Travel Plan Sharing and Regulation for Managing Traffic Bottleneck Based on Blockchain Technology

Abstract

To alleviate traffic congestion, it is necessary to effectively manage traffic bottlenecks. In existing research, travel demand prediction for traffic bottlenecks is based on travel behavior assumptions, and prediction accuracy is low in practice. Thus, the effect of traffic bottleneck management strategies cannot be guaranteed. Management strategies are often mandatory, leading to problems such as unfairness and low social acceptance. To address such issues, this paper proposes managing traffic bottlenecks based on shared travel plans. To solve the information security and privacy problems caused by travel plan sharing and achieve information transparency, travel plans are shared and regulated by blockchain technology. To optimize the operation level of traffic bottlenecks, travel plan regulation models under scenarios where all/some travelers share travel plans are proposed and formulated as linear programming models, and these models are integrated into the blockchain with smart contract technology. Furthermore, travel plan regulation models are tested and verified using traffic flow data from the Su-Tong Yangtze River Highway Bridge, China. The results indicate that the proposed travel plan regulation models are effective for alleviating traffic congestion. The vehicle transfer rate and total delay rate increase as the degree of total demand increases; the vehicle transfer rate increases as the length of the time interval decreases; and the vehicle transfer rate and total delay rate increase as the number of vehicles not sharing their travel plans increases. By using the model and method proposed in this paper, the sustainability of urban economy, society, and environment can be promoted. However, there are many practical situations that have not been considered in this paper, such as multiple entry and exit bottlenecks, multiple travel modes, and other control strategies. In addition, this paper considers only one bottleneck rather than road networks because of the throughput limitations of blockchain technology.

1. Introduction

Traffic congestion has become an important global problem that restricts the sustainability of urban economy and society. Vehicle exhaust emissions caused by traffic congestion also restrict the achievement of environment sustainability. Thus, to promote the sustainability of urban economy, society, and environment, it is important to alleviate traffic congestion. Due to factors such as the nature of land use and residents’ daily commuting habits, locations that are prone to traffic congestion during daily and holiday periods are generally fixed and concentrated, namely, traffic bottlenecks. Therefore, to alleviate or solve traffic congestion problems, the effective management of traffic bottlenecks is necessary.

The premise for the effective management of traffic bottlenecks is to accurately analyze the behavior of travelers and predict travel demand at bottlenecks. The first traffic bottleneck model for analyzing travel behavior was proposed by Vickrey [1]. In this model, it is assumed that there is a road connecting residential and work areas, with a bottleneck with limited capacity on the road (such as a bridge, a tunnel, a ramp, or another feature). Except for the bottleneck, the capacity of other road segments is sufficient. When the arrival rate at the bottleneck exceeds the bottleneck capacity, a queue is formed. Furthermore, many researchers have extended and improved this model by considering features such as user heterogeneity, multiple travel modes, and travel chains [2,3,4]. Although the bottleneck model is constantly improving, it is still difficult to match real conditions, and there are significant errors in the analysis and prediction of travel behavior based on the bottleneck model.

Based on the analysis of travel behavior at traffic bottlenecks, many researchers have conducted research on control measures for traffic bottlenecks. The most studied topic is congestion pricing for traffic bottlenecks [5,6,7]. Many researchers have also studied management strategies from other perspectives, such as optimizing parking fees, parking capacity, working hours, speed limits, and other management measures [8,9,10,11]. The above traffic bottleneck management strategies are often mandatory measures, and due to differences in the nature of work and income levels of travelers, problems such as unfairness and low social acceptance persist. Additionally, many travelers believe that traffic managers do not develop corresponding strategies to address traffic problems but rather consider other interests, such as increasing the fiscal revenue of government departments. Therefore, they are often resistant to these regulatory strategies, leading to a lack of trust in traffic managers. In addition, traffic bottleneck management strategies are often based on the prediction of travel behavior, and the accuracy of this approach is low in practice. Therefore, the expected effect cannot be achieved through the implementation of management strategies.

In summary, the existing research on traffic bottlenecks has the following shortcomings: (a) travel demand is predicted by a bottleneck model constructed based on travel behavior assumptions, resulting in low prediction accuracy in practical applications; (b) the implementation effect of current traffic bottleneck management strategies is often based on the prediction of travelers’ behaviors; thus, neither the prediction accuracy nor the model implementation effect can be guaranteed; and (c) the current traffic bottleneck management strategies are often mandatory measures, with a certain degree of unfairness. Travelers normally distrust managers, and social acceptance is not very high.

To improve the accuracy of travel demand prediction, the traffic demand is predicted in this paper based on shared travel plans (i.e., the planned arrival time at the considered bottleneck). Furthermore, the behavior of travelers is regulated from the planning level based on the constructed travel plan regulation model, and travelers are free to choose whether to accept regulatory suggestions to change their travel plans, which is not mandatory. However, sharing travel plans poses potential data privacy and information security issues. Blockchain technology has been used to obtain valuable research results in the field of information sharing. One of the advantages of blockchain technology is that it can effectively solve information security problems and protect the personal privacy of travelers. Therefore, a travel plan sharing and regulation system is constructed for traffic bottleneck management based on blockchain technology, which effectively solves potential problems related to information security and privacy caused by travel plan sharing. The travel plan regulation model is integrated into the constructed blockchain system using smart contract technology, effectively achieving transparency in the regulation process and increasing travelers’ trust in managers. The main contributions of this paper are twofold:

(1) Traffic bottleneck is managed using shared travel plan data. In addition, to solve potential problems related to information security and privacy, blockchain technology is adopted. (2) Traffic bottleneck travel plan regulation models are constructed considering scenarios in which all travelers and some travelers share travel plans.

The remainder of this paper is arranged as follows. In the next section, the relevant literature is reviewed. Section 3 provides an overview of the traffic bottleneck management system based on blockchain technology. The travel plan regulation models are formulated in Section 4. Section 5 presents the results of simulation experiments with the regulation model and real data. The final section concludes the paper.

2. Literature Review

2.1. Traffic Bottleneck Model

The first traffic bottleneck model for analyzing travel behavior at traffic bottlenecks was proposed by Vickrey [1]. Based on Vickrey’s traffic bottleneck model, many researchers have conducted extensive research on travel behavior at traffic bottlenecks. Guo et al. [12] studied the daily departure time choice behaviors of commuters with a congestion model, accounting for the bounded rationality of travelers. Chen et al. [13] studied an early peak commuting problem with bottleneck settings, where the bottleneck capacity varied with queue length. Li and Huang [14] explored the user equilibrium state of single-entry transportation corridors and proposed a new mathematical model considering travelers’ preferences for specific departure times. Frascaria et al. [15] studied the emergence of super-congestion in Vickrey bottleneck networks, and the departure time of travelers was determined by the second price auction mechanism. They analyzed the conditions for the occurrence of super-congestion and discussed possible policy interventions to prevent congestion. Chen et al. [16] proposed a new modeling framework that combines Vickrey theory with macroscopic data to analyze traffic dynamics in a transportation network from the outskirts of the city to the city center. In the above models, it is assumed that the time value cost and ideal time to reach the work area (or ideal time to pass through a bottleneck) are the same for all travelers.

To make the bottleneck model more realistic, many researchers have improved and extended the classic bottleneck model by considering heterogeneous travelers (i.e., different travelers have different time value costs and ideal times to pass through a bottleneck). Liu et al. [2] proposed a semi-analytical method to solve bottleneck models with general user heterogeneity. They used a dichotomy method to decompose the problem into multiple linear subproblems and then used matrix decomposition techniques to solve these subproblems, ultimately obtaining a closed analytical expression. Lamotte and Geroliminis [17] considered the problem of morning peak congestion for travelers with different travel distances in urban areas. They proposed a new mixed flow model to describe this heterogeneity, where travel time and residence time are set based on different travel distances and destinations, respectively. Qian and Zhang [18] regarded user heterogeneity as a parameter with a continuous distribution and incorporated it into the general equilibrium theory framework. They proposed a solution method that expresses the equilibrium conditions as a set of nonlinear integral equations based on optimal decision making and solved them using an iterative algorithm. Akamatsu et al. [19] recently proposed a new departure time selection equilibrium model that considers user heterogeneity and incomplete information.

Some researchers have constructed corresponding bottleneck models considering random demand, while others have constructed corresponding theoretical models for Y-type bottlenecks, capacity decline, and other situations [20,21,22]. The classic bottleneck model only considers activities from residential to work areas, and some researchers have extended the classic model by considering the travel chain [23,24]. With the development of autonomous vehicles, some researchers have proposed corresponding bottleneck models for autonomous vehicles. Zhao, Y. et al. [25] investigated the impact of autonomous vehicles on commute ridesharing, particularly considering uncertain work end times. This study explored potential changes in commuting dynamics with the introduction of autonomous vehicles. Su, Q. et al. [26] addressed the morning commute problem in the era of autonomous vehicles, focusing on distant parking options. This research delved into how autonomous vehicles may influence commuting patterns and parking choices. Zhang, X. et al. [27] examined the equilibrium analysis of morning commuting and parking in the context of spatial capacity allocation within an autonomous vehicle environment. This study aims to understand the implications of autonomous vehicles on commuting behaviors and parking dynamics. Yu, X. et al. [28] explored the relationship between autonomous cars and the activity-based bottleneck model. They investigated how in-vehicle activities contribute to shaping aggregate travel patterns, providing insights into the interaction between autonomous technology and travel behavior. Lu, G. et al. [29] focused on trajectory-based traffic management within an autonomous vehicle zone. This research delved into methods for effectively managing traffic patterns in areas where autonomous vehicles are prevalent, with an emphasis on trajectory-based approaches. Additionally, researchers have considered the effects of transportation mode choice and activities on travelers and studied travel choice behaviors based on bottleneck models [30,31].

2.2. Traffic Bottleneck Management

In terms of traffic bottleneck management, the most studied area is congestion pricing for traffic bottlenecks. The development of congestion pricing models is closely related to the development of traffic bottleneck models. The initial congestion pricing models for commuting corridors were based on bottleneck models that considered homogeneous travelers, such as Vickrey’s [32] application of queuing theory to consider the effect of time-varying fees on bottleneck travel efficiency. Based on Vickrey’s research, many researchers have conducted extended research on congestion pricing strategies for bottlenecks. Xiao et al. [33] studied the effect of implementing affordable pricing and strategic waiting schemes for toll roads during morning peak commuting.

With the development of bottleneck models considering heterogeneous travelers, many researchers have studied static (fixed fees) and dynamic (different charging standards for different time intervals) pricing strategies based on the consideration of heterogeneous travelers [34,35]. A small number of researchers have studied bottleneck pricing strategies considering random demand [36,37,38], while others have studied corresponding pricing strategies by considering travel chains and constructing bottleneck models based on activities [39,40]. In addition, many researchers have conducted extended research on and explored applications involving congestion pricing, such as bottleneck control strategies based on road tickets and charging strategies for travel mode adjustment [41,42,43,44].

Although congestion charging has attracted the most attention from researchers, it cannot be effectively implemented in many countries and regions due to its unfairness and low acceptance among travelers. Therefore, many researchers have studied traffic bottleneck control strategies from other perspectives, such as carpooling behavior and parking restrictions. Xiao, L. et al. [45] delved into the dynamics of carpooling behavior within the morning commute problem, particularly when facing constraints on parking space. Their focus is on optimizing commuting solutions in scenarios with limited parking availability. Xiao, L. et al. [46] examined the temporal and spatial allocation of bottleneck capacity in the context of managing the morning commute with carpooling. Their aim was to improve overall efficiency through a strategic allocation approach. Fu, Y. et al. [47] addressed the issue of parking management during the morning commute, specifically in the context of ridesharing. They explored how effective parking resource management can enhance the entire morning commute experience. Zhong, L. et al. [48] investigated dynamic carpooling during the morning commute, shedding light on the significance of high-occupancy-vehicle (HOV) and high-occupancy-toll (HOT) lanes. They analyzed the impact of these elements on shaping carpooling behaviors. Liu and Li [49] contributed to the discourse by exploring the design of pricing schemes for ridesharing programs addressing the morning commute problem. Their focus was on devising pricing strategies that establish a fair and effective system. Wang, J. et al. [50] introduced a dynamic ridesharing scheme, proposing a variable-ratio charging–compensation approach for the morning commute. Their contribution lies in aiming to enhance the appeal of ridesharing through the implementation of flexible pricing mechanisms. Ma and Zhang [51] delved into the morning commute problem, considering both ridesharing and dynamic parking charges. Their contribution involves exploring the dynamic adjustment of ridesharing and parking charges to optimize the overall commuting experience. In addition, some researchers studied control strategies considering parking charges and parking capacity restrictions [52], the optimization of working hours [10], travel chains [53,54], speed limits [11], and other measures. A small number of researchers have also studied the effect of incentive strategies on traffic bottleneck management [55].

2.3. Blockchain Applications

Blockchain technology was invented by Satoshi Nakamoto in 2008 as a public ledger [56] for Bitcoin transactions. In an environment that is not completely trusted, it can be used to verify and store data by building a peer-to-peer network using a chained data structure. The blockchain structure is determined by a distributed consensus mechanism to ensure the security of data transmission and access through cryptography. Data can be uploaded and accessed by using a smart contract composed of automated script code. Thus, this technology is based on a brand-new distributed infrastructure and computing paradigm. Its inherent characteristics of transparency, trustworthiness, tamper resistance, traceability, and high reliability give it unique advantages in data authentication, storage, privacy protection, and tokenization. Additionally, blockchain technology is not a single information technology. It can reconfigure and develop existing technologies to create new application functionalities. The many advantages and characteristics of this technology indicate that it can theoretically meet the requirements of interconnectivity, safety, and efficiency in the sharing and management of transportation and travel information.

At present, blockchain technology has received research attention from many researchers and enterprises in the fields of supply chains, public management, logistics, and transportation. Sensen et al. [57] proposed a solution for an organic agriculture supply chain framework based on blockchain and edge computing technology, aiming to solve the trust crisis. Yu et al. [58] proposed a solution for the quality control system of a green composite wind turbine blade supply chain based on blockchain technology. Zhang et al. [59] studied the effect of digital transformation based on blockchain technology on the cold supply chain of third-party logistics service providers. Zhong et al. [60] explored the effect of product information traceability in a dual-channel supply chain based on blockchain technology under government subsidies. Dong et al. [61] considered the phenomenon of green washing and the effect of blockchain technology on logistics outsourcing. Wang et al. [62] studied the effect of blockchain technology on port logistics capabilities, focusing on two different application methods: exclusivity and sharing. Li et al. [63] considered the application of blockchain technology in sustainable supply chains, with a focus on fairness and green investment.

Research on the application of blockchain technology in traffic congestion management is still lacking, often only consisting of a framework description [64,65] and lacking application analyses to solve specific problems.

3. Blockchain-Based Traffic Bottleneck Management System

To alleviate congestion on bottleneck sections in cities, a traffic bottleneck control system based on blockchain technology and shared travel plans is proposed. In this paper, time is discretized.

The workflow of the system is shown in Figure 1. First, travelers share their travel plans through the system before traveling, informing the system of the time they plan to arrive at the bottleneck. Second, the system calculates the number of vehicles arriving at the bottleneck in each time interval and evaluates the operational level of the traffic bottleneck based on the shared travel plans of travelers. Furthermore, if the operational level of the bottleneck is acceptable, the system stores travel plans and other information into the blockchain. If the operational level of the bottleneck is not acceptable, the system uses an optimization model to automatically generate travel plan regulation schemes and chooses travelers to provide travel suggestions. Then, travelers are free to choose whether to accept the travel suggestions provided by the system and change their travel plans. Next, the system checks whether all chosen travelers accept the travel suggestions. If all chosen travelers accept the travel suggestions, the system stores travel plans and other information in the blockchain. If not all the chosen travelers accept the travel suggestions, the system checks whether all alternative travelers have been provided with travel suggestions. If all alternative travelers have been provided with travel suggestions, the system stores travel plans and other information in the blockchain. If not all alternative travelers have been provided with travel suggestions, the system returns to the step of choosing travelers to provide travel suggestions to and continues. This method uses hash algorithm encryption, and each traveler has a private key and a public key. Through public key and private key technology, travel plans can be shared while protecting each traveler’s privacy. To incentivize travelers to share travel plans and accept the travel suggestions provided by the system, travelers can be rewarded with points in the form of smart contracts, which can be used to redeem daily consumption vouchers for gas and parking fees.

The core technology of the system proposed in this paper is a blockchain-based sharing platform, which needs to integrate information, as shown in Figure 2; this information is threefold: (1) traveler, including static traveler information (name, age, gender, private car license plate number, etc.) and dynamic traveler information that is dynamically adjusted every day (such as the travel plan); (2) traffic bottleneck information, including the traffic capacity and locations of traffic bottlenecks; and (3) internet of things (IoTs), such as historical traffic demand data based on IoT reserves, real-time traffic conditions, and estimation of real-time travel time. Traveler information is used to accurately predict traffic demand. Traffic bottleneck information is used to conduct a matching analysis of supply and demand, evaluate the operational level, and serve as the basic input information for travel plan regulation. IoTs information is designed to assist in predicting traffic demand and improving prediction accuracy when only some travelers are willing to share travel plans.

To integrate the multisource information mentioned above, a multilayer blockchain system is adopted for data storage and processing, as shown in Figure 3, and it includes the recognition layer, privacy layer, contract layer, consensus layer, and incentive layer. (a) Recognition layer: used to store and process dynamic data, static data, and predictive data. Dynamic data include dynamic traveler information and dynamic traffic bottleneck information. Static data include static traveler information and static traffic bottleneck information. Predicted data include the predicted results of dynamic traffic demand. (b) Privacy layer: used to identify travelers and store and process travel plans; (c) contract layer: used to evaluate operational level, optimize travel plans, and provide travel suggestions; (d) consensus layer: used for proof of work and data transmission; and (e) incentive layer: used to store consensus incentives and implement incentive functions, including obeying incentives and sharing incentives.

Because each traveler is treated as a node in the proposed blockchain system and the amount of travel data related to each node is relatively large, a high level of computer processing is needed to upload travel information to the blockchain system. To solve this problem, travelers’ information is divided into static information and dynamic information. Static information refers to information that remains unchanged for a long time, such as name, age, gender, and private car license plate number, while dynamic information refers to information that frequently changes over time, such as travel plans. As shown in Figure 4, to improve the upload speed of the blockchain system, static information is registered and stored through regulatory authorities such as urban traffic management departments, and dynamic information is shared through the blockchain platform. When uploading information to the blockchain system, each traveler’s static information corresponds to an independent ID for uploading, reducing the computational complexity, and ensuring the operational efficiency of the system.

Similarly, as shown in Figure 5, static traffic bottleneck information is registered and stored with independent IDs by regulatory authorities. By linking an ID with a traveler’s travel plan information when uploading shared data to the blockchain system, the computational complexity is reduced, and the extraction of key bottlenecks or areas is facilitated based on the ID approach.

4. Travel Plan Regulation Models

To alleviate congestion at bottlenecks, the number of arriving vehicles entering a bottleneck during each time interval should not exceed the bottleneck capacity. In this section, travel plan regulation models considering scenarios in which all/some travelers share travel plans are formulated.

4.1. Regulation Model When All Travelers Share Their Travel Plans

First, considering the most ideal scenario in which all travelers are willing to share their travel plans before peak hours, based on all the shared plans, the number of shared and planned arriving vehicles $r_i$ in each time interval $i\in T$ = [0, 1, 2, …, T] can be determined. Let $\mathrm{s}$ denote the bottleneck capacity, with units given by the number of vehicles per time interval, $\overline{r_i}$ denote the number of shared arriving vehicles in time interval $i$ after the regulation, and $f_{i,j}$ denote the number of transferred arriving vehicles from time interval $i$ to time interval $j$. This means that the arriving times of these $f_{i,j}$ vehicles need to be transferred from time interval $i$ to time interval $j$.

Let $f_{i,j}^{*}$ denote the optimal solution to the following linear programming (LP) problem:

$$Min {\displaystyle \sum }_i{\displaystyle \sum }_j\sqrt{{\left(i-j\right)}^2}{f}_{i,j}$$

(1a)

$$s.t. \overline{r_i}=r_i+{{\displaystyle \sum }}_{j\in T\backslash i}{f}_{j,i}-{{\displaystyle \sum }}_{j\in T\backslash i}{f}_{i,j} \forall i\in T$$

(1b)

$${\displaystyle \sum }_{j\in T\backslash i}{f}_{i,j}\le r_i \forall i\in T$$

(1c)

$$0\le \overline{r_i}\le s \forall i\in T$$

(1d)

$${\displaystyle \sum }_i{r}_i={\displaystyle \sum }_i\overline{r_i}$$

(1e)

$$f_{i,j}\ge 0 \forall i,j\in T$$

(1f)

Based on the travel plans shared by travelers, the number of travelers in a certain time interval may exceed the capacity of the bottleneck, causing the bottleneck to be congested. Therefore, we can change the travel plans of some travelers and transfer some travelers in congested time intervals to noncongested time intervals. However, changing travel plans may inconvenience travelers. Hence, in the LP problem, the objective function (1a) involves minimizing the total number of transferred vehicles $f_{i,j}$, and the weight coefficient $\sqrt{{\left(i-j\right)}^2}$ of $f_{i,j}$ allows the regulated time interval to not be as far apart from the original planned time interval as possible.

Constraint (1b) is the demand conservation constraint for each time interval. With this constraint, for each time interval, the number of arriving vehicles ${\overline{r}}_i$ after regulation equals the original number of shared and planned arriving vehicles $r_i$ plus the number of vehicles transferred from other time intervals ${\displaystyle \sum }_{j\in T\backslash i}{f}_{j,i}$ and minus the number of vehicles transferred to other time intervals ${\displaystyle \sum }_{j\in T\backslash i}{f}_{i,j}$.

Equation (1c) ensures that the number of vehicles transferred from the target time interval does not exceed the initial demand of the target time interval, i.e., the total number of vehicles transferred from time interval $i$ to other time intervals cannot exceed the original number of vehicles at time interval $i$.

Equation (1d) ensures that the travel demand in each time interval after regulation is nonnegative and that there is no delay after regulation, i.e., the travel demand in each time interval after regulation does not exceed the capacity of the traffic bottleneck. This constraint allows travelers who change their travel plans to have a better travel experience, as it is expected that they will be able to pass through traffic bottlenecks without any delay after regulation; therefore, they will be more willing to accept system regulation in their future travels based on this positive experience.

Equation (1e) ensures that the total travel demand before and after regulation is equal. Equation (1f) is a nonnegative constraint on the transfer demand.

The travel plan regulation model can be integrated into the constructed blockchain system using smart contract technology. In practice, the amount of shared data from travel plans are usually large, so the efficiency of obtaining the regulation model solution should be very high. Hence, the travel plan regulation model is formulated as an LP model that is easy to solve and highly practical.

4.2. Regulation Model When Some Travelers Share Their Travel Plans

The above travel plan regulation model is formulated considering the most ideal scenario in which all travelers are willing to share their travel plans. However, in practice, it is impossible for every traveler to use the constructed blockchain system and share their travel plans. Hence, we need to build a travel plan regulation model in which only some travelers share their travel plans.

Let $r_i^{predict}$ denote the number of arriving vehicles in time interval $i$, which can be predicted based on historical traffic information and with methods such as deep learning, scientometric analysis methods, etc. [66,67]. The demand $r_i$ of travelers sharing travel plans can be derived based on the shared plans. Then, the number of nonsharing arriving vehicles $r_i^{other}$ in time interval $i$ can be derived as $r_i^{other}=r_i^{predict}$ − $r_i$. Note that the travel plan regulation model should only regulate the travel choices of travelers sharing travel plans, and the choices of travelers not sharing travel plans are assumed to be unchangeable.

In the regulation model, when all travelers share their travel plans, some travelers in congested time intervals are transferred to noncongested time intervals to alleviate congestion at the bottleneck. Similarly, in the regulation model, when some travelers share their travel plans, we can transfer a portion of these travelers in congested time intervals to noncongested time intervals. The difference is that since the choices of travelers not sharing travel plans are unchangeable, to ensure that the travel demand in the regulated time intervals does not exceed the capacity of the traffic bottleneck, the maximum number ${\overline{s}}_i$ (denoted as residual capacity in this paper) of travelers sharing travel plans at each time interval after regulation needs to be recalculated based on the predicted number of unchanged and nonsharing vehicles $r_i^{other}$ using the following formulas:

$$l_0=\max \left(0,r_0^{other}-s\right)$$

(2)

$$l_i=\max \left(0,l_{i-1}+r_i^{other}-s\right)$$

(3)

$${\overline{s}}_0=\max \left(0,s-r_0^{other}\right)$$

(4)

$${\overline{s}}_i=\max \left(0,s-r_i^{other}-l_{i-1}\right)$$

(5)

where $l_i$ represents the number of travelers not sharing travel plans lagged from time interval $i$ to the next time interval.

Equations (2) and (3) are recursive formulations used to calculate the number of travelers not sharing travel plans lagged to the next time interval at each time interval. Specifically, if $r_i^{other}+l_{i-1}>s$, $l_i=r_i^{other}+l_{i-1}-s$; otherwise, $l_i=0$. Equations (4) and (5) are recursive formulations used to calculate the residual capacity in each time interval. Specifically, if $r_i^{other}+l_{i-1}<s$, ${\overline{s}}_i=s-r_i^{other}-l_{i-1}$; otherwise, ${\overline{s}}_i=0$.

Given the calculated residual capacity of each time interval, the travel plan regulation modelunder scenario in which some travelers share their travel plans is formulated by modifying the above LP model as follows:

$$Min {\displaystyle \sum }_i{\displaystyle \sum }_j\sqrt{{\left(i-j\right)}^2}{f}_{i,j}$$

(6a)

$$s.t. \overline{r_i}=r_i+{\displaystyle \sum }_{j\in T\backslash i}{f}_{j,i}-{\displaystyle \sum }_{j\in T\backslash i}{f}_{i,j} \forall i\in T$$

(6b)

$${\displaystyle \sum }_{j\in T\backslash i}{f}_{i,j}\le r_i \forall i\in T$$

(6c)

$$0\le \overline{r_i}\le \overline{s_i} \forall i\in T$$

(6d)

$${\displaystyle \sum }_i{r}_i={\displaystyle \sum }_i\overline{r_i}$$

(6e)

$$f_{i,j}\ge 0 \forall i,j\in T$$

(6f)

Note that similar to the regulation model under scenarios in which all travelers share their travel plans, in this case, objective (6a) also minimizes the total transferred number of vehicles, and constraints are almost the same. The difference is related to constraints (1d) and (6d). Constraint (1d) requires the travel demand after regulation to not exceed the bottleneck capacity to ensure that travelers experience no travel delays after changing their plans. Since the choices of travelers not sharing travel plans are unchangeable, to ensure that the travel demand in the regulated time intervals does not exceed the capacity of the traffic bottleneck, constraint (6d) requires that the regulated demand $\overline{r_i}$ of travelers sharing travel plans at time interval $i$ should not exceed the residual capacity, i.e., $\overline{s_i}$.

5. Case Study

In this section, the proposed travel plan regulation models are validated based on case studies using real traffic flow data from the Su-Tong Yangtze River Highway Bridge in China, as shown in Figure 6. The Su-Tong Yangtze River Highway Bridge is an important pathway crossing the Yangtze River, and it is also an important component of the main backbone of the highway network in Jiangsu Province. The main bridge deck of the Su-Tong Yangtze River Highway Bridge is arranged in six lanes in both directions, with a width of 31.0 m. During holidays, the Su-Tong Yangtze River Highway Bridge often experiences severe congestion, which leads to travelers wasting considerable time waiting on the bridge and unable to reach their destination in a timely manner. The designed capacity of the Su-Tong Yangtze River Highway Bridge is about 80,000 vehicles per day. Thus, the capacity is set to 3333 vehicles per hour. Please note that the capacity of a bottleneck does not refer to the capacity of a road segment. It depends on the entrances associated with the bottleneck, such as intersections that merge into this bottleneck from other road sections, toll stations, etc. The Su-Tong Yangtze River Highway Bridge selected in this paper is a typical case, and the place where congestion is most likely to occur is the toll station. The 80,000 vehicles per day mentioned above are the designed traffic capacity of the Su-Tong Yangtze River Highway Bridge toll station in one direction.

For the experiment, as shown in Figure 7, we select the holiday data for one day from a dataset of daily and hourly traffic flows at the starting position of the Su-Tong Yangtze River Highway Bridge from 2017 to 2020 and divide the data into 24 time intervals. The length of each time interval is one hour. Because this is a period of holiday, the peak period is relatively long, and the period with V/C (volume-to-capacity ratio) exceeding one occurs between the 10th and 23rd time intervals.

To evaluate the performance of the system, two experiments are conducted in this section. (1) The first experiment involves verifying the effectiveness of the optimization model under scenarios in which all travelers share their travel plans. (2) The second experiment involves verifying the effectiveness of the optimization model under scenarios in which some travelers share their travel plans.

To test the regulation effect, two indicators are defined as the vehicle transfer rate $\mathrm{C}$, the total delay rate $\overline{W}$, and the delay rate $\overline{d_i}$ of time interval $i$. The vehicle transfer rate $C$ is defined using the following formula:

$$C=\frac{{{\displaystyle \sum }}_i{{\displaystyle \sum }}_k\sqrt{{\left(i-k\right)}^2}{f}_{i,k}}{{{\displaystyle \sum }}_i{r}_i}$$

(7)

The total delay rate $\overline{W}$ is defined using the following formulas:

$$\begin{gathered} {\overline{l}}_0=\max \left(0, \overline{r_0}+r_0^{other}-s\right) \\ {\overline{l}}_i=\max \left(0,{\overline{l}}_{i-1}+\overline{r_i}+r_i^{other}-s\right) \\ \overline{W}=\frac{{{\displaystyle \sum }}_i^{ }{\overline{l}}_i}{{{\displaystyle \sum }}_i^{ }\mathrm{s}} \end{gathered}$$

(8)

The delay rate $\overline{d_i}$ of time interval $i$ is defined using the following formulas:

$$\begin{gathered} {\overline{l}}_0=\max \left(0, \overline{r_0}+r_0^{other}-s\right) \\ {\overline{l}}_i=\max \left(0,{\overline{l}}_{i-1}+\overline{r_i}+r_i^{other}-s\right) \\ \overline{d_i}=\frac{{\overline{l}}_i}{\mathrm{s}} \end{gathered}$$

(9)

Formulas (8) and (9) mentioned above are used to calculate the total delay rate and the delay rate for a single time interval after regulation. When calculating the total delay rate and the delay rate for a single time interval before regulation, we should replace $\overline{r_i}$ with $r_i$ in the formula.

5.1. Regulation Model for All Travelers Willing to Share Their Travel Plans

First, we test the regulation model in the most ideal scenario, in which the traffic conditions on the Su-Tong Yangtze River Highway Bridge are optimized and all travelers share their travel plans.

Figure 8 and Figure 9 show the regulated number of arriving vehicles in each time interval and the number of vehicles transferred in each time interval, respectively. Notably, in Figure 8, after regulation, the number of vehicles in each time interval does not exceed the capacity; thus, there are no delays. This verifies the effectiveness of the proposed regulation model. In Figure 9, both the x-axis and y-axis represent time intervals, while the z-axis represents the number of vehicles transferred from time intervals on the x-axis to time intervals on the y-axis. From Figure 9, We can see that the data of transferred vehicles are mainly near a diagonal line from left to right in the figure. This indicates that for most travelers who need to change their travel plans, the regulated time interval is very close to the original planned time interval. Changing travel plans may inconvenience travelers, especially when the regulated time interval is far from the original planned time interval, and the regulation model can minimize such inconveniences.

Table 1. Vehicle transfer rate for different time interval lengths and different degrees of total demand.

	Total Demand	120%	110%	100%	90%	80%	70%
Length of the Time Interval
1 h		2.1172	1.1788	0.3603	0.0095	0.0	0.0
30 min		4.2087	2.3386	0.7151	0.023	0.0	0.0
15 min		8.4036	4.6684	1.4348	0.0516	0.0	0.0

shows the vehicle transfer rate (i.e., $C$ in Equation (7)) for different time interval lengths and different degrees of total demand. In Table 1, for example, the total demand is set to 110%, which indicates that the planned number of arriving vehicles based on real data is synchronously multiplied by 110% for each time interval.

Table 1 shows that as the total demand increases, the vehicle transfer rate increases. Note that as the total demand increases, the degree of congestion increases, meaning that more vehicles exceed the capacity in each time interval and more vehicles need to be regulated. In contrast, when the total demand is low, the corresponding vehicle transfer rate is low. When there is no delay in the total demand derived from the original travel plans, there is no need to regulate the travel plan; thus, the vehicle transfer rate is 0, as shown in cases in which the total demand is set to less than 80%.

Additionally, as the length of the time interval becomes shorter, the vehicle transfer rate increases. Moreover, as the length of the time interval becomes shorter, the number of time intervals increases, meaning that the time step is more refined. In this case, some travelers who do not need to regulate their planned travel times when the length of the time interval is large may change their planned travel times when the length of the time interval is shortened; thus, more vehicles need to be regulated, and the vehicle transfer rate increases.

5.2. Regulation Model for Some Travelers Willing to Share Their Travel Plans

In this section, considering the situation in which some travelers are willing to share their travel plans, the vehicle transfer rate and total delay rate (i.e., $\overline{W}$ in Equation (8)) are compared under conditions with different percentages of travelers who do not share travel plans and different total demands. In this experiment, the length of the time interval is fixed and set to 30 min.

Figure 10 shows the delay rate (i.e., $\overline{d_i}$ in Equation (9)) in each time interval for 100% total demand when 90% of travelers do not share their travel plans before regulation and after regulation. Figure 10 shows that after regulation, the delay rate decreases in each time interval, and the number of time intervals with delays also decreases. This verifies the effectiveness of the proposed regulation model.

Table 2. Vehicle transfer rate for different degrees of total demand and different percentages of travelers who do not share their plans.

	Total Demand	120%	110%	100%	90%	80%	70%
Percentages of Nonsharing Travelers
90%		20.5948	17.4559	7.5788	0.2277	0.0	0.0
80%		18.2094	11.7455	3.5706	0.1141	0.0	0.0
70%		14.0207	7.7879	2.3811	0.0761	0.0	0.0

and

Table 3. Total delay rate for different degrees of total demand and different percentages of travelers who do not share their plans.

	Total Demand	120%	110%	100%	90%	80%	70%
Percentages of Nonsharing Travelers
90%		1.7355	0.7049	0.0404	0.0	0.0	0.0
80%		0.3923	0.0119	0.0	0.0	0.0	0.0
70%		0.0008	0.0	0.0	0.0	0.0	0.0

show the vehicle transfer rate and the total delay rate, respectively, at different degrees of total demand and for different percentages of travelers who do not share their plans.

Table 1 and Table 2 show that as the degree of total demand increases, the vehicle transfer rate increases. As the degree of total demand increases, more vehicles exceed the capacity in each time interval, and more vehicles need to be regulated, as observed in the ideal case. Additionally, Table 2 shows that as the percentage of nonsharing travelers increases, the vehicle transfer rate increases. Since only those travelers sharing travel plans can be regulated, when the number of nonsharing travelers increases, travelers sharing travel plans may be regulated to time intervals far from the original planned time intervals; thus, the vehicle transfer rate increases.

Table 3 indicates that as the degree of total demand and the percentage of nonsharing travelers increase, the total delay rate of vehicles after regulation increases. As the degree of total demand increases, the total number of nonsharing travelers synchronously increases. Since the choices of nonsharing travelers are unchangeable, traffic delays may remain in time intervals in which the number of nonsharing travelers exceeds the capacity, even if all travelers sharing travel plans are transferred to other time intervals. Hence, as the number of nonsharing travelers increases, the original total delay rate of vehicles increases and the number of time intervals in which the number of nonsharing travelers exceeds the capacity increases; thus, the total delay rate of vehicles after regulation increases. Similarly, as the percentage of nonsharing travelers increases, the number of time intervals in which the number of nonsharing travelers exceeds the capacity increases; thus, the total delay rate of vehicles after regulation increases. These results imply that to improve the effect of the regulation model, more travelers need to be motivated to share their travel plans and accept travel regulations.

6. Conclusions

In this paper, a traffic bottleneck management system based on shared travel plans is proposed. To address potential issues such as data privacy and information security in travel plan sharing, blockchain technology with decentralized and transparent information characteristics is adopted. The workflow and information fusion process of the proposed system are described, and a multilayer data structure is used. To reduce computational complexity, the information for travelers and traffic bottlenecks is divided into static information and dynamic information. Static information is registered and stored through regulatory authorities based on an independent ID for uploading.

Furthermore, with smart contracts in the proposed blockchain system, travel plan regulation models under conditions in which all/some travelers share travel plans are proposed. These models regulate the travel plans of travelers, transferring some vehicles from congested time intervals to noncongested time intervals. Moreover, to minimize the inconvenience of travelers, travelers should be regulated to a time interval that is as close as possible to the originally planned time interval.

The results of experiments based on real data from the Su-Tong Yangtze River Highway Bridge in China are as follows: (1) as the degree of total demand increases, the vehicle transfer rate and total delay rate increase; (2) as the length of the time interval decreases, the vehicle transfer rate increases; and (3) as the number of travelers who do not share their travel plans increases, the vehicle transfer rate and total delay rate increase. Therefore, to reduce the vehicle transfer rate and total delay rate, we should encourage more travelers to share their travel plans and accept regulation.

By using the model and method proposed in this paper, traffic managers can reasonably regulate the travel behavior of travelers, alleviate the traffic congestion of traffic bottlenecks, and promote the sustainability of urban economy, society, and environment; therefore, travelers can make reasonable travel decisions and have a better travel experience. However, there are many practical situations that have not been considered in this paper, such as multiple entry and exit bottlenecks, multiple travel modes, and other control strategies. In addition, this paper considers only one bottleneck rather than road networks, because blockchain technology has throughput limitations and the amount of data in the road network is too large to apply blockchain technology. Therefore, in the future, it is worth exploring the regulation of travel behaviors considering additional practical situations and factors to improve the applicability of the proposed regulation method, and it is also worth expanding this study to road networks in further research.