释放，而不是更微观的视角，即现实铁路网络每个部分的容量释放。

Existing researches on passenger flow allocation model mainly focus on three aspects: architecture of network model (Xu et al., 2023b, Wu et al., 2022), passenger behavior assumptions (Yu et al., 2023, Li et al., 2020), and passenger flow allocation theory (Wang, 2020, Ma et al., 2022b). Xu et al. (2023a) developed an equilibrium passenger flow assignment model for common-line operation mode with multi-routing, solved by a successive averages mixed algorithm. Fan et al. (2022) constructed a general fixed-point model that combines the CNL-based (Cross-Nested Logit) mode split and the VI-based (Variational Inequality) traffic assignment model for CMSTA problem. Javani et al. (2019) proposed a path-based dynamic traffic assignment algorithm and a systematic way of link segmentation to make the algorithm rapidly converges. However, the above-mentioned researches are usually applied to small or medium-scale networks, few studies focus on the solution for the CMSTA problem in realistic large-scale networks.
现有的客流分配模型研究主要集中在三个方面：网络模型架构（Xu et al.， 2023b， Wu et al.， 2022）、乘客行为假设（Yu et al.， 2023， Li et al.， 2020）和客流分配理论（Wang， 2020，马 et al.， 2022b）。Xu et al. （2023a）开发了一种多路线共线运营模式的平衡客流分配模型，通过连续平均混合算法求解。Fan et al. （2022）构建了一个通用的定点模型，该模型结合了基于 CNL 的（Cross-Nested Logit）模式拆分和基于 VI 的（变分不等式）流量分配模型来解决 CMSTA 问题。Javani et al. （2019）提出了一种基于路径的动态流量分配算法和一种系统化的链路分割方式，以使算法快速收敛。然而，上述研究通常适用于中小型网络，很少有研究关注现实大规模网络中 CMSTA 问题的解决方案。

The Frank-Wolfe algorithm is applied to solve the passenger flow allocation model, which mainly consists of two parts: flow update strategy and line search technologies. Different flow update strategies and line search techniques are applied to four different sizes of transport networks, and the results show that the One-OD-at-a-time strategy and the golden section method make the FW algorithm converge the fastest (Xu et al., 2008). Ren et al. (2012) improved the flow update strategy, the initialization linear search, and shortest path search of the FW algorithm, and the convergence rate of the algorithm was reduced by nearly 15 % after the improvement. An adaptive FW algorithm with Nesterov acceleration strategy was proposed for matrix completion problem, and rank of the matrix in iterations was reduced to improve the convergence rate of the algorithm (Wang et al., 2021).
采用 Frank-Wolfe 算法求解客流分配模型，该模型主要由流更新策略和线路搜索技术两部分组成。将不同的流更新策略和线路搜索技术应用于四种不同规模的传输网络，结果表明，一次 One-OD 策略和黄金分割方法使 FW 算法收敛最快（Xu et al.， 2008）。任 et al. （2012）改进了FW算法的流更新策略、初始化线性搜索和最短路径搜索，改进后算法的收敛率降低了近15%。针对矩阵完成问题提出了一种具有 Nesterov 加速策略的自适应 FW 算法，并降低了矩阵在迭代中的排名，以提高算法的收敛率（Wang et al.， 2021）。

To some extent, changes of the railway passenger capacity have an impact on the existing railway freight capacity (Chen et al., 2016). Most of the current studies focus on the calculation of passenger (freight) flow split rate among the existing modes of transportation in the corridor so as to allocate passenger (freight) capacity. There is a lack of research on the released freight capacity of each section on the existing railways caused by the newly-built HSR. The utility function and Logit model are established in this paper to calculate the passenger flow split rate between the existing railways and the newly-built HSR in the corridor, and the passenger flow after diversion on the existing railways is allocated in the railway network to obtain the exact passenger flow on each section of existing railways. In terms of passenger (freight) flow allocation methods, the traditional FW algorithm is mostly used, which has a slow convergence rate and can hardly obtain path information (Xu et al., 2008).
在某种程度上，铁路客运能力的变化对现有的铁路货运能力产生了影响（Chen et al.， 2016）。目前的大多数研究都集中在计算走廊内现有运输方式之间的客（货运）分流率，以便分配客（货运）运力。由于新建高铁导致现有铁路上各路段的释放货运能力缺乏研究。本文建立效用函数和 Logit 模型，计算廊道内现有铁路与新建高铁的客流分流率，将现有铁路改道后的客流分配到铁路网络中，得到既有铁路各路段的准确客流。在客（货）流分配方法方面，多采用传统的FW算法，收敛速度慢，难以获取路径信息（Xu et al.， 2008）。

In this paper, the contributions are as follows: 1) We analyze the available surveys of travelers’ choice behavior, in order to calculate the modal splits of HSR and existing railways. 2) The One-OD-at-a-time strategy is chosen to replace the traditional All-at-once strategy in terms of flow update strategy, and the linear search is improved to speed up the calculation. Meanwhile, the improved FW algorithm is compared with the traditional one to verify the effectiveness. 3) Based on network analysis and the deduction coefficient, we propose a method for measuring the freight capacity release of sections on existing railways due to the construction of HSR routes in realistic railway network.
在本文中，贡献如下：1）我们分析了对旅行者选择行为的现有调查，以计算 HSR 和现有铁路的模式拆分。2）在流更新策略方面，选择 One-OD-at-a-time 策略代替传统的 All-at-once 策略，并改进线性搜索以加快计算速度。同时，将改进的FW算法与传统算法进行比较，以验证其有效性。3）基于网络分析和推演系数，提出了一种测量现实铁路网络中高铁线路建设导致既有铁路段运力释放的方法。

The remainder of this paper is organized as follows. Section 2 illustrates the utility function and Logit model of passenger travel choice, constructs the passenger flow allocation model, and improves the FW algorithm for solving the passenger flow allocation model. The deduction coefficient method for the calculation of released freight capacity is introduced as well. Section 3 conducts an empirical study on the freight capacity release of the existing railways in the Yangtze River Delta and verifies the effectiveness of the improved algorithm. Section 4 summarizes the conclusions of this study and offers relevant policy recommendations for releasing railway freight capacity in the Yangtze River Delta, and proposes directions for future research. The structure of the proposed methodology is shown in Fig. 1.
本文的其余部分组织如下。第 2 节说明了乘客出行选择的效用函数和 Logit 模型，构建了乘客流分配模型，并改进了求解乘客流分配模型的 FW 算法。还介绍了用于计算释放货运能力的扣除系数方法。第 3 节对长三角现有铁路的货运能力释放进行了实证研究，并验证了改进算法的有效性。第 4 节总结了本研究的结论，为释放长三角铁路货运能力提供了相关政策建议，并提出了未来研究的方向。所提出的方法的结构如图 1 所示。

3. Materials and methods 3. 材料和方法

The construction of HSR has a diversion effect on the passenger flow of existing railways, which is calculated first. Travelers will consider factors such as travel cost, time and comfort, and choose HSR or existing railways with the greater utility. Based on the factors of travel modes, utility function is established to calculate the utility value of the newly-built HSR and the existing railways. The probability of travelers choosing HSR or existing railways with different utility is calculated through Logit model and the diversion effect of HSR on passenger flow of existing railways is obtained. The passenger OD (Origin and Destination) flows of existing railways before and after the diversion of HSR are substituted into the passenger flow allocation model, respectively. Based on the principle of user equilibrium, the passenger OD flows are allocated in the railway network, so as to obtain passenger flow of the existing railways of each section before and after the diversion of HSR.
高铁的建设对现有铁路的客流有分流效应，首先计算。旅行者会考虑旅行成本、时间和舒适度等因素，并选择 HSR 或实用性更强的现有铁路。基于出行方式因素，建立效用函数计算新建高铁和现有铁路的效用值。通过 Logit 模型计算旅行者选择高铁或具有不同效用的现有铁路的概率，并得到高铁对现有铁路客流的改道路流效应。HSR 改道前后现有铁路的客运 OD（始发地和目的地）流分别被替换为客流分配模型。基于用户均衡原则，在铁路网络中分配客运OD流量，从而得到高铁改道前后各路段现有铁路的客流。

3.1. Utility function of travelers’ choice behavior
3.1. 旅客选择行为的效用函数

Based on the random utility theory, HSR or existing railways will produce different utilities for travelers. Travelers will choose HSR or existing railways with the greater perceived utility which is affected by the characteristics of travel modes, traveler’s subject characteristics and other factors (Wang and Zhao, 2009). The main characteristic indicators of the traveler’s choice behavior include the travel cost, time and comfort etc. (Lin et al., 2024), thus the above attributes are selected as indicators of the utility function, which can be calculated as follows.
基于随机效用理论，HSR 或现有铁路将为旅行者产生不同的效用。旅行者会选择高铁或具有更大感知效用的现有铁路，这受出行方式特征、旅行者的主题特征和其他因素的影响（Wang 和 Zhao，2009）。旅行者选择行为的主要特征指标包括出行成本、时间和舒适度等（Lin et al.， 2024），因此选择上述属性作为效用函数的指标，可以计算如下。

1) Travel cost. Travel cost reflects the economic expense during the travel. The railway fare is usually positively correlated with the transport mileage, and different modes of travel have different fare rate.(1)

Q = R L

Where, Q represents travel cost; R represents the fare rate of transport mode; L represents transport mileage, km.
1）差旅费。差旅成本反映了差旅期间的经济费用。铁路票价通常与运输里程呈正相关，不同的出行方式有不同的票价。 (1)

Q = R L

其中，Q 表示差旅成本;R 表示运输方式的票价率;L 代表运输里程，公里。

2) Travel time. Travel time includes travelers' waiting time and in-transit time, which reflects the efficiency of transferring and the running speed of travel mode, respectively. In-transit time refers to the travel time consumed by choosing different types of passenger trains. Considering the development of different cities, value of time

V_{t}

is added to measure the importance of travel time for travelers in different cities.(2)

F = (L / v + w) V_{t}

(3)

V_{t} = \frac{G}{R W_{t}}

In formula (2), F represents travel time; v represents the running speed, km/h; w represents waiting time, h. In formula (3), G represents Gross Domestic Product; R represents the regional population;

W_{t}

represents the average labor time of the regional population, h/week.
2）旅行时间。出行时间包括出行人员的等待时间和在途时间，分别反映了换乘效率和出行方式的运行速度。在途时间是指选择不同类型的客运列车所消耗的旅行时间。考虑到不同城市的发展，增加了时间

V_{t}

价值来衡量旅行时间对不同城市旅行者的重要性。 (2)

F = (L / v + w) V_{t}

(3)

V_{t} = \frac{G}{R W_{t}}

在公式（2）中，F 表示旅行时间;v 表示运行速度，km/h;w 表示等待时间，h 表示。在公式（3）中，G 代表国内生产总值;R 表示区域人口;

W_{t}

表示区域人口的平均劳动时间，小时/周。

3) Comfort. Comfort measures the service level, the vehicle environment, and the degree of congestion during travel. The fatigue of travelers can reflect the comfort level of various transport mode services (Zhang et al., 2019).(4)

C = 7.5 e - 5 t^{6} - 0.0032 t^{5} + 0.054 t^{4} - 0.42 t^{3} + 1.5 t^{2} - 0.73 t + 0.035

Where, C represents comfort, indicates the effect of travel time on fatigue of travelers; t represents the travel time, h.
3）舒适。舒适度衡量服务水平、车辆环境和出行中的拥堵程度。旅行者的疲劳程度可以反映各种交通方式服务的舒适度（Zhang et al.， 2019）。 (4)

C = 7.5 e - 5 t^{6} - 0.0032 t^{5} + 0.054 t^{4} - 0.42 t^{3} + 1.5 t^{2} - 0.73 t + 0.035

其中，C 表示舒适度，表示旅行时间对旅行者疲劳的影响;t 表示旅行时间 h。

Combining the utility of the various modes of travel, the utility of the travel modes can be expressed as(5)

V_{m} = θ_{Q} Q + θ_{F} F + θ_{C} C

where,

V_{m}

represents an observable fixed term in the utility function;

θ_{Q}

θ_{F}

θ_{C}

represents the sensitivities of travel cost, travel time and onboard comfort, respectively.
结合各种出行模式的效用，出行模式的效用可以表示为 (5)

V_{m} = θ_{Q} Q + θ_{F} F + θ_{C} C

其中，

V_{m}

表示效用函数中可观察的固定项;

θ_{Q}

，

θ_{F}

分别

θ_{C}

表示旅行成本、旅行时间和机上舒适度的敏感性。

3.2. Logit model of passenger travel choices
3.2. 乘客出行选择的 Logit 模型

Due to the different requirements of travelers and the different service level of various travel modes, travelers will choose the transport mode with the greatest utility, and the probability is determined by the utility of the mode. Logit model is applied to calculate the probability of traveler’s choice of travel mode with different utilities. According to the theory of utility maximization, the probability of traveler’s choice of travel mode m can be expressed as(6)

P_{(m)} = prob (U_{m} ⩾ U_{n}), \forall n \in M, m \neq n

(7)

U_{m} = V_{m} + ε_{m}

where,

U_{m}

and

U_{n}

represent the utility of travel mode m and n, respectively; M represents a set of travel modes. In formula (7),

V_{m}

represents an observable fixed term in the utility function;

ε_{m}

represents the random term, caused by unobservable factors or variable biases (Wang and Zhao, 2009).
由于出行方式的需求不同，各种出行方式的服务水平不同，出行方式会选择效用最大的交通方式，而概率则由出行方式的效用决定。Logit 模型用于计算旅行者选择具有不同实用程序的出行模式的概率。根据效用最大化理论，旅行者选择出行模式 m 的概率可以表示为 (6)

P_{(m)} = prob (U_{m} ⩾ U_{n}), \forall n \in M, m \neq n

(7)

U_{m} = V_{m} + ε_{m}

where，

U_{m}

分别

U_{n}

表示出行模式 m 和 n 的效用;M 表示一组出行模式。在公式（7）中，

V_{m}

表示效用函数中的可观察固定项;

ε_{m}

代表由不可观察的因素或可变偏差引起的随机项（Wang 和 Zhao，2009）。

The general expression of the Logit model is(8)

P_{(m)} = exp (V_{m}) / \sum_{m \in M} exp (V_{m})

Logit 模型的一般表达式为 (8)

P_{(m)} = exp (V_{m}) / \sum_{m \in M} exp (V_{m})

To eliminate the bias caused by exponential growth, the utility values are averaged, thus the probability of travel mode m chosen by the travelers can be expressed as (Wu, 2011)(9)

P_{(m)} = \exp (V_{m} / \bar{V}) / \sum_{m \in M} \exp (V_{m} / \bar{V})

where,

\bar{V}

represents the average utility of the various travel modes.
为了消除指数增长引起的偏差，对效用值进行平均，因此旅行者选择出行模式 m 的概率可以表示为（Wu， 2011）， (9)

P_{(m)} = \exp (V_{m} / \bar{V}) / \sum_{m \in M} \exp (V_{m} / \bar{V})

其中，

\bar{V}

表示各种出行模式的平均效用。

3.3. Passenger flow allocation model
3.3. 客流分配模型

The user equilibrium assumes that travelers can accurately obtain the information of the network and estimate the travel cost of the path, thus this paper applies the passenger flow allocation model based on the user equilibrium to assign paths for travelers, calculates the passenger flow of each section on the existing railways, and obtain the number of passenger trains on sections of existing railways. The impedance in the passenger flow allocation model is generally expressed by the BPR (Bureau of Public Roads) model, while there is no traffic congestion in railway transportation. Thus, this paper considers the factors including travel cost, time, congestion perception during travel, the new impedance function is proposed which is more relevant to the railway transportation.
用户均衡假设旅客能够准确获取网络信息并估算路径的出行成本，因此采用基于用户均衡的客流分配模型为旅客分配路径，计算现有铁路上各区段的客流，得到现有铁路区间的客运列车数量。客流分配模型中的阻抗一般用 BPR（Bureau of Public Roads）模型表示，而铁路运输中没有交通拥堵。因此，本文考虑了出行成本、时间、出行拥堵感知等因素，提出了与铁路运输更相关的新阻抗函数。

3.3.1. Notations 3.3.1. 符号

The detailed notations and descriptions are given in Table 1.
表 1 中给出了详细的符号和描述。

Table 1. Notations.
表 1.符号。

Notation 表示法	Description 描述
Sets 集
$K_{ij}$	Set of the paths from i to j, $\forall k \in K_{ij}$ 从 i 到 j 的路径集， $\forall k \in K_{ij}$
H	Set of sections in the railway network, $\forall s \in H$ 铁路网中的一组部分， $\forall s \in H$
I	Set of origins, $\forall i \in I$ 一组原点， $\forall i \in I$
J	Set of destinations, $\forall j \in J$ 目标集、 $\forall j \in J$
$W_{ij}$	Set of the shortest paths from i to j, $\forall w_{ij} \in W_{ij}$ 从 i 到 j 的最短路径集， $\forall w_{ij} \in W_{ij}$

Parameters 参数
$α$	Additional time-expenditure factor up to authorized strength, $α = 1$ 额外的时间消耗系数，最高可达授权强度， $α = 1$
R	Fare rate, $R = 0.18$ 票价， $R = 0.18$
$d_{s}$	Mileage of section s s 区间里程
$β$	Respective train capacity on average, $β = 600$ 各自的列车平均载客量， $β = 600$
n	Number of iterations 迭代次数
$λ$	Iteration step 迭代步骤
$η$	Convergence accuracy, $η = 10^{- 4}$ 收敛精度 / $η = 10^{- 4}$

Variables 变量
$z_{s}$	Impedance of section s 截面 s 的阻抗
$x_{s}$	Passenger flow of section s S 段客流
$f_{ijk}$	Passenger flow on path k from origin i to destination j 路径 k 上从起点 i 到目的地 j 的客流
$q_{ij}$	Passenger flow from origin i to destination j 从出发地 i 到目的地 j 的客流
$C_{ijk}$	Travel cost on path k from origin i to destination j 路径 k 从起点 i 到目的地 j 的行程成本
$δ_{s, k}$	For section s on path k, the value is 1; otherwise, the value is 0 对于路径 k 上的部分 s，该值为 1;否则，值为 0
$Y (x_{s})$	Extra time overhead function due to congestion 由于拥塞而导致的额外时间开销功能
$w_{ij}^{n}$	The shortest paths from i to j in the nth iteration, $\forall w_{ij} \in W_{ij}$ 第 n次迭代 $\forall w_{ij} \in W_{ij}$ 中从 i 到 j 的最短路径
$x_{s, i j}^{n}$	Passenger flow of section s from origin i to destination j in the nth iteration 第 n次迭代中从起点 i 到目的地 j 的路段 s 的客流
$δ_{s, w_{ij}^{n}}$	For section s on path $w_{ij}^{n}$ , the value is 1; otherwise, the value is 0 对于 section s on path $w_{ij}^{n}$ ，值为 1;否则，值为 0
$b_{s}^{n}$	Background flow, which equals to the section flow of network in the allocation of last pair of OD minus the section flow generated by the current OD in the last allocation 后台流，等于最后一对 OD 分配中网络的截面流减去上次分配中当前 OD 生成的截面流
$y_{s}^{n}$	Auxiliary flow, i.e., add the current OD’s section flow generated in the current allocation to the background flows for solving the descent direction 辅助流，即将当前分配中生成的 OD 截面流添加到背景流中，以求解下降方向

3.3.2. Assumptions 3.3.2. 假设

1) All passengers can make fully informed path choices, with information regarding all available travel paths, including travel time, fare and other relevant factors.
1）所有乘客都可以做出充分知情的路径选择，包括所有可用旅行路径的信息，包括旅行时间、票价和其他相关因素。

2) The travel demand between each OD pair is fixed and known. The changes of demand that results from variations in the quality of rail service are not considered in this research.
2）每个 OD 对之间的行程需求是固定的和已知的。本研究未考虑铁路服务质量变化导致的需求变化。

3) Passenger’s total travel cost is assumed to be additive, which can be expressed as the sum of the costs of individual paths.
3）假设乘客的总旅行成本是累加的，可以表示为各个路径的成本之和。

4) It is assumed that passengers’ path choices and the state of the rail network remains constant over the iteration and the model does not account for dynamic changes over time.
4）假设乘客的路径选择和铁路网络的状态在迭代过程中保持不变，并且模型没有考虑随时间变化的动态变化。

5) Passengers’ travel costs are influenced solely by the intrinsic factors of paths, while external factors such as weather conditions or unexpected incident are not considered in this research.
5）乘客的旅行成本仅受路径内在因素的影响，而本研究未考虑天气条件或意外事件等外部因素。

3.3.3. Mathematical model
3.3.3. 数学模型

(10)

Min F_{1} = \sum_{s} \int_{0}^{x_{s}} z_{s} (x_{s}) d (x_{s})

s.t.(11)

f_{ijk} ⩾ 0, \forall i \in I, \forall j \in J, \forall k \in K_{ij}

(12)

\sum_{k \in K_{ij}} f_{ijk} = q_{ij}, \forall i \in I, \forall j \in J

(13)

x_{s} = \sum_{i} \sum_{j} \sum_{k} f_{ijk} δ_{s, k}, \forall s \in H, \forall i \in I, \forall j \in J, \forall k \in K_{ij}

(14)

C_{ijk} = \sum_{s} z_{s} (x_{s}) δ_{s, k}, \forall s \in H, \forall i \in I, \forall j \in J, \forall k \in K_{ij}

(15)

z_{s} (x_{s}) = R d_{s} + V_{t} (d_{s} / v + d_{s} Y (x_{s}) / v)

(16)

Y (x_{s}) = α (x_{s} / β)

Where, Eq. (10) is the objective function, which is to attain the user equilibrium. Constraint (11) is the non-negative constraint of the passenger flow on paths. Constraint (12) establishes the conservation of passenger flow that the sum of the passenger flows along paths between an OD pair is equal to the total OD flows from origin i to destination j. Constraint (13) indicates that the passenger flow on section s equals to the sum of passenger flows of all OD pairs through section s. Constraint (14) indicates that the travel cost of path k from origin i to destination j equals to the sum of the impedance of all the sections on path k. Constraint (15) represents the impedance of the railway network, including travel cost, time, congestion, etc. The congestion impedance is expressed as an additional time cost. Constraint (16) express the congestion impedance, which represents the perceived impedance of the passenger due to congestion during travel (Liu et al., 2018b).
其中，方程（10）是目标函数，即实现用户均衡。约束（11）是路径上客流的非负约束。约束（12）建立客流守恒，即沿 OD 对之间路径的客流之和等于从起点 i 到目的地 j 的总 OD 流。约束（13）表示路段 s 上的客流等于通过路段 s 的所有 OD 对的客流之和。约束（14）表示路径 k 从起点 i 到目的地 j 的行程成本等于路径 k 上所有截面的阻抗之和。约束（15）表示铁路网络的阻抗，包括旅行成本、时间、拥堵等。拥塞阻抗表示为额外的时间成本。约束（16）表示拥堵阻抗，它表示乘客在旅行过程中由于拥堵而感知到的阻抗（Liu et al.， 2018b）。

3.3.4. Solution algorithm
3.3.4. 解算法

Flow update strategy is the core element of FW algorithm, and the most common one is the All-at-once strategy, i.e., update the shortest path set of all the ODs with the flows allocated on the shortest paths each time. The flow update strategy is improved with One-OD-at-a-time strategy, which solves the shortest path of only one pair of OD at a time and updates the set of shortest paths with passenger flows, while the impedance is updated after all the ODs have finished updating.
流更新策略是防火墙算法的核心元素，最常见的是 All-at-once 策略，即每次更新所有 OD 的最短路径集，并将分配的流分配到最短路径上。流更新策略采用 One-OD-at-a-a 策略进行改进，该策略一次只求解一对 OD 的最短路径，并随乘客流更新最短路径集，而阻抗在所有 OD 完成更新后更新。

The One-OD-at-a-time strategy in the FW algorithm offers several notable advantages compared to the All-at-once and One-origin-at-a-time strategies. By updating only one OD pair’s flow per iteration, this approach facilitates faster convergence (Chen, 2001), particularly in large-scale network problems, by minimizing potential oscillations that can arise from the simultaneous updates in the All-at-once strategy. Unlike the One-origin-at-a-time strategy, which updates flows for all destinations from a single origin, the One-OD-at-a-time method provides more granular control and adaptability, especially in handling complex constraints such as capacity limitations and multi-path routing. Additionally, this method reduces computational complexity by decomposing the problem into smaller, more manageable subproblems, making it particularly effective in networks with a high number of nodes.
与 All-at-once 和 One-origin-at-time 策略相比，FW 算法中的 One-OD-at-time 策略具有几个显着优势。通过每次迭代只更新一个 OD 对的流程，这种方法通过最大限度地减少 All-at-once 策略中同时更新可能引起的潜在振荡，促进了更快的收敛（Chen，2001），特别是在大规模网络问题中。与一次一个源策略不同，一次一个源更新所有目的地的流，而一次一个 OD 方法提供了更精细的控制和适应性，尤其是在处理容量限制和多路径路由等复杂约束时。此外，这种方法通过将问题分解为更小、更易于管理的子问题来降低计算复杂性，使其在具有大量节点的网络中特别有效。

The One-OD-at-a-time strategy applies one-dimensional search for each pair of updated OD flows, and the updated flows can be used in time for the next pair of OD to find the shortest path, which shifts the computation from shortest path to linear search. To reduce the frequency of linear search while improving the flow update strategy, the linear search is improved on the principle of ignoring OD pairs under specific conditions. If there is only one path, the flow update for the OD with single path is ignored; if the result of the flow allocation for a particular pair of OD fails to reduce the value of objective function, the updates of the linear search step and flow are ignored (Ren et al., 2012). The flow of the improved FW algorithm is shown in Table 2.
一次 1 OD 策略对每对更新的 OD 流应用一维搜索，更新的流可以及时用于下一对 OD 以找到最短路径，从而将计算从最短路径转变为线性搜索。为了在改进流更新策略的同时降低线性搜索的频率，在特定条件下忽略 OD 对的原则上改进了线性搜索。如果只有一条路径，则忽略具有单个路径的 OD 的流更新;如果特定OD对的流分配结果未能减少目标函数的值，则线性搜索步骤和流的更新将被忽略（任等人，2012）。改进的 FW 算法的流程如表 2 所示。

Table 2. Flow of One-OD-at-a-time flow update strategy.
表 2.一次一个 OD 的流更新策略的流程。

FW algorithm under One-OD-at-a-time flow update strategy One-OD-at-a-a flow update 策略下的 FW 算法
Step 1: Input $z_{s}^{0} (x_{s})$ and $W_{ij}$ 步骤1：Input $z_{s}^{0} (x_{s})$ 和 $W_{ij}$
Step 2: Number of iterations: n = n + 1 步骤2：迭代次数：n = n + 1
Step 3: Updated flow 步骤3：更新的流程 3.1 Update $z_{s}^{n}$ 3.1 更新 $z_{s}^{n}$ 3.2 Find the shortest path of the next OD pair $w_{ij}^{n}$ , update $W_{ij}$ 3.2 找到下一个OD对 $w_{ij}^{n}$ 的最短路径，更新 $W_{ij}$ 3.3 All-or-nothing allocation, $x_{s, i j}^{n} = q_{ij} δ_{s, w_{ij}^{n}}$ , $δ_{s, w_{ij}^{n}} = \{\begin{matrix} 1, if s is o n w_{ij}^{n} \\ 0, otherwise \end{matrix}$ 3.3 全有或全无分配、 $x_{s, i j}^{n} = q_{ij} δ_{s, w_{ij}^{n}}$ $δ_{s, w_{ij}^{n}} = \{\begin{matrix} 1, if s is o n w_{ij}^{n} \\ 0, otherwise \end{matrix}$ 3.4 Judge: if size ( $W_{ij}$ , 1) = 1, turn to Step 4; otherwise, turn to Step 3.5 3.4 判断：如果大小（ $W_{ij}$ ， 1） = 1，则转到第 4 步;否则，请转到步骤 3.5 3.5 Background flow: $b_{s}^{n} = x_{s}^{n} - \sum_{w_{ij} \in W_{ij}^{n - 1}} f_{ijk}^{n - 1} δ_{s, w_{ij}^{n - 1}}$ 3.5 后台流程： $b_{s}^{n} = x_{s}^{n} - \sum_{w_{ij} \in W_{ij}^{n - 1}} f_{ijk}^{n - 1} δ_{s, w_{ij}^{n - 1}}$ 3.6 Auxiliary flow: $y_{s}^{n} = b_{s}^{n} + x_{s, i j}^{n}$ 3.6 辅助流程： $y_{s}^{n} = b_{s}^{n} + x_{s, i j}^{n}$ 3.7 Judge: if $\sum_{s \in H} F (x_{s}) (y_{s}^{n} - x_{s}^{n}) < 0$ , turn to Step 3.8; otherwise, turn to Step 4 3.7 判断：如果 $\sum_{s \in H} F (x_{s}) (y_{s}^{n} - x_{s}^{n}) < 0$ ，转到步骤 3.8;否则，请转到步骤 4 3.8 The descent direction is $y_{s}^{n} - x_{s}^{n}$ , $x_{s}^{n^{'}} = x_{s}^{n} + λ (y_{s}^{n} - x_{s}^{n})$ 3.8 下降方向为 $y_{s}^{n} - x_{s}^{n}$ ， $x_{s}^{n^{'}} = x_{s}^{n} + λ (y_{s}^{n} - x_{s}^{n})$ 3.9 Obtain step size $λ$ , minimize $F (x_{s}) = \sum_{s} \int_{0}^{x_{s}^{n} + λ (y_{s}^{n} - x_{s}^{n})} z_{s} (x_{s}) d (x_{s})$ 3.9 获取步长 $λ$ ，最小化 $F (x_{s}) = \sum_{s} \int_{0}^{x_{s}^{n} + λ (y_{s}^{n} - x_{s}^{n})} z_{s} (x_{s}) d (x_{s})$
Step 4: Judge if all OD have not been fully updated, turn to Step 3.2 and update the next pair of OD; if the update of all OD have finished, turn to Step 5 步骤4：判断是否所有 OD 都没有完全更新，转到步骤 3.2 并更新下一对 OD;如果所有 OD 的更新都已完成，请转到步骤 5
Step 5: Judge if $\sqrt{\sum {(x_{s}^{n^{'}} - x_{s}^{n})}^{2}} / \sum x_{s}^{n} < η$ , turn to Step 6; otherwise, turn to Step 2 步骤5：判断 if $\sqrt{\sum {(x_{s}^{n^{'}} - x_{s}^{n})}^{2}} / \sum x_{s}^{n} < η$ ，转到步骤 6;否则，请转到步骤 2
Step 6: Output the shortest path sets and results of flow, $x_{s} = x_{s}^{n^{'}}$ 步骤6：输出最短路径集和流结果， $x_{s} = x_{s}^{n^{'}}$

3.4. Freight capacity release
3.4. 运力释放

After the construction of the HSR, the reduction of passenger flow on the existing railways leads to a decrease of passenger trains, and the capacity released for freight transportation can be calculated by the deduction coefficient method.
高铁建设后，现有铁路客流减少导致客运列车减少，释放的货运运力可以用扣除系数法计算。

The theorem of calculating the deduction coefficient is to draw a passenger train line in the lines of freight train operation, and calculate the number of freight trains deducted from the line of operation due to the drawing of passenger train, which is taken as the single passenger train deduction coefficient. The Schematic diagram of occupied section for single passenger train crossing the line is shown in Fig. 2.
计算扣减系数的定理是在货运列车运行线路中绘制一条客运列车线，计算因绘制客运列车而从运营线路扣除的货运列车数量，作为单列客运列车扣减系数。单客运列车越线占用区间示意图如图 2 所示。

Where,

I_{a}

and

I_{d}

represents the arrival and departure intervals of train, min;

I

represents the interval of the trailing train, min;

t_{p}

represents additional time caused by passenger train overtaking, min.
其中，

I_{a}

和

I_{d}

表示火车的到达和离开间隔，min;

I

表示尾随列车的间隔，min;

t_{p}

表示客运列车超车引起的额外时间，min。

The single passenger train deduction coefficient consists of basic deduction coefficient and additional deduction coefficient. The basic deduction coefficient is generated by the train’s arrival and departure intervals, and the additional start-stop time of train. The additional deduction coefficient is caused when the ratio between the running time of passenger and freight trains is not an integral multiple of the interval of trailing train. The single passenger train deduction coefficient can be expressed as formula (17) (Zhu et al., 2023).(17)

ε = ε_{b} + ε_{a} = \frac{I_{a} + I_{d} + t_{a}}{I} + \frac{t_{p}}{I}

Where,

ε

represents the single passenger train deduction coefficient;

ε_{b}

represents the basic deduction coefficient;

ε_{a}

represents additional deduction coefficient;

I_{a}

and

I_{d}

represents the arrival and departure intervals of train, min;

t_{a}

represents the additional start-stop time of train, min;

t_{p}

represents additional time caused by passenger train overtaking;

I

represents the interval of the trailing train, min.
单列客运列车扣减系数由基本扣减系数和附加扣减系数组成。基本扣除系数由列车的到达和出发间隔以及列车的额外起停时间得出。当客货列车运行时间之比不是尾随列车间隔的整数倍时，会产生加扣系数。单列客运列车扣除系数可以表示为公式（17）（Zhu et al.， 2023）。 (17)

ε = ε_{b} + ε_{a} = \frac{I_{a} + I_{d} + t_{a}}{I} + \frac{t_{p}}{I}

其中，

ε

表示单列客运列车扣减系数;

ε_{b}

表示基本扣除系数;

ε_{a}

表示附加扣除系数;

I_{a}

，

I_{d}

表示火车的到达和出发间隔，min;

t_{a}

表示列车的额外启停时间，min;

t_{p}

表示客运列车超车造成的额外时间;

I

表示尾随列车的间隔 min。

The multiple train deduction coefficient is calculated base on the single train deduction coefficient, considering the factors such as the number of passenger trains, consecutive and non-consecutive trains, and the interval between passenger trains, which is expressed as follows (Jia and Xu, 2013)(18)

E = \frac{n_{nc} t_{e} + \sum_{j}^{J} n_{c} J_{c}}{n_{p} I}

(19)

n_{nc} = n_{p} - \sum_{j}^{J} n_{c}

where, E represents the multiple passenger train deduction coefficient;

n_{c}

and

n_{nc}

are the number of consecutive and non-consecutive trains, respectively;

t_{e}

represents the time taken by single passenger express crossing freight train;

J_{c}

is the interval of the consecutive passenger train, min; j and J are the minimum and maximum interval of the consecutive passenger train, min;

n_{p}

represents the number of passenger trains, columns.
多列扣减系数是根据单列扣减系数计算的，考虑了客运列车数量、连续和非连续列车、客运列车间隔等因素，表示如下（Jia and Xu， 2013）， (18)

E = \frac{n_{nc} t_{e} + \sum_{j}^{J} n_{c} J_{c}}{n_{p} I}

(19)

n_{nc} = n_{p} - \sum_{j}^{J} n_{c}

其中，E表示多列列车扣减系数;

n_{c}

和

n_{nc}

分别是连续和非连续列车的编号;

t_{e}

表示单人快速穿越货运列车所用的时间;

J_{c}

是连续客运列车的间隔，min;j 和 J 是连续客运列车的最小和最大间隔，min;

n_{p}

表示客运列车、列的数量。

Since the coefficient varies with the ratio and gap between the running times of passenger and freight trains, combined with the railway operation in China, the multiplication of

ε

with the corresponding parameter a is used as an approximation of the multiple train deduction coefficient. The value of the parameter a depends on the number of passenger trains and the interval time of the trailing freight train (Jia and Xu, 2013). Formula (20) and formula (21) demonstrate the calculation of the multiple and single deduction coefficients, respectively, which are applied in this study.(20)

E = ε a = ε [1.07 - 5.3 \times 10^{- 3} n_{p} + 10^{- 5} n_{p}^{2}]

(21)

ε = 2 Δ + 0.05 - 0.0375 t_{d} + (1.025 t_{d} + 3.6) / I

Where, E represents the multiple passenger train deduction coefficient;

ε

represents the single passenger train deduction coefficient; a is the parameter;

n_{p}

represents the number of passenger trains, columns;

Δ

and

t_{d}

are the ratio and gap between the running time of passenger and freight trains, respectively, min;

I

represents the interval of the trailing train, min.
由于该系数随客运列车和货运列车运行时间之间的比率和间隙而变化，结合我国的铁路运营，将的

ε

乘以相应参数 a 用作多列列车扣除系数的近似值。参数 a 的值取决于客运列车的数量和尾随货运列车的间隔时间（Jia 和 Xu，2013）。公式（20）和公式（21）分别演示了本研究中应用的倍数和单项扣除系数的计算。 (20)

E = ε a = ε [1.07 - 5.3 \times 10^{- 3} n_{p} + 10^{- 5} n_{p}^{2}]

(21)

ε = 2 Δ + 0.05 - 0.0375 t_{d} + (1.025 t_{d} + 3.6) / I

其中，E 表示多班客运列车扣除系数;

ε

代表单列客运列车扣除系数;a 是参数;

n_{p}

表示客运列车的数量，列;

Δ

和

t_{d}

分别是客运和货运列车运行时间之间的比率和差距，min;

I

表示尾随列车的间隔 min。

4. Case study 4. 案例研究

The construction of HSR in the Yangtze River Delta is taken as a case to calculate the released freight capacity after its construction. In 2022, the Yangtze River Delta has accelerated the construction of HSR network, with over 130 km of newly-built HSR, and the total mileage of HSR in operation exceed 6,600 km. The under-construction and planned HSR network in the Yangtze River Delta are shown in Fig. 3.
以长三角高铁建设为例，计算建成后释放的运力。2022 年，长三角加快高铁网络建设，新建高铁超过 130 公里，高铁运营总里程超过 6,600 公里。长江三角洲在建和规划中的高铁网络如图 3 所示。

4.1. Passenger flow split rate
4.1. 客流分摊率

To calculate the passenger flow split rate of travel modes, the utility of HSR and existing railways in the Yangtze River Delta should be obtained firstly. In the calculation of travel cost, the fare rate of HSR and the existing railways are taken as 0.46 yuan/km and 0.18 yuan/km, respectively (Wu, 2011). In the calculation of travel time, the running speed of HSR and existing railways are taken as 300 km/h and 80 km/h, respectively. The travelers’ waiting time is taken as 0.5 h on average (Wang et al., 2018). In the calculation of the time value of travelers, the data of population and GDP are taken from Statistical Yearbook of each province in 2021, and the regional labor time on average was taken from the China Labor Statistical Yearbook in 2021, which is 47 h/week. Yang et al. obtained the sensitivities of the indicators in equation (5) by collecting 168 valid questionnaires and the sensitivities of the indicators in equation (5) are calibrated as −2.719, −9.461 and −0.217, which is applicable to the Yangtze River Delta (Yang et al., 2022).
要计算出行方式的客流分流率，应首先获得高铁与长三角现有铁路的效用。在计算出行成本时，高铁和现有铁路的票价分别为 0.46 元/公里和 0.18 元/公里（Wu，2011）。在计算行驶时间时，高铁和现有铁路的运行速度分别为 300 公里/小时和 80 公里/小时。旅行者的等待时间平均为 0.5 小时（Wang et al.， 2018）。在计算出行时间价值时，人口和 GDP 数据取自各省份 2021 年统计年鉴，区域平均劳动时间取自 2021 年中国劳动统计年鉴，为 47 小时/周。Yang et al. 通过收集 168 份有效问卷获得了方程（5）中指标的敏感性，并将方程（5）中指标的敏感性校准为 −2.719、−9.461 和 −0.217，适用于长江三角洲（Yang et al.， 2022）。

The utility and passenger flow split rate of travel modes are calculated via Utility function and Logit model. The utility and split rate of travel modes between selected ODs are shown in Table 3, where

m_{1}

and

m_{2}

represent the newly-built HSR and the existing general-speed railways, respectively.
出行模式的效用和客流拆分率是通过效用函数和 Logit 模型计算的。表 3 显示了所选 OD 之间出行模式的效用和拆分率，其中

m_{1}

和

m_{2}

分别代表新建的高铁和现有的通用高速铁路。

Table 3. Utility and Split rate of travel modes.
表 3.Utility 和 Split rate of travel modes.

OD	Cost 成本		Time 时间		Comfort 安慰		Split rate 分摊率
OD	$J_{m_{1}}$	$J_{m_{2}}$	$F_{m_{1}}$	$F_{m_{2}}$	$C_{m_{1}}$	$C_{m_{2}}$	$P_{m_{1}}$	$P_{m_{2}}$
Xinyi-Suzhou 信义-苏州	85.10	33.30	12.32	31.02	6.81	2.66	0.651	0.349
Hefei-Nanjing 合肥-南京	76.36	29.88	35.58	86.98	6.11	2.39	0.798	0.202
Suzhou-Shanghai 苏州-上海	44.16	17.28	30.56	63.35	3.53	1.38	0.783	0.217
Hangzhou-Jiaxing 杭州-嘉兴	40.94	16.02	23.19	46.94	3.28	1.28	0.761	0.239
Jinhua-Wenzhou 金华-温州	110.86	43.38	21.33	57.49	8.87	3.47	0.721	0.279
Taizhou-Huaian 台州-淮安	309.58	121.14	56.98	185.11	24.77	9.69	0.768	0.232
Nantong-Ningbo 南通-宁波	152.72	59.76	50.51	146.19	12.22	4.78	0.810	0.190
Fuyang-Bengbu 富阳-蚌埠	83.26	32.58	11.45	28.67	6.66	2.61	0.640	0.360
Huzhou-Yangzhou 湖州-扬州	99.36	38.88	32.87	86.22	7.95	3.11	0.784	0.216
Xuancheng-Huaibei 宣城-怀北	212.06	82.98	29.40	90.41	16.96	6.64	0.706	0.294

The passenger flow in the Yangtze River Delta is obtained from survey and multiplied by passenger flow split rate of the existing railways. The passenger flow of existing railways after the diversion of HSR is shown in Table 4.
长三角的客流是通过调查得到的，并乘以现有铁路的客流分流率。高铁改道后现有铁路的客流量如表 4 所示。

Table 4. Passenger flow of existing railways after diversion (Unit: people).
表 4.现有铁路改道后的客流（单位：人）。

Empty Cell	Hefei 合肥	Nanjing 南京	Wuxi 无锡	Suzhou 苏州	Shanghai 上海	Hangzhou 杭州	Jiaxing 嘉兴	Jinhua 金华	Wenzhou 温州	Nantong 南通	Ningbo	Bengbu	Wuhu	Xuzhou	Yangzhou
Hefei 合肥	0	1,000	2,551	529	594	858	62	157	234	46	192	362	4,685	1,248	85
Nanjing 南京	1,060	0	10,297	1,990	2,213	1,063	294	298	322	72	278	1,025	1,472	6,021	394
Wuxi 无锡	2,830	8,783	0	8,514	9,109	1,765	1,438	515	607	202	531	2,558	705	3,244	1,175
Suzhou 苏州	510	1942	10,292	0	2,654	450	452	134	130	33	126	654	641	3,723	244
Shanghai 上海	663	2,260	11,321	2,590	0	1,716	1,569	905	375	301	308	713	757	5104	326
Hangzhou 杭州	918	1,103	1,953	447	1,744	0	1,633	1,698	978	59	868	254	1,629	4,354	66
Jiaxing 嘉兴	308	340	1,536	422	1,489	1,179	0	1,173	440	41	409	123	164	829	31
Jinhua 金华	157	311	591	147	890	1,078	1,061	0	678	8	182	107	514	503	8
Wenzhou 温州	242	330	493	114	368	1,069	319	784	0	33	503	127	653	415	24
Nantong 南通	31	118	36	145	401	72	80	39	25	0	14	58	88	629	228
Ningbo 宁波	237	376	581	152	435	1,287	360	199	647	46	0	105	629	669	28
Bengbu 蚌埠	656	673	1,286	279	383	436	37	125	159	9	119	0	926	4,532	36
Wuhu 芜湖	5,156	4,163	2,215	1,800	2,115	5,308	88	1,143	1,019	50	679	188	0	364	429
Xuzhou 徐州	1,750	8,668	4,508	5,273	7,000	2,955	979	515	579	869	555	4,656	314	0	995
Yangzhou 扬州	85	491	1,365	289	361	73	54	28	40	256	28	36	429	857	0

4.2. Passenger flow allocation model
4.2. 客流分配模型

The improved FW algorithm with One-OD-at-a-time strategy is compared with the traditional All-at-once strategy to verify the effectiveness of improved FW algorithm, in which the accuracy is set to 10^-4, as shown in Fig. 4. The FW algorithm with One-OD-at-a-time strategy converges faster in the early stage with fewer iterations. The passenger flow on the existing railways after diversion is allocated to the sections of existing railways which is shown in Fig. 5.
将采用 One-OD-at-a-time 策略的改进 FW 算法与传统的 All-at-once 策略进行比较，以验证改进 FW 算法的有效性，其中精度设置为 ^10-4，如图 4 所示。采用 One-OD-at-a-a 策略的 FW 算法在早期收敛更快，迭代次数更少。改道后现有铁路的客流被分配到现有铁路的路段，如图 5 所示。

4.3. Freight capacity release
4.3. 运力释放

The total capacity of existing railways is calculated first. The respective daily capacity of existing railways is 150 trains theoretically (Yang et al., 2022). The passenger flow is converted into the number of passenger trains. According to research, the capacity of high-speed train in in the Yangtze River Delta is 952 people on average and the attendance rate is about 60 %, thus the passenger capacity of existing general-speed train is taken as 600 persons/train. Finally, the passenger trains after diversion are converted into freight trains according to the deduction coefficient method, and the capacity occupied by these trains is deducted from the total capacity of existing railways to obtain the freight capacity of sections after released. Similarly, the initial freight capacity of sections before released is obtained. The freight capacity after released is compared with the initial freight capacity and the released freight capacity is obtained, which is shown in Table 5.
首先计算现有铁路的总容量。理论上，现有铁路的日运力分别为 150 列火车（Yang et al.， 2022）。客流被转换为客运列车的数量。据研究，长三角地区的高速列车平均载客量为 952 人，上座率约为 60%，因此现有普速列车的载客量为 600 人/车。最后，将改道后的客运列车按照扣除系数法转换为货运列车，从现有铁路总运力中扣除这些列车占用的运力，得到释放后的区段货运能力。同样，获得下达前各段的初始货运能力。将释放后的运力与初始运力进行比较，得到释放的运力，如表 5 所示。

Table 5. Freight capacity on sections of existing railways.
表 5.现有铁路路段的货运能力。

Section nodes Section 节点	Passenger flow after diversion 改道后的客流	Passenger train after diversion 改道后的客运列车	Deducted freight train 扣除货运列车	Freight capacity after released 释放后的货运能力	Initial passenger trains 初始客运列车	Initial freight capacity 初始货运能力	Released freight capacity 释放的货运能力
Xinyi-Huaian 信义怀安	12,257	20	51	99	26	87	11
Suzhou-Bengbu 苏州-蚌埠	22,417	37	86	64	50	41	23
Hefei-Wuhu 合肥芜湖	25,871	43	98	52	67	13	39
Hefei-Liuan 合肥柳安	20,000	33	80	70	46	44	26
Nanjing-Wuxi 南京-无锡	27,957	47	104	46	74	10	36
Nanjing-Yangzhou 南京-扬州	15,837	26	65	85	31	76	10
Wuxi-Suzhou 无锡-苏州	30,917	52	112	38	75	7	31
Suzhou-Shanghai 苏州-上海	31,466	52	114	36	77	5	31
Shanghai-Jiaxing 上海-嘉兴	33,476	56	121	29	62	23	7
Jiaxing-Hangzhou 嘉兴-杭州	29,060	48	107	43	59	28	15
Hangzhou-Jinhua 杭州-金华	29,060	48	105	43	59	28	15
Hangzhou-Ningbo 杭州-宁波	17,966	30	72	78	34	70	8
Huzhou-Hangzhou 湖州-杭州	34,602	58	119	31	64	15	16
Wenzhou-Jinhua 温州-金华	13,582	23	56	94	26	86	8
Jinhua-Taizhou 金华-台州	2,531	4	11	139	13	116	23
Ningbo-Jinhua 宁波-金华	11,382	19	48	102	27	85	17
Taizhou-Wenzhou 台州-温州	3,554	6	15	135	19	102	32
Ningbo-Taizhou 宁波-台州	4,659	8	20	130	24	92	38
Yangzhou-Haian 扬州-海安	7,180	12	31	119	23	93	26
Huaibei-Fuyang 淮北富阳	9,323	16	40	110	23	92	18
Wuhu-Xuancheng 芜湖-宣城	28,113	47	103	47	52	37	10

After the construction of the HSR in the Yangtze River Delta, the freight capacity of each section on the existing railways will be released 12.5 pairs of freight trains on average. The freight capacity of Hefei-Wuhu section will be released the most, which is 19.5 pairs of trains, while that of Shanghai-Jiaxing section is the least, which is only 3.5 pairs, following by Wenzhou-Jinhua and Hangzhou-Ningbo sections, which are 4 pairs. Thus, it can be seen that the construction of the HSR in Yangtze River Delta has an obvious promoting effect on the release of freight capacity and the freight capacity of sections on existing railways in the Yangtze River Delta is released to varying degrees.
长三角高铁建设后，现有铁路上每段货运能力平均将释放 12.5 对货运列车。合肥至芜湖段的运力释放最多，为 19.5 对，而沪嘉段的运力最少，仅为 3.5 对，其次是温金和杭甬段，均为 4 对。由此可见，长三角高铁建设对运力释放具有明显的促进作用，长三角既有铁路段运力得到不同程度的释放。

5. Results and discussion
5. 结果和讨论

The results obtained in this study will be compared with the current freight capacity utilization of the Yangtze River Delta railway network.
本研究获得的结果将与目前长三角铁路网的货运能力利用率进行比较。

1) Xinyi-Huainan, Jiaxing-Shanghai, Hangzhou-Jiaxing, Hangzhou-Ningbo, Wuhu-Xuancheng, Wenzhou-Jinhua and other sections have less freight capacity release. While these sections also have saturated freight capacity in the realistic freight railway transportation that the utilization rate of capacity are above 75 %. In particular, the freight capacity of the Shanghai-Kunming line and the Jinhua-Wenzhou freight line has been severely strained, and the capacity utilization rate has reached 100 % already. The planned HSR currently has limited effect on the capacity release of above sections. In the subsequent planning, the release of freight capacity in these sections should be focused on.
1）信义-淮南、嘉兴-上海、杭州-嘉兴、杭-甬、芜湖-宣城、温州-金华等航段运力释放较少。虽然这些路段在实际货运铁路运输中也具有饱和的货运能力，但运力利用率都在 75% 以上。特别是沪昆线和金华-温州货运线的货运能力受到严重压力，运力利用率已达到 100%。计划中的高铁目前对上述路段的容量释放影响有限。在后续规划中，应重点关注这些部分的货运能力释放。

2) The Beijing-Shanghai railway, one of the most critical transportation corridors in China, is currently facing severe capacity constraints in freight transportation, with a utilization rate exceeding 90 %, approaching its maximum limit. Upon the completion of the HSR, various sections along the Beijing-Shanghai line, particularly those sections like Nanjing-Wuxi, Wuxi-Suzhou, and Suzhou-Shanghai, will experience a significant release in freight capacity, with an expected increase of over 15 pairs of freight trains. However, the section of Bengbu-Suzhou will see a more limited increase, with only 8 pairs of additional freight trains, potentially creating a bottleneck for the entire Beijing-Shanghai line.
2）京沪铁路作为中国最重要的运输走廊之一，目前货物运输容量严重受限，利用率超过 90%，接近极限。高铁建成后，京沪线沿线各路段，尤其是南京至无锡、无锡至苏州和苏州至上海等路段，货运运力将显著释放，预计将增加超过 15 对货运列车。然而，蚌埠至苏州的路段将出现更有限的增长，仅增加 8 对货运列车，这可能会给整个京沪线造成瓶颈。

3) The Nanjing-Wuxi and Wuhu-Hefei sections currently have freight capacity utilization rates of 72.6 % and 94.7 %, respectively, nearing saturation. The construction of the HSR will significantly boost the freight capacity of these two sections, with an anticipated increase of 18 and 19 pairs of freight trains respectively, effectively alleviating the current capacity constraints.
3）南京—无锡和芜湖—合肥段目前的运力利用率分别为 72.6% 和 94.7%，接近饱和。高铁的建设将显著提高这两个路段的货运能力，预计将分别增加 18 对和 19 对货运列车，有效缓解目前的运力限制。

4) In other regions where freight capacity is relatively sufficient, such as the Huzhou-Hangzhou section, which has a utilization rate of 53.7 %, the additional capacity released by the HSR can serve as a reserve to meet the future growth in demand for sea-rail intermodal transport, thereby laying a solid foundation for regional economic development.
4）在其他货运能力相对充足的地区，如湖杭段，利用率为 53.7%，高铁释放的额外运力可以作为储备，满足未来海铁联运需求的增长，从而为区域经济发展奠定坚实的基础。

6. Conclusions 6. 结论

6.1. Conclusion 6.1. 总结

This study focuses on the released fright capacity of each section on existing railways due to the releasing effect of the newly-built HSR. Logit model is established to calculate the passenger flow split rate. The passenger flow allocation model is solved by the improved FW algorithm with One-OD-at-a-time flow update strategy which converge faster, and the effectiveness and superiority of the algorithm are verified. The passenger flow after diversion is allocated to each section of the existing railways, which obtain the capacity release from a more microscopic perspective, instead of the capacity release of the macro channel. Based on deduction coefficient, a method is proposed for measuring the freight capacity release of sections on existing railways due to the construction of HSR routes in realistic railway network. This method is suitable for large-scale networks in reality and can also be used in other geographical regions. Yangtze River Delta is taken as a case, the released freight capacity of existing railways after the construction of HSR in the Yangtze River Delta is calculated, and the following conclusions are obtained:
本研究侧重于由于新建高铁的释放效应而释放的现有铁路上每个路段的恐惧容量。建立 Logit 模型来计算客流分流率。采用收敛速度较快的 One-OD-at-time 流更新策略，采用改进的 FW 算法对客流分配模型进行求解，验证了该算法的有效性和优越性。改道后的客流被分配到现有铁路的每个路段，从更微观的角度获得运力释放，而不是宏观通道的运力释放。基于推导系数，提出了一种测量现实铁路网络中高铁线路建设导致现有铁路路段运力释放的方法。这种方法适用于现实中的大规模网络，也可以在其他地理区域使用。以长三角为例，计算了长三角高铁建设后既有铁路释放的货运运力，得出以下结论：

1) The construction of HSR has obvious diversion effect on the passenger flow of existing railways. The passenger flow split rate is related to the travel cost, time, comfort and other utility indicators of travel modes. HSR with higher utility induces a greater probability of travelers’ choice and stronger diversion effect of passengers from existing railways.
1）高铁的建设对现有铁路的客流具有明显的分流效应。客流分摊率与出行方式的出行成本、时间、舒适度等效用指标有关。实用性较高的高铁诱导了更大的旅客选择概率和更强的现有铁路乘客分流效应。

2) The increase of travel distance leads to a higher utility of HSR compared with general-speed railways. Thus, HSR carries a greater proportion of long-distance transportation, while general-speed railway is inclined to carry short or medium-distance transportation. According to the utility function and Logit model, the increase in the operating speed of HSR and reduction in fares are conducive to attracting more passengers and enhancing the passenger flow split rate of HSR in the transport corridor.
2）与一般高速铁路相比，行驶距离的增加导致 HSR 的实用性更高。因此，高铁承载的长途运输比例更大，而普铁倾向于承载短途或中途运输。根据效用函数和 Logit 模型，高铁运营速度的提高和票价的降低有利于吸引更多乘客并提高高铁在运输走廊的客流分流率。

3) According to the passenger flow allocation model, after the transfer of passenger flow from existing railways to HSR, the reduction of passenger flow on existing railways will divert part of passenger flow from surrounding railway sections, and the freight capacity of these sections around the corridor will be released to a certain extent accordingly.
3）根据客流分配模型，在现有铁路将客流转移到高铁后，现有铁路客流的减少将使部分客流从周围的铁路路段分流，走廊周围这些路段的货运能力将在一定程度上得到相应释放。

4) The FW algorithm is improved by adopting the One-OD-at-a-time strategy, and the improved FW algorithm converges faster in the early stage with fewer iterations. When the accuracy is set to 10^-4, obvious oscillation occurs, and the effect of the accuracy setting on the convergence of the FW algorithm can be studied subsequently.
4）采用 One-OD-at-a a 策略对 FW 算法进行了改进，改进的 FW 算法在早期收敛更快，迭代次数更少。当精度设置为 ^10-4 时，会出现明显的振荡，后续可以研究精度设置对 FW 算法收敛的影响。

5) The operation of the HSR in the Yangtze River Delt is of great significance to enhance the freight capacity of existing railways, releasing 12.5 pairs of freight trains in each section on average. The released freight capacity in Shanghai-Jiaxing section is the least, followed by Wenzhou-Jinhua section and Hangzhou-Ningbo section, which will largely limit the overall freight capacity of network. Therefore, it is essential to consider the enhance measures of freight capacity in these sections while constructing the HSR in the Yangtze River Delt.
5）长江代尔特高铁的运营对提升现有铁路的货运能力具有重要意义，平均每段释放 12.5 对货运列车。沪嘉路段释放的运力最少，其次是温州-金华路段和杭甬路段，这将在很大程度上限制网络的整体运力。因此，在长江三角洲建设高铁时，必须考虑加强这些路段的货运能力措施。

The construction of HSR can effectively release the freight capacity of existing railways, however, the released freight capacity varies greatly in different sections. Furthermore, the overall released freight capacity is limited due to the fact that the railway capacity is mainly limited by the restricted sections. To alleviate the tension of railway freight capacity in the Yangtze River Delta and promote the realization of shifting freight flow from roads to rails, it is inevitable to emphasis the construction of freight railway or mixed passenger and freight railway.
高铁的建设可以有效释放现有铁路的货运能力，但不同路段释放的货运能力差异很大。此外，由于铁路运力主要受限制路段的限制，因此整体释放的货运能力受到限制。为缓解长三角铁路货运能力紧张局势，推动实现货流由公路转轨，重点建设货运铁路或客货混合铁路是必然的。

Nevertheless, the research is based on current data and does not account for potential future changes in freight demand or technological advancements that could affect railway operations. The study assumes a linear relationship between capacity release and the number of freight trains, which may oversimplify the complex interactions within the railway network. Due to the complexity of the factors affecting the travelers’ choice behavior, the impact of HSR on the passenger flow of existing railways is focused on, which in turn promotes the release of freight capacity. While passenger flow is impacted by factors including highways, self-driving cars and travel characteristics of passengers at different time as well, which will be investigated in depth in the future.
尽管如此，该研究基于当前数据，并未考虑可能影响铁路运营的货运需求或技术进步的未来潜在变化。该研究假设运力释放与货运列车数量之间存在线性关系，这可能会过度简化铁路网络内复杂的交互。由于影响旅客选择行为的因素复杂，HSR 对现有铁路客流的影响受到关注，进而促进货运运力的释放。而客流也受到高速公路、自动驾驶汽车和不同时期乘客出行特性等因素的影响，未来将对此进行深入研究。

6.2. Policy recommendations
6.2. 策略建议

1) In highly saturated sections like Xinyi-Huainan, Jiaxing-Shanghai, Hangzhou-Jiaxing, Hangzhou-Ningbo, and Wenzhou-Jinhua, expedite the construction of dedicated freight lines or upgrade existing lines. For critical routes like the Shanghai-Kunming and Jinhua-Wenzhou lines, consider adding double-track freight corridors or constructing parallel lines to meet growing demand.
1）在信沂—淮南、嘉兴—上海、杭—嘉兴、杭—甬、温金等高饱和路段，加快建设货运专线或升级现有线路。对于上海-昆明和金华-温州线等关键路线，考虑增加双轨货运走廊或建设平行线路，以满足不断增长的需求。

2) In bottleneck sections such as Bengbu-Suzhou, improve freight train dispatching through intelligent scheduling systems, maximizing the utilization of existing capacity. Implement off-peak freight operations, particularly during nighttime, to leverage underutilized capacity and reduce interference with passenger services.
2）在蚌埠-苏州等瓶颈路段，通过智能调度系统改善货运列车调度，最大限度地利用现有运力。实施非高峰货运运营，尤其是在夜间，以利用未充分利用的运力并减少对客运服务的干扰。

3) In areas with sufficient capacity, like the Huzhou-Hangzhou section, strengthen multimodal transport infrastructure, particularly the integration of rail with ports and highways. Establish container terminals and logistics hubs at key nodes to facilitate the shift from road to rail transport. Improve the efficiency of freight hubs around major cities (e.g., Shanghai, Nanjing, Hangzhou) to better connect railways with ports, warehouses, and industrial parks, reducing transit times and costs.
3）在运力充足的地区，如湖杭段，加强多式联运基础设施，特别是铁路与港口和高速公路的整合。在关键节点建立集装箱码头和物流枢纽，促进公路运输向铁路运输的转变。提高主要城市（如上海、南京、杭州）周围货运枢纽的效率，以更好地将铁路与港口、仓库和工业园区连接起来，从而减少运输时间和成本。

4) With the deepening of the supply-side structural reform of China’s transportation, it is a trend for freight flow to be transferred from road to rail in order to promote energy saving and emission reduction in the transportation industry. While constructing HSR, attention should be paid to the capacity development of freight railways, achieving compromise between passenger and freight.
4）随着我国交通运输供给侧结构性改革的深入，为促进交通运输行业节能减排，货物流由公路转轨是大势所趋。在建设高铁的同时，应关注货运铁路的容量建设，实现客货之间的妥协。

5) While planning the construction of HSR, it is essential to consider the passenger diversion effect on existing railways, and Gaining adaptability between the freight capacity of existing railways and the future demand for shifting freight flow from road to rail. Optimize the layout planning of freight railway to avoid insufficient freight capacity and the phenomenon of virtual exhaustion, and give full play to the efficiency and effectiveness of railway investment.
5）在规划高铁建设时，必须考虑对现有铁路的客流分流影响，并在现有铁路的货运能力与未来将货物流从公路转移到铁路的需求之间获得适应性。优化货运铁路的布局规划，避免货运运力不足和虚拟耗尽的现象，充分发挥铁路投资的效率和效果。

6) The diversionary effect of the HSR depends on the density of passenger flow in different zones, and there is difference between the released capacity of different sections. Therefore, when the government departments carry out the railway planning, targeted attention should be paid to the sections with tight freight transportation capacity. And there are two available ways: diverse passengers from existing railways through the construction of HSR and construct general-speed railways, making scientific policy decision.
6）高铁的分流效应取决于不同区间的客流密度，不同路段的释放容量存在差异。因此，政府部门在进行铁路规划时，应有针对性地关注货物运输能力紧张的路段。并且有两种方式：通过高铁建设从现有铁路的多样化乘客和建设普高速铁路，做出科学的政策决策。

7) It should be noted that, in addition to choosing the travel mode with the greatest utility, passengers are also affected by the passenger transport products such as train timetable. With the goal of fully utilizing the capacity, various train timetable should be conducted through the design of train operation plan on different line, and guide travelers’ choice behavior. The split rate between HSR and existing railway should be adjusted through “driving and diverting” to further release the freight capacity of existing railways.
7）需要注意的是，除了选择实用性最大的出行方式外，乘客还会受到火车时刻表等客运产品的影响。在充分利用运力的前提下，通过设计不同线路的列车运行计划，制定各种列车时刻表，引导旅客的选择行为。高铁与现有铁路的分运价应通过“驾驶和分流”进行调整，以进一步释放现有铁路的货运能力。

CRediT authorship contribution statement
CRediT 作者贡献声明

Chuanzhong Yin: Writing – review & editing, Writing – original draft, Project administration, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization. Xiaoxue Feng: Writing – review & editing, Writing – original draft, Software, Methodology, Conceptualization.
尹传中：写作 - 审查和编辑，写作 - 原始草稿，项目管理，方法论，资金获取，正式分析，数据管理，概念化。小雪峰：写作 - 审查和编辑，写作 - 原始草稿，软件，方法论，概念化。

Declaration of competing interest
利益争夺声明

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者声明，他们没有已知的竞争性经济利益或个人关系，这些利益或个人关系似乎可能会影响本文报告的工作。

Acknowledgements 确认

This work was supported by the Humanities and Social Sciences Fund of Ministry of Education of People's Republic of China [Grant 23YJA630120]; the Key Project of Technologies Research & Development Program of China State Railway Group Co., Ltd. [Grant N2023X023]; and National Natural Science Foundation of China [Grant 72074141].
这项工作得到了中华人民共和国教育部人文和社会科学基金 [Grant 23YJA630120] 的支持;中国国家铁路集团有限公司技术研发计划重点项目 [Grant N2023X023];和中国国家自然科学基金 [Grant 72074141]。

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Zhu et al., 2023
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Outline 大纲

Figures (5) 手办（5）

Tables (5) 桌子（5）

Case Studies on Transport Policy
交通政策案例研究

Highlights 突出

Abstract 抽象

Keywords 关键字

1. Introduction 1. 引言

2. Literature review 2. 文献综述

3. Materials and methods 3. 材料和方法

3.1. Utility function of travelers’ choice behavior
3.1. 旅客选择行为的效用函数

3.2. Logit model of passenger travel choices
3.2. 乘客出行选择的 Logit 模型

3.3. Passenger flow allocation model
3.3. 客流分配模型

3.3.1. Notations 3.3.1. 符号

3.3.2. Assumptions 3.3.2. 假设

3.3.3. Mathematical model
3.3.3. 数学模型

3.3.4. Solution algorithm
3.3.4. 解算法

3.4. Freight capacity release
3.4. 运力释放

4. Case study 4. 案例研究

4.1. Passenger flow split rate
4.1. 客流分摊率

4.2. Passenger flow allocation model
4.2. 客流分配模型

4.3. Freight capacity release
4.3. 运力释放

5. Results and discussion
5. 结果和讨论

6. Conclusions 6. 结论

6.1. Conclusion 6.1. 总结

6.2. Policy recommendations
6.2. 策略建议

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益争夺声明

Acknowledgements 确认

References

Cited by (0)

Case Studies on Transport Policy交通政策案例研究

Impact of high-speed railway construction on freight capacity on sections of existing railways- A case on the Yangtze River Delta高速铁路建设对既有铁路路段货运能力的影响——以长三角为例

Highlights 突出

Abstract 抽象

Keywords 关键字

1. Introduction 1. 引言

2. Literature review 2. 文献综述

3. Materials and methods 3. 材料和方法

3.1. Utility function of travelers’ choice behavior3.1. 旅客选择行为的效用函数

3.2. Logit model of passenger travel choices3.2. 乘客出行选择的 Logit 模型

3.3. Passenger flow allocation model3.3. 客流分配模型

3.3.1. Notations 3.3.1. 符号

3.3.2. Assumptions 3.3.2. 假设

3.3.3. Mathematical model3.3.3. 数学模型

3.3.4. Solution algorithm3.3.4. 解算法

3.4. Freight capacity release3.4. 运力释放

4. Case study 4. 案例研究

4.1. Passenger flow split rate4.1. 客流分摊率

4.2. Passenger flow allocation model4.2. 客流分配模型

4.3. Freight capacity release4.3. 运力释放

5. Results and discussion5. 结果和讨论

6. Conclusions 6. 结论

6.1. Conclusion 6.1. 总结

6.2. Policy recommendations6.2. 策略建议

CRediT authorship contribution statementCRediT 作者贡献声明

Declaration of competing interest利益争夺声明

Acknowledgements 确认

References

Case Studies on Transport Policy
交通政策案例研究

Impact of high-speed railway construction on freight capacity on sections of existing railways- A case on the Yangtze River Delta
高速铁路建设对既有铁路路段货运能力的影响——以长三角为例

3.1. Utility function of travelers’ choice behavior
3.1. 旅客选择行为的效用函数

3.2. Logit model of passenger travel choices
3.2. 乘客出行选择的 Logit 模型

3.3. Passenger flow allocation model
3.3. 客流分配模型

3.3.3. Mathematical model
3.3.3. 数学模型

3.3.4. Solution algorithm
3.3.4. 解算法

3.4. Freight capacity release
3.4. 运力释放

4.1. Passenger flow split rate
4.1. 客流分摊率

4.2. Passenger flow allocation model
4.2. 客流分配模型

4.3. Freight capacity release
4.3. 运力释放

5. Results and discussion
5. 结果和讨论

6.2. Policy recommendations
6.2. 策略建议

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益争夺声明