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Evolutionary dynamics of traveling behavior in social networks
Journal Pre-proof Evolutionary dynamics of travelling behavior in social networks Qiaoru Li, Zhe Zhang, Kun Li, Liang Chen, Zhenlin Wei, Jingchun Zhang
PII: DOI: Reference:
S0378-4371(19)32043-6 https://doi.org/10.1016/j.physa.2019.123664 PHYSA 123664
To appear in:
Physica A
Received date : 6 August 2019 Revised date : 4 November 2019 Please cite this article as: Q. Li, Z. Zhang, K. Li et al., Evolutionary dynamics of travelling behavior in social networks, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123664. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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*Highlights (for review)
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An evolutionary game model for travel choice in social networks is established. Commuters' travel behavior is influenced by heterogeneity of individuals’ characteristics. A travel mode for transfers between cycle highways and rail transit is proposed in this paper. Management recommendations for various travel modes are proposed to alleviate traffic congestion.
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Journal Pre-proof *Manuscript Click here to view linked References
Evolutionary dynamics of travelling behavior in social networks Qiaoru Lia, Zhe Zhanga, Kun Lia,∗, Liang Chena, Zhenlin Weia, Jingchun Zhanga a
School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China
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Abstract
In this paper, the topology of complex network is used to characterize the interactions among travelers. Based on the
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assumption of travelers’ limited rationality and the wisdom of crowds, an evolutionary game model of travelers was established. Combining these research findings, we study commuters' travel behavior rules during peak traffic periods and make some recommendations that have the potential to relieve traffic congestion. In the first section, we analyze the effect of heterogeneity on travel choice behavior by Monte Carlo simulations, which explains why the total amount of traffic during peak hours is hard to decrease. The experimental results indicate that increasing fees would not reduce traffic flow during peak hours. Moreover, controlling price for the management of travel demand needs to be coordinated with the management
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of traffic system under the condition of limited road resources. On this foundation, the second section proposes an environmental travel mode for the transfer between cycle highways and rail transit. We verify the effectiveness of this travel mode in alleviating traffic congestion. Furthermore, considering the interactions between different travel modes in transportation system, we suggest some management recommendations with reference to the characteristics of different travel modes.
Keywords: Travel behavior, Networks, Cycle highways, Travel mode, Evolutionary game
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____________________________________________________________________________________________________ 1. INTRODUCTION
Traffic congestion has been endemic to metropolises, especially during peak hours. The initial idea to address this is to
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alleviate the contradiction between the supply and demand of traffic by expanding road traffic capacity [1]. However, Downs
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and Braess verified that widening the road system provides no value in solving it and will cause more crowded roads and
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longer commuting time instead [2,3]. The comprehension of travel behavior is prerequisite for the guidance of transportation
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∗Corresponding author
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Email addresses: [email protected]
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demand. Generally, travel behavior refers to the fact that the value of enjoying traffic service is lower than the cost of traffic
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itself [4-6]. Therefore, due to this price, the implementation of congestion charges to control traffic volumes has become a
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heated topic [7]. Vickrey [8] applied the Queuing Theory and proposed a dynamic model of road traffic system based on
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travel costs, namely, the bottlenecks. Arnott et al. [9,10] considered congestion charging into the bottlenecks and studied the
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behavior of travelers. Laih et al. [11] proposed the concept of multi-step tolls. Xiao et al. [12] optimized different charging
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systems and proposed time-varying toll and single-step coarse toll. These models are often referred to as congestion charge
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models. Some researchers have explored solutions from the perspective of public transportation. For example, Gkritza [13]
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has studied the impact of the price structure of different travel modes on the demand for public transportation in the context
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of the competition and cooperation of multiple travel modes. Pel et al. [14] proved that travel time and congestion are also
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two major factors affecting the service level of public transportation. Van den Berg et al. [15] considered travel time and
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delay to be the impact of the social welfare on heterogeneous travelers in a continuous situation.
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In recent years, bicycle transit, a green environmental travel mode, have provided new ideas for alleviating traffic
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congestion [16-18]. To promote the development of bicycle transportation, some countries have even built cycle highways,
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also known as “cycle superhighways”, to meet the demand of long distance and high quality bicycle routes for bicycle
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commuters [19,20]. Researchers proved that boosting the cycle highways as a mode of transport is a good opportunity to
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alleviate traffic congestion [21,22]. Based on the background of cycle highways, this paper proposes that the travel mode for
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transfer between cycle highways to rail transit. Additionally, combined with traditional research, considering congestion
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charges and the management of public transportation, we provide management suggestions for traffic congestion.
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To grasp the wisdom of crowds [23,24] in traffic system and achieve the coordinated management of various traffic
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modes, we adopted an effective tool for the research of collective behavior: complex networks [25-29]. Recently, complex
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networks have generated significant development in the field of traffic congestion with broad applicability and have provided
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insights into the structure and function of both natural and designed systems [30,31]. Meanwhile, evolutionary game theory
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has been proved to be a basic and effective tool to explain the maintenance of cooperative crowd behaviors in structured
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populations [32-34], which are necessary and critical to solve traffic congestion [35]. Co-evolutionary process [36,37], group
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interaction [38,39], punishment behavior [40,41], as well as social psychological [42] are all prime examples of exploring
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collective behavior in the evolutionary process of strategy invasion on networks.
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In this work, combining the theories of evolutionary game and complex networks, we study the travel rules during peak
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hours and explore the reasons of traffic congestion. For both environmental protection and energy conservation, this paper
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presents a travel mode of the transfer between cycle highways and rail transit, which is in parallel with traditional travel
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modes. Considering the integrality of traffic system, we propose the management of bicycle transit to promote the transition
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of cars to public transportation to alleviate traffic congestion. The rest of the paper is arranged as follows. In Section II, we
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investigate the game models of travelers adapting to networks, model for choosing whether to travel and model for travel
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modes choice. Section III is divided into two parts. In the first part, we explore the impact of heterogeneity on travel choices ,
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and find that increasing congestion charges during peak hours cannot alleviate traffic congestion; In the second part, the
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evolutionary stable results of travel modes choice verify the effectiveness of the transfer of cycle highways to rail transit in
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relieving traffic congestion. Section IV is the conclusion.
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2. MODELS
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2.1. Model for choosing whether to travel
In this section, we discuss travel choice behaviors during peak hours from the view of evolutionary game. The travel
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choice game is arranged on a square lattice with N 3600 nodes, where every node is surrounded by four nearest neighbors
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and is a member in their corresponding groups. Each node refers to a travel group which contains many travelers. There are
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two strategies for players to choose from, to travel or not to travel. If player i chooses not to travel during peak hours, it
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represents cooperation, and Si 1 . Otherwise, i is a defector, and Si 0 . Node i plays with its neighbors as a group of size
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Gi =5 , whose members g are likely to develop competitive relationship for road resources because of the same travel route
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Li . A cooperator takes losses caused by uncompleted tasks, which is related to the importance, , of the task. Additionally,
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for the players is heterogeneous. Each cooperator contributes 1 to traffic on the routes of participating groups, while
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defectors contribute nothing. In each group, the sum of traffic n is subsequently multiplied by the factor r > 1, reflecting that
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the traffic cost of every uncooperative player is r n . In addition, we assume that charge c exists, which depends on the
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average growth triggered by congestion charges and includes the economic congestion toll and other increased costs, such as
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the perceived cost caused by the transfer of car users to public transportation. So, c is identical for every route. The cost of
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defector consists of two parts, the traffic cost r n and the charge c . Each player participates in five groups, a self-centered
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and four neighbor-centered groups, while the total cost of a defector expended in all the groups is thus：
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Pi g pig = g rn g c ,
the total cost of a cooperator expended in all the groups is：
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(1)
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Pi g pig = g f ,
(2)
where is the importance of the task and f is the loss of importance per unit. The importance of each individual, i , is
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denoted by a parameter i ( 0 i 1 ). We distinguish individuals into groups of three classes regarding their value of on
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the square lattice:
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i) Low-Importance class, whenever i
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ii) Medium-Importance class, whenever
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iii) High-Importance class, whenever
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Initially, each individual i is designated either as a cooperator or a defector with equal probability, and assigned by
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random values. According to Eq.1 and Eq.2, strategy competitions are carried out between nearest neighbors on the given
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network. After collecting payoffs, player i can adopt the strategy s j of one of its randomly chosen nearest neighbors j with
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a probability determined by the Fermi Function：
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si
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1 exp pi p j / k
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(3)
where we set k 2 . The selected value ensures that better performing players are readily followed by their neighbors,
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although adopting the strategy of a player that performs worse is not impossible either. The results remain qualitatively
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similar in a wide range within the k 20 intervals. Each player has a chance to adjust its strategy once during a Monte Carlo
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step. In our results, each data point is the mean value of 200 independent experiments, and the result of each experiment is
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obtained by averaging over 1000 generations after 10,000 generations as an iterative process.
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2.2. Model for travel modes choice
Taking the cycle highways as the background, we propose a travel mode for transfers between cycle highways and rail
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transit. We also utilize square lattice with N 3600 nodes to represent the game relationship in which travelers compete for
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road resources. Players make their own travel mode choices using game strategy. We set three commuting modes: S 0
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serves as traveling by car, S 1 serves as traveling by transitions from bus to rail transit (bus-rail), S 2 serves as traveling
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by transitions from bicycle on the highways to rail transit (bicycle-rail). Taking into consideration the three aspects of time,
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economy and crowded perception
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flow travel time, economic costs before congestion charges and the crowded perception when there is only one player. The
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payoff collecting process and strategy imitation rules are consistent with those introduced above.
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[43], player’s payoff is available. We assume that the expectation of players includes free-
By car is the most comfortable travel mode where congestion perceptions are not sensitive. We set the expected
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congestion perception cost equal to the actual congestion perception cost. Congestion charging has few economic
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consequences for public transportation and bicycle transit, so the expected economic cost of railways, buses and bicycles are
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the same as their actual economic costs. In terms of time, the relatively stable operation schedule enables the travel time to be
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consistent with expectations. The payoff to a player is：
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veh veh pcar time 2 1 t gveh / t0veh cos t 1 ccar g veh veh veh veh bus rail , pbus rail g time 1 1 t g / t0 per rg cycle cycle cycle bicycle rail pbicycle rail g tcycl ime 1 t g / t0 per rg
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(4)
where ccar is the ratio of the economic cost after congestion charges to the original economic cost, the payoff of
bus rail 1 mgbus rail perception rg
, mgbus rail is the number of players choosing bicycle-rail in group g, is the
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comprehensive crowded sensitivity coefficient per player when travelers choose the bus-rail travel mode, and 0 .
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Similarly, rbicycle rail 1 mgbicycle rail , and the comprehensive crowded sensitivity coefficient of the bicycle-rail travel mode
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veh veh cycle cycle k =1 , cos 0 . We set time t =1 , time =1 , and per =1 . Travel time t g k veh, cycle is calculated by Eq. (5). Notably, the
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travel time t gveh is calculated by an average for the motorway. Considering the characteristics of different travel modes, the
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travel time of each travel mode is calculated by multiplying average travel times by a coefficient. For the travel time of a bus
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tg,bus 1tgveh and that of car tg,car 2tgveh , we set 1 1.2 , 2 0.8 .
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Regarding travel time functions, we adopt Akcelik function for urban street characteristics [44-47]. In addition,
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researchers have demonstrated that bicycle traffic flow applies [48-50]. t gk t0k 0.25T xgk 1
x
k g
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8 J k xgk , (k=veh, cycle) C kT
(5)
where t0k is free-flow travel time per unit distance， T is the time period of analysis， xgk is the degree of saturation
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(volume( Vg )/capacity(C)), C k is capacity, and J k is delay parameter. We suppose that the volume of traffic vgveh on
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motorway and the total volume of buses and cars on the network are linearly related within a game group, i.e., Vgveh veh vgveh ,
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where veh is a coefficient. The total volume of vehicles vgveh k k vgveh, k k 1, 2 , where vveh , k is the number of buses or
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cars, k is Passenger Car Unit (PCU), the ratio of equivalent unit to passenger volume. Equivalent unit for car is 1 and for
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bus is 2 [51]. In this paper, we set the capacity of the bus to 5 times that of the car, so car 1 , and bus 0.4 . On cycle
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highways, Vgcycle cycle mgbicyclerail , where mgbicyclerail is the number of bicycles.
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3. RESULTS
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3.1. Results for choosing whether to travel
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Fig. 1 shows the roles of the loss f and charge c on each route in the process of the evolution. From an overall
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perspective, c promotes the emergence of cooperation, and f is precisely the opposite. Comparing the six different colored
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lines in Fig. 1, it can be found that there were obvious differences in the growth rate. A higher value of f results in a lower
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growth rate of cooperation. Even if the charge c is high, stubborn players choosing to travel during rush hour are always
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present. And increasing f will cause the increment of these stubborn players.
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Fig. 1: Influence of charge c on the cooperation rate c for different values of the loss f . f values are set as 5, 10, 30, 50, 80, and 100 respectively. In fact, c represents the proportion of non-travelers during peak hours.
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Meanwhile, the persistence of defectors may be related to the trip purpose, or in other words, biases players’
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judgment. Thus, we analyze how influences the evolutionary outcome. As shown in panel (a1) in Fig. 2 , is a critical
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issue in determining how fast the system could converge to the full cooperation state. The most resistant individuals are those
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having important tasks to be accomplished from the High-Importance class. After a series of repeated shocks, the High-
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Importance class reaches a stable equilibrium and realizes full cooperation. And in the group (a2) that did not achieve full
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cooperation, High-Importance class is of a feature of growing opposition. They are the hindrance to full cooperation.
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Therefore, we believe that high fees and congestion cannot prevent travelers from traveling during peak hours because
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of the importance of their travel purpose, such as going to work. However, peak hours are usually commuting time, and
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traveling players are mostly those commuting to work or to school. It can be proved that individuals who travel during peak
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hours have a high f value. Especially in the early morning, they have to travel. Simply charging fees has no benefit in
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reducing the total amount of traffic. Controlling the price to manage travel demands and coordinate the rational management
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of travel modes under the condition of limited road resources is important so that travelers can reach their destinations
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without causing traffic congestion.
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Fig. 2: Time-dependence of the fraction of cooperators for the three classes. The value of f is 30 in panel (a1), and 80 in
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panel (a2). Here, c 20 , and other parameters are consistent with those in Fig. 1.
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3.2. Results for travel modes choice
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In this section, traffic status is determined by the ratio of the driving speed to the free-flow speed, referring to the
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Highway Capacity Manual (HCM). Generally, when the ratio is less than 40%, it is considered as intolerable congestion
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status. Bounded by the traffic condition with a ratio of 40%, a reasonable proportion of travel modes assigned should be such
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that t / t0 is less than 2.5. Each experimental value of t / t0 is the average of all players of the three travel modes on the
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network.
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Fig. 3: t / t0 as a function of both and c for different values of the sensitivity coefficient . (b1-b3) are the traffic statuses
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with the coexistence of the three travel modes under the conditions of =1, 5, and 10 respectively. (c) is the result of only
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two travel modes, car and bus-rail. According to the code for the design of China and research on cycleways [50,51], the free-
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travel by car or bicycle. According to u0 t10 , tm t0
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and cycle 1150.4348 .
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flow speed u0veh 60km / h , and u0cycle 20km / h , the capacity in one direction Cveh 4200veh / h , and C cycle 2100bicycles / h on arterial roads. We set T 0.5h and um / u0 0.5 . Assume that um / u0 0.1 when all players 0.25 J C
[45], we can get J veh 4.6667 , J cycle 21 , veh 1334.1216 ,
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In Fig. 3, for a given value of the sensitivity coefficient , a larger domain of small t / t0 (non-red) means that the larger
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adjustable range of parameters, the less sensitive the traffic conditions are to parameter changes, and thus the less prone the
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traffic system is to be trapped in a serious congestion. Therefore, we can consider the size of the non-red color range in each
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panel to be the delay evaluation under the corresponding conditions. As shown in panels (b1-b3), when the three travel
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modes coexist, the value of is not positively correlated with the delay. The increment of first reduces the delay; When
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exceeds the critical value, increasing leads to more serious delay instead. Comparing (b1-b3) with the (c), the former is
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obviously better than the latter in terms of alleviating delay. Even if is small ( =1), the delay of only two travel modes
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(car and bus-rail) is terrible. This result shows that the coexistence of the three modes, rather than two modes, can
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significantly relieve delays, and it is necessary to develop a travel mode of transfers from cycle highways to railways.
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Moreover, to explore the optical method for the management of bicycle transit, we investigate the combined effect of
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sensitivity coefficients and upon the final evolutionary outcome. we first analyze travel mode choice behaviors when
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congestion charges are implemented. As shown in Fig. 4, by exploring the correlation between the fractions of travel modes
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in the first three rows (d1, e1, f1; d2, e2, f2; d3, e3, f3) and the ratio of t / t0 presenting traffic delays in the last row (d4, e4,
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f4), we find that the value of t / t0 and the fraction of car travelers are roughly positively correlated and are negatively related
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to the fraction of bus-rail or bicycle-rail travelers. Excessive car travelers are the main factors resulting in serious congestion.
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Comparing the columns in Fig. 4, congestion charges promote the shift of the travel mode of car to the other two travel
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modes, and an increase in c reduces delays.
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As presented in Fig. 4, the resources for all kinds of travel modes are utilized without serious congestion if and
are within a certain range. This range corresponds to the non-red and non-blue domain of the panel of t / t0 (see Fig. 4 (d4, e4,
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f4)). Despite the value of c , the ideal fraction of car modes and bus-rail modes is about 0.4 (light blue); while for bicycle-rail
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modes, the optimal fraction is approximately 0.2 (between light blue and dark blue). More importantly, elevating c values
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promotes sensitivity coefficients (comparing (d4, e4 and f4)), which help to alleviate traffic congestions. However, for social
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and traffic stability, too large c values are often prohibited in real situations. When c 1 , the optimal range is related to <5,
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<1. If the value of c is increased, the sensitivity coefficient can be allowed to rise correspondingly.
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Fig. 4: Stationary fraction of evolutionary outcomes in dependence on sensitivity coefficients and for different c values. The columns from left to right are respectively the results with condition of c 1 , c 5 , and c 10 . Each row shows the fractions of travelers by car, bus-rail, and bicycle-rail, as well as the corresponding values of t / t0 from top to bottom.
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4. CONCLUSION
As a typical example of collective behaviors [52], travelling demonstrates obvious self-organization process of imitation
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[53,54]. We have exploited the wisdom of crowds on network to display the evolutionary process of travel choice [55], trying
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to provide a new insight to help manage and relieve traffic congestion. We have exploited the wisdom of crowds on network
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to display the evolutionary process of travel choice, trying to provide a new insight to help manage and relieve traffic
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congestion. Initially, based on the concept of cost function, we explored travel rules considering congestion charges.
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Obviously, the stabilization of cooperation (not travel) is obstructed by the fact that travelers must travel for important tasks
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which are not negatively influenced by congestion charges. It is inevitable that travelers commute to work during rush hours,
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also called commuting time. Thus, unquestioning acceptance of congestion charges is unscientific during peak times. We next
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proposed an environmentally friendly travel mode for transfers between cycle highways and railways based on the strong
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support for bicycle transit in various countries. By comparing with and analyzing traditional travel modes, experimental
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results have indicated that the addition of bicycle-rail travel mode is advantageous to relieving traffic congestion. Finally, by
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utilizing the strategy competition behaviors to express travel mode choice, we have studied how to promote the management
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of bicycle transit. In this scenario, the ideal travel fraction of the bicycle-rail mode is lower than those of car mode and bus-
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rail mode. The comprehensive crowded sensitivity coefficient of bicycle-rail mode and the coefficient of bus-rail mode
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should be restricted in a certain range to avoid congestions. When congestion charges are promoted, road managers can
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appropriately elevate the sensitivity coefficients. In summary, the management of public transportation and cycle highways
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can be adjusted according to the congestion charges, which can further better manage and save resources.
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ACKNOWLEDGMENTS
This work was partially supported by Colleges and universities in Hebei province science and technology research
project and technology research project, China (QN2018231), China Scholarship Council.
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REFERENCES
202
[1] J.D. Murchland, Braess's paradox of traffic flow, Transportation Research, 4 (1970) 391-394.
203 204 205 206 207 208 209 210 211
[2] A. Downs, Stuck in traffic: Coping with peak-hour traffic congestion, Brookings Institution Press, Washington D.C., 1992.
212 213 214 215 216 217 218 219 220
[7] M. Börjesson, J. Eliasson, C. Hamilton, Why experience changes attitudes to congestion pricing: The case of Gothenburg,
221 222 223 224 225 226 227
Transportation Science, 49 (2013) 46-65.
p ro
of
200
[3] D. Braess, A. Nagurney, T. Wakolbinger, On a paradox of traffic planning, Transportation science, 39 (2005) 446-450.
Pr e-
[4] T.F. Golob, Structural equation modeling for travel behavior research, Transportation Research Part B: Methodological, 37 (2003) 1-25.
[5] J. De Vos, P.L. Mokhtarian, T. Schwanen, V. Van Acker, F. Witlox, Travel mode choice and travel satisfaction: bridging the gap between decision utility and experienced utility, Transportation, 43 (2016) 771-796. [6] M. Kroesen, S. Handy, C. Chorus, Do attitudes cause behavior or vice versa? An alternative conceptualization of the attitude-behavior relationship in travel behavior modeling, Transportation Research Part A: Policy and Practice, 101 (2017) 190-202.
al
Transportation Research Part A: Policy and Practice, 85 (2016) 1-16. [8] W.S. Vickrey, Congestion theory and transport investment, The American Economic Review, 59 (1969) 251-260.
urn
[9] R. Arnott, A. De Palma, R. Lindsey, Economics of a bottleneck, Journal of urban economics, 27 (1990) 111-130. [10] R. Arnott, A. de Palma, R. Lindsey, Departure time and route choice for the morning commute, Transportation Research Part B: Methodological, 24 (1990) 209-228.
[11] C.-H. Laih, Queueing at a bottleneck with single-and multi-step tolls, Transportation Research Part A: Policy and Practice, 28 (1994) 197-208.
Jo
[12] L.-L. Xiao, H.-J. Huang, R. Liu, Congestion behavior and tolls in a bottleneck model with stochastic capacity,
[13] K. Gkritza, M.G. Karlaftis, F.L. Mannering, Estimating multimodal transit ridership with a varying fare structure, Transportation Research Part A: Policy and Practice, 45 (2011) 148-160. [14] A.J. Pel, N.H. Bel, M. Pieters, Including passengers’ response to crowding in the Dutch national train passenger assignment model, Transportation Research Part A: Policy and Practice, 66 (2014) 111-126. [15] V. van den Berg, E.T. Verhoef, Congestion tolling in the bottleneck model with heterogeneous values of time, Transportation Research Part B: Methodological, 45 (2011) 60-78.
14
Journal Pre-proof
228
[16] K. Martens, The bicycle as a feedering mode: experiences from three European countries, Transportation Research Part
229 230 231 232 233 234 235 236 237 238
D: Transport and Environment, 9 (2004) 281-294.
239
Transportation Research Part A: Policy and Practice, (2019).
240 241 242 243 244 245 246 247
[22] S.E. Vedel, J.B. Jacobsen, H. Skov-Petersen, Bicyclists’ preferences for route characteristics and crowding in
248 249 250 251 252 253 254 255 256
[26] A. Szolnoki, M. Perc, Evolutionary dynamics of cooperation in neutral populations, New Journal of Physics, 20 (2018)
257 258 259 260 261 262 263 264
Physica A: Statistical Mechanics and its Applications, 456 (2016) 281-287.
[17] S.A. Bagloee, M. Sarvi, M. Wallace, Bicycle lane priority: Promoting bicycle as a green mode even in congested urban area, Transportation Research Part A: Policy and Practice, 87 (2016) 102-121.
Intelligent Transportation Systems, 19 (2018) 2279-2289.
of
[18] G. Tang, S. Keshav, L. Golab, K. Wu, Bikeshare pool sizing for bike-and-ride multimodal transit, IEEE Transactions on
[19] H. Li, H. Ding, G. Ren, C. Xu, Effects of the London Cycle Superhighways on the usage of the London Cycle Hire, Transportation research part A: policy and practice, 111 (2018) 304-315.
p ro
[20] S. Céspedes, J. Salamanca, A. Yáñez, D. Vinasco, Group Cycling Meets Technology: A Cooperative Cycling CyberPhysical System, IEEE Transactions on Intelligent Transportation Systems, 99 (2018) 1-11. [21] A. Agarwal, D. Ziemke, K. Nagel, Bicycle superhighway: An environmentally sustainable policy for urban transport,
Pr e-
Copenhagen–A choice experiment study of commuters, Transportation research part A: policy and practice, 100 (2017) 53-64. [23] A. Szolnoki, M. Perc, A. Szolnoki, M. Perc, Conformity enhances network reciprocity in evolutionary social dilemmas, Journal of the Royal Society Interface, 12 (2015) 20141299-20141299.
[24] A. Szolnoki, X. Chen, Competition and partnership between conformity and payoff-based imitations in social dilemmas, New Journal of Physics, 20 (2018) 093008.
[25] N. He, X. Chen, A. Szolnoki, Central governance based on monitoring and reporting solves the collective-risk social
013031.
al
dilemma, Applied Mathematics and Computation, 347 (2019) 334-341.
[27] Y. Zhang, A. Liu, C. Sun, Impact of migration on the multi-strategy selection in finite group-structured populations,
urn
Scientific reports, 6 (2016) 35114.
[28] Y. Zhang, X. Chen, A. Liu, C. Sun, The effect of the stake size on the evolution of fairness, Applied Mathematics and Computation, 321 (2018) 641-653.
[29] F. Fu, M.A. Nowak, Global migration can lead to stronger spatial selection than local migration, Journal of statistical physics, 151 (2013) 637-653.
Jo
[30] J. Ma, W. Han, Q. Guo, Z. Wang, Traffic dynamics on two-layer complex networks with limited delivering capacity,
[31] X. Jiang, X. Wen, M. Wu, M. Song, C. Tu, A complex network analysis approach for identifying air traffic congestion based on independent component analysis, Physica A: Statistical Mechanics and its Applications, 523 (2019) 364-381. [32] M.A. Nowak, R.M. May, Evolutionary games and spatial chaos, Nature, 359 (1992) 826. [33] R. Cong, B. Wu, Y. Qiu, L. Wang, Evolution of Cooperation Driven by Reputation-Based Migration, Plos One, 7 (2012) e35776. [34] M. Perc, J. Gomez-Gardenes, A. Szolnoki, L.M. Floría, Y. Moreno, Evolutionary dynamics of group interactions on structured populations: a review, Journal of the royal society interface, 10 (2013) 20120997.
15
Journal Pre-proof
265
[35] K. Li, Z. Kang, L. Zhang, Group structures facilitate emergency evacuation, Europhysics Letters, 124 (2019) 68002.
266 267 268 269 270 271 272 273 274 275
[36] M. Perc, A. Szolnoki, Coevolutionary games—a mini review, BioSystems, 99 (2010) 109-125.
276
[42] K. Li, R. Cong, T. Wu, L. Wang, Bluffing promotes overconfidence on social networks, Scientific Reports, 4 (2014)
277 278 279 280 281 282 283 284
5491.
285 286 287 288 289 290 291 292 293
[47] H. Spiess, Conical Volume-Delay Functions, Transportation Science, 24 (1990) 153-158.
294 295 296 297 298 299 300 301
[52] A. Szolnoki, Z. Wang, M. Perc, Wisdom of groups promotes cooperation in evolutionary social dilemmas, Scientific
[37] K. Li, A. Szolnoki, R. Cong, L. Wang, The coevolution of overconfidence and bluffing in the resource competition game, Scientific reports, 6 (2016) 21104. [38] Y. Zhang, F. Fu, X. Chen, G. Xie, L. Wang, Cooperation in group-structured populations with two layers of interactions,
of
Scientific reports, 5 (2015) 17446.
[39] K. Li, R. Cong, T. Wu, L. Wang, Social exclusion in finite populations, Physical Review E, 91 (2015) 042810. [40] X. Chen, A. Szolnoki, Punishment and inspection for governing the commons in a feedback-evolving game, PLoS
p ro
computational biology, 14 (2018) e1006347.
[41] A. Szolnoki, M. Perc, Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment, Physical Review X, 7 (2017) 041027.
Pr e-
[43] F.J. Bahamonde-Birke, U. Kunert, H. Link, J. de Dios Ortúzar, About attitudes and perceptions: finding the proper way to consider latent variables in discrete choice models, Transportation, 44 (2017) 475-493. [44] D. Branston, Link capacity functions: A review, Transportation Research, 10 (1976) 223-236. [45] R. Akcelik, Travel time functions for transport planning purposes: Davidson's function, its time dependent form and alternative travel time function, Australian Road Research, 21 (1991) 3.
[46] E.T. Mtoi, R. Moses, Calibration and evaluation of link congestion functions, Journal of Transportation Technologies, 4 (2014) 2.
al
[48] G. Gould, A. Karner, Modeling bicycle facility operation: cellular automaton approach, Transportation research record, 2140 (2009) 157-164.
urn
[49] S. Zhang, G. Ren, R. Yang, Simulation model of speed–density characteristics for mixed bicycle flow—Comparison between cellular automata model and gas dynamics model, Physica A: Statistical Mechanics and its Applications, 392 (2013) 5110-5118.
[50] S. Jin, X. Qu, D. Zhou, C. Xu, D. Ma, D. Wang, Estimating cycleway capacity and bicycle equivalent unit for electric bicycles, Transportation Research Part A: Policy and Practice, 77 (2015) 225-248.
Jo
[51] K. He, Z. F. Zhu, Code for design of urban road engineering, China Architecture & Building Press, Beijing, 2012.
Reports, 2 (2012) 576.
[53] A. Szolnoki, M. Mobilia, L.-L. Jiang, B. Szczesny, A.M. Rucklidge, M. Perc, Cyclic dominance in evolutionary games: a review, Journal of the Royal Society Interface, 11 (2014) 20140735. [54] M. Perc, J.J. Jordan, D.G. Rand, Z. Wang, S. Boccaletti, A. Szolnoki, Statistical physics of human cooperation, Physics Reports, 687 (2017) 1-51. [55] Z. Kang, L. Zhang, K. Li, An improved social force model for pedestrian dynamics in shipwrecks, Applied Mathematics and Computation, 348 (2019) 355-362.
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Journal Pre-proof *Declaration of Interest Statement
Declaration of interests
☑The authors declare that they have no known competing financial interests or personal relationships
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that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered
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as potential competing interests:
PII: DOI: Reference:
S0378-4371(19)32043-6 https://doi.org/10.1016/j.physa.2019.123664 PHYSA 123664
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Physica A
Received date : 6 August 2019 Revised date : 4 November 2019 Please cite this article as: Q. Li, Z. Zhang, K. Li et al., Evolutionary dynamics of travelling behavior in social networks, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123664. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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An evolutionary game model for travel choice in social networks is established. Commuters' travel behavior is influenced by heterogeneity of individuals’ characteristics. A travel mode for transfers between cycle highways and rail transit is proposed in this paper. Management recommendations for various travel modes are proposed to alleviate traffic congestion.
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Evolutionary dynamics of travelling behavior in social networks Qiaoru Lia, Zhe Zhanga, Kun Lia,∗, Liang Chena, Zhenlin Weia, Jingchun Zhanga a
School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China
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Abstract
In this paper, the topology of complex network is used to characterize the interactions among travelers. Based on the
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assumption of travelers’ limited rationality and the wisdom of crowds, an evolutionary game model of travelers was established. Combining these research findings, we study commuters' travel behavior rules during peak traffic periods and make some recommendations that have the potential to relieve traffic congestion. In the first section, we analyze the effect of heterogeneity on travel choice behavior by Monte Carlo simulations, which explains why the total amount of traffic during peak hours is hard to decrease. The experimental results indicate that increasing fees would not reduce traffic flow during peak hours. Moreover, controlling price for the management of travel demand needs to be coordinated with the management
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of traffic system under the condition of limited road resources. On this foundation, the second section proposes an environmental travel mode for the transfer between cycle highways and rail transit. We verify the effectiveness of this travel mode in alleviating traffic congestion. Furthermore, considering the interactions between different travel modes in transportation system, we suggest some management recommendations with reference to the characteristics of different travel modes.
Keywords: Travel behavior, Networks, Cycle highways, Travel mode, Evolutionary game
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____________________________________________________________________________________________________ 1. INTRODUCTION
Traffic congestion has been endemic to metropolises, especially during peak hours. The initial idea to address this is to
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alleviate the contradiction between the supply and demand of traffic by expanding road traffic capacity [1]. However, Downs
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and Braess verified that widening the road system provides no value in solving it and will cause more crowded roads and
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longer commuting time instead [2,3]. The comprehension of travel behavior is prerequisite for the guidance of transportation
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__________________________
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∗Corresponding author
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Email addresses: [email protected]
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demand. Generally, travel behavior refers to the fact that the value of enjoying traffic service is lower than the cost of traffic
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itself [4-6]. Therefore, due to this price, the implementation of congestion charges to control traffic volumes has become a
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heated topic [7]. Vickrey [8] applied the Queuing Theory and proposed a dynamic model of road traffic system based on
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travel costs, namely, the bottlenecks. Arnott et al. [9,10] considered congestion charging into the bottlenecks and studied the
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behavior of travelers. Laih et al. [11] proposed the concept of multi-step tolls. Xiao et al. [12] optimized different charging
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systems and proposed time-varying toll and single-step coarse toll. These models are often referred to as congestion charge
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models. Some researchers have explored solutions from the perspective of public transportation. For example, Gkritza [13]
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has studied the impact of the price structure of different travel modes on the demand for public transportation in the context
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of the competition and cooperation of multiple travel modes. Pel et al. [14] proved that travel time and congestion are also
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two major factors affecting the service level of public transportation. Van den Berg et al. [15] considered travel time and
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delay to be the impact of the social welfare on heterogeneous travelers in a continuous situation.
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In recent years, bicycle transit, a green environmental travel mode, have provided new ideas for alleviating traffic
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congestion [16-18]. To promote the development of bicycle transportation, some countries have even built cycle highways,
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also known as “cycle superhighways”, to meet the demand of long distance and high quality bicycle routes for bicycle
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commuters [19,20]. Researchers proved that boosting the cycle highways as a mode of transport is a good opportunity to
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alleviate traffic congestion [21,22]. Based on the background of cycle highways, this paper proposes that the travel mode for
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transfer between cycle highways to rail transit. Additionally, combined with traditional research, considering congestion
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charges and the management of public transportation, we provide management suggestions for traffic congestion.
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To grasp the wisdom of crowds [23,24] in traffic system and achieve the coordinated management of various traffic
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modes, we adopted an effective tool for the research of collective behavior: complex networks [25-29]. Recently, complex
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networks have generated significant development in the field of traffic congestion with broad applicability and have provided
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insights into the structure and function of both natural and designed systems [30,31]. Meanwhile, evolutionary game theory
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has been proved to be a basic and effective tool to explain the maintenance of cooperative crowd behaviors in structured
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populations [32-34], which are necessary and critical to solve traffic congestion [35]. Co-evolutionary process [36,37], group
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interaction [38,39], punishment behavior [40,41], as well as social psychological [42] are all prime examples of exploring
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collective behavior in the evolutionary process of strategy invasion on networks.
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In this work, combining the theories of evolutionary game and complex networks, we study the travel rules during peak
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hours and explore the reasons of traffic congestion. For both environmental protection and energy conservation, this paper
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presents a travel mode of the transfer between cycle highways and rail transit, which is in parallel with traditional travel
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modes. Considering the integrality of traffic system, we propose the management of bicycle transit to promote the transition
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of cars to public transportation to alleviate traffic congestion. The rest of the paper is arranged as follows. In Section II, we
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investigate the game models of travelers adapting to networks, model for choosing whether to travel and model for travel
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modes choice. Section III is divided into two parts. In the first part, we explore the impact of heterogeneity on travel choices ,
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and find that increasing congestion charges during peak hours cannot alleviate traffic congestion; In the second part, the
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evolutionary stable results of travel modes choice verify the effectiveness of the transfer of cycle highways to rail transit in
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relieving traffic congestion. Section IV is the conclusion.
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2. MODELS
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2.1. Model for choosing whether to travel
In this section, we discuss travel choice behaviors during peak hours from the view of evolutionary game. The travel
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choice game is arranged on a square lattice with N 3600 nodes, where every node is surrounded by four nearest neighbors
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and is a member in their corresponding groups. Each node refers to a travel group which contains many travelers. There are
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two strategies for players to choose from, to travel or not to travel. If player i chooses not to travel during peak hours, it
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represents cooperation, and Si 1 . Otherwise, i is a defector, and Si 0 . Node i plays with its neighbors as a group of size
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Gi =5 , whose members g are likely to develop competitive relationship for road resources because of the same travel route
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Li . A cooperator takes losses caused by uncompleted tasks, which is related to the importance, , of the task. Additionally,
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for the players is heterogeneous. Each cooperator contributes 1 to traffic on the routes of participating groups, while
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defectors contribute nothing. In each group, the sum of traffic n is subsequently multiplied by the factor r > 1, reflecting that
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the traffic cost of every uncooperative player is r n . In addition, we assume that charge c exists, which depends on the
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average growth triggered by congestion charges and includes the economic congestion toll and other increased costs, such as
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the perceived cost caused by the transfer of car users to public transportation. So, c is identical for every route. The cost of
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defector consists of two parts, the traffic cost r n and the charge c . Each player participates in five groups, a self-centered
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and four neighbor-centered groups, while the total cost of a defector expended in all the groups is thus：
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Pi g pig = g rn g c ,
the total cost of a cooperator expended in all the groups is：
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(1)
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Pi g pig = g f ,
(2)
where is the importance of the task and f is the loss of importance per unit. The importance of each individual, i , is
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denoted by a parameter i ( 0 i 1 ). We distinguish individuals into groups of three classes regarding their value of on
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the square lattice:
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i) Low-Importance class, whenever i
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ii) Medium-Importance class, whenever
1 2 i and finally 3 3
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iii) High-Importance class, whenever
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Initially, each individual i is designated either as a cooperator or a defector with equal probability, and assigned by
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random values. According to Eq.1 and Eq.2, strategy competitions are carried out between nearest neighbors on the given
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network. After collecting payoffs, player i can adopt the strategy s j of one of its randomly chosen nearest neighbors j with
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a probability determined by the Fermi Function：
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w s
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si
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1 exp pi p j / k
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(3)
where we set k 2 . The selected value ensures that better performing players are readily followed by their neighbors,
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although adopting the strategy of a player that performs worse is not impossible either. The results remain qualitatively
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similar in a wide range within the k 20 intervals. Each player has a chance to adjust its strategy once during a Monte Carlo
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step. In our results, each data point is the mean value of 200 independent experiments, and the result of each experiment is
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obtained by averaging over 1000 generations after 10,000 generations as an iterative process.
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2.2. Model for travel modes choice
Taking the cycle highways as the background, we propose a travel mode for transfers between cycle highways and rail
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transit. We also utilize square lattice with N 3600 nodes to represent the game relationship in which travelers compete for
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road resources. Players make their own travel mode choices using game strategy. We set three commuting modes: S 0
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serves as traveling by car, S 1 serves as traveling by transitions from bus to rail transit (bus-rail), S 2 serves as traveling
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by transitions from bicycle on the highways to rail transit (bicycle-rail). Taking into consideration the three aspects of time,
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economy and crowded perception
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flow travel time, economic costs before congestion charges and the crowded perception when there is only one player. The
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payoff collecting process and strategy imitation rules are consistent with those introduced above.
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[43], player’s payoff is available. We assume that the expectation of players includes free-
By car is the most comfortable travel mode where congestion perceptions are not sensitive. We set the expected
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congestion perception cost equal to the actual congestion perception cost. Congestion charging has few economic
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consequences for public transportation and bicycle transit, so the expected economic cost of railways, buses and bicycles are
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the same as their actual economic costs. In terms of time, the relatively stable operation schedule enables the travel time to be
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consistent with expectations. The payoff to a player is：
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veh veh pcar time 2 1 t gveh / t0veh cos t 1 ccar g veh veh veh veh bus rail , pbus rail g time 1 1 t g / t0 per rg cycle cycle cycle bicycle rail pbicycle rail g tcycl ime 1 t g / t0 per rg
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(4)
where ccar is the ratio of the economic cost after congestion charges to the original economic cost, the payoff of
bus rail 1 mgbus rail perception rg
, mgbus rail is the number of players choosing bicycle-rail in group g, is the
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comprehensive crowded sensitivity coefficient per player when travelers choose the bus-rail travel mode, and 0 .
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Similarly, rbicycle rail 1 mgbicycle rail , and the comprehensive crowded sensitivity coefficient of the bicycle-rail travel mode
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veh veh cycle cycle k =1 , cos 0 . We set time t =1 , time =1 , and per =1 . Travel time t g k veh, cycle is calculated by Eq. (5). Notably, the
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travel time t gveh is calculated by an average for the motorway. Considering the characteristics of different travel modes, the
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travel time of each travel mode is calculated by multiplying average travel times by a coefficient. For the travel time of a bus
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tg,bus 1tgveh and that of car tg,car 2tgveh , we set 1 1.2 , 2 0.8 .
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Regarding travel time functions, we adopt Akcelik function for urban street characteristics [44-47]. In addition,
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researchers have demonstrated that bicycle traffic flow applies [48-50]. t gk t0k 0.25T xgk 1
x
k g
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8 J k xgk , (k=veh, cycle) C kT
(5)
where t0k is free-flow travel time per unit distance， T is the time period of analysis， xgk is the degree of saturation
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(volume( Vg )/capacity(C)), C k is capacity, and J k is delay parameter. We suppose that the volume of traffic vgveh on
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motorway and the total volume of buses and cars on the network are linearly related within a game group, i.e., Vgveh veh vgveh ,
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where veh is a coefficient. The total volume of vehicles vgveh k k vgveh, k k 1, 2 , where vveh , k is the number of buses or
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cars, k is Passenger Car Unit (PCU), the ratio of equivalent unit to passenger volume. Equivalent unit for car is 1 and for
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bus is 2 [51]. In this paper, we set the capacity of the bus to 5 times that of the car, so car 1 , and bus 0.4 . On cycle
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highways, Vgcycle cycle mgbicyclerail , where mgbicyclerail is the number of bicycles.
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3. RESULTS
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3.1. Results for choosing whether to travel
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Fig. 1 shows the roles of the loss f and charge c on each route in the process of the evolution. From an overall
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perspective, c promotes the emergence of cooperation, and f is precisely the opposite. Comparing the six different colored
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lines in Fig. 1, it can be found that there were obvious differences in the growth rate. A higher value of f results in a lower
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growth rate of cooperation. Even if the charge c is high, stubborn players choosing to travel during rush hour are always
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present. And increasing f will cause the increment of these stubborn players.
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Fig. 1: Influence of charge c on the cooperation rate c for different values of the loss f . f values are set as 5, 10, 30, 50, 80, and 100 respectively. In fact, c represents the proportion of non-travelers during peak hours.
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Meanwhile, the persistence of defectors may be related to the trip purpose, or in other words, biases players’
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judgment. Thus, we analyze how influences the evolutionary outcome. As shown in panel (a1) in Fig. 2 , is a critical
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issue in determining how fast the system could converge to the full cooperation state. The most resistant individuals are those
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having important tasks to be accomplished from the High-Importance class. After a series of repeated shocks, the High-
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Importance class reaches a stable equilibrium and realizes full cooperation. And in the group (a2) that did not achieve full
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cooperation, High-Importance class is of a feature of growing opposition. They are the hindrance to full cooperation.
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Therefore, we believe that high fees and congestion cannot prevent travelers from traveling during peak hours because
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of the importance of their travel purpose, such as going to work. However, peak hours are usually commuting time, and
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traveling players are mostly those commuting to work or to school. It can be proved that individuals who travel during peak
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hours have a high f value. Especially in the early morning, they have to travel. Simply charging fees has no benefit in
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reducing the total amount of traffic. Controlling the price to manage travel demands and coordinate the rational management
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of travel modes under the condition of limited road resources is important so that travelers can reach their destinations
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without causing traffic congestion.
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Fig. 2: Time-dependence of the fraction of cooperators for the three classes. The value of f is 30 in panel (a1), and 80 in
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panel (a2). Here, c 20 , and other parameters are consistent with those in Fig. 1.
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3.2. Results for travel modes choice
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In this section, traffic status is determined by the ratio of the driving speed to the free-flow speed, referring to the
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Highway Capacity Manual (HCM). Generally, when the ratio is less than 40%, it is considered as intolerable congestion
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status. Bounded by the traffic condition with a ratio of 40%, a reasonable proportion of travel modes assigned should be such
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that t / t0 is less than 2.5. Each experimental value of t / t0 is the average of all players of the three travel modes on the
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network.
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Fig. 3: t / t0 as a function of both and c for different values of the sensitivity coefficient . (b1-b3) are the traffic statuses
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with the coexistence of the three travel modes under the conditions of =1, 5, and 10 respectively. (c) is the result of only
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two travel modes, car and bus-rail. According to the code for the design of China and research on cycleways [50,51], the free-
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travel by car or bicycle. According to u0 t10 , tm t0
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and cycle 1150.4348 .
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flow speed u0veh 60km / h , and u0cycle 20km / h , the capacity in one direction Cveh 4200veh / h , and C cycle 2100bicycles / h on arterial roads. We set T 0.5h and um / u0 0.5 . Assume that um / u0 0.1 when all players 0.25 J C
[45], we can get J veh 4.6667 , J cycle 21 , veh 1334.1216 ,
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In Fig. 3, for a given value of the sensitivity coefficient , a larger domain of small t / t0 (non-red) means that the larger
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adjustable range of parameters, the less sensitive the traffic conditions are to parameter changes, and thus the less prone the
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traffic system is to be trapped in a serious congestion. Therefore, we can consider the size of the non-red color range in each
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panel to be the delay evaluation under the corresponding conditions. As shown in panels (b1-b3), when the three travel
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modes coexist, the value of is not positively correlated with the delay. The increment of first reduces the delay; When
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exceeds the critical value, increasing leads to more serious delay instead. Comparing (b1-b3) with the (c), the former is
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obviously better than the latter in terms of alleviating delay. Even if is small ( =1), the delay of only two travel modes
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(car and bus-rail) is terrible. This result shows that the coexistence of the three modes, rather than two modes, can
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significantly relieve delays, and it is necessary to develop a travel mode of transfers from cycle highways to railways.
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Moreover, to explore the optical method for the management of bicycle transit, we investigate the combined effect of
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sensitivity coefficients and upon the final evolutionary outcome. we first analyze travel mode choice behaviors when
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congestion charges are implemented. As shown in Fig. 4, by exploring the correlation between the fractions of travel modes
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in the first three rows (d1, e1, f1; d2, e2, f2; d3, e3, f3) and the ratio of t / t0 presenting traffic delays in the last row (d4, e4,
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f4), we find that the value of t / t0 and the fraction of car travelers are roughly positively correlated and are negatively related
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to the fraction of bus-rail or bicycle-rail travelers. Excessive car travelers are the main factors resulting in serious congestion.
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Comparing the columns in Fig. 4, congestion charges promote the shift of the travel mode of car to the other two travel
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modes, and an increase in c reduces delays.
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As presented in Fig. 4, the resources for all kinds of travel modes are utilized without serious congestion if and
are within a certain range. This range corresponds to the non-red and non-blue domain of the panel of t / t0 (see Fig. 4 (d4, e4,
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f4)). Despite the value of c , the ideal fraction of car modes and bus-rail modes is about 0.4 (light blue); while for bicycle-rail
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modes, the optimal fraction is approximately 0.2 (between light blue and dark blue). More importantly, elevating c values
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promotes sensitivity coefficients (comparing (d4, e4 and f4)), which help to alleviate traffic congestions. However, for social
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and traffic stability, too large c values are often prohibited in real situations. When c 1 , the optimal range is related to <5,
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<1. If the value of c is increased, the sensitivity coefficient can be allowed to rise correspondingly.
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Fig. 4: Stationary fraction of evolutionary outcomes in dependence on sensitivity coefficients and for different c values. The columns from left to right are respectively the results with condition of c 1 , c 5 , and c 10 . Each row shows the fractions of travelers by car, bus-rail, and bicycle-rail, as well as the corresponding values of t / t0 from top to bottom.
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4. CONCLUSION
As a typical example of collective behaviors [52], travelling demonstrates obvious self-organization process of imitation
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[53,54]. We have exploited the wisdom of crowds on network to display the evolutionary process of travel choice [55], trying
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to provide a new insight to help manage and relieve traffic congestion. We have exploited the wisdom of crowds on network
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to display the evolutionary process of travel choice, trying to provide a new insight to help manage and relieve traffic
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congestion. Initially, based on the concept of cost function, we explored travel rules considering congestion charges.
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Obviously, the stabilization of cooperation (not travel) is obstructed by the fact that travelers must travel for important tasks
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which are not negatively influenced by congestion charges. It is inevitable that travelers commute to work during rush hours,
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also called commuting time. Thus, unquestioning acceptance of congestion charges is unscientific during peak times. We next
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proposed an environmentally friendly travel mode for transfers between cycle highways and railways based on the strong
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support for bicycle transit in various countries. By comparing with and analyzing traditional travel modes, experimental
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results have indicated that the addition of bicycle-rail travel mode is advantageous to relieving traffic congestion. Finally, by
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utilizing the strategy competition behaviors to express travel mode choice, we have studied how to promote the management
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of bicycle transit. In this scenario, the ideal travel fraction of the bicycle-rail mode is lower than those of car mode and bus-
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rail mode. The comprehensive crowded sensitivity coefficient of bicycle-rail mode and the coefficient of bus-rail mode
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should be restricted in a certain range to avoid congestions. When congestion charges are promoted, road managers can
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appropriately elevate the sensitivity coefficients. In summary, the management of public transportation and cycle highways
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can be adjusted according to the congestion charges, which can further better manage and save resources.
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ACKNOWLEDGMENTS
This work was partially supported by Colleges and universities in Hebei province science and technology research
project and technology research project, China (QN2018231), China Scholarship Council.
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REFERENCES
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[1] J.D. Murchland, Braess's paradox of traffic flow, Transportation Research, 4 (1970) 391-394.
203 204 205 206 207 208 209 210 211
[2] A. Downs, Stuck in traffic: Coping with peak-hour traffic congestion, Brookings Institution Press, Washington D.C., 1992.
212 213 214 215 216 217 218 219 220
[7] M. Börjesson, J. Eliasson, C. Hamilton, Why experience changes attitudes to congestion pricing: The case of Gothenburg,
221 222 223 224 225 226 227
Transportation Science, 49 (2013) 46-65.
p ro
of
200
[3] D. Braess, A. Nagurney, T. Wakolbinger, On a paradox of traffic planning, Transportation science, 39 (2005) 446-450.
Pr e-
[4] T.F. Golob, Structural equation modeling for travel behavior research, Transportation Research Part B: Methodological, 37 (2003) 1-25.
[5] J. De Vos, P.L. Mokhtarian, T. Schwanen, V. Van Acker, F. Witlox, Travel mode choice and travel satisfaction: bridging the gap between decision utility and experienced utility, Transportation, 43 (2016) 771-796. [6] M. Kroesen, S. Handy, C. Chorus, Do attitudes cause behavior or vice versa? An alternative conceptualization of the attitude-behavior relationship in travel behavior modeling, Transportation Research Part A: Policy and Practice, 101 (2017) 190-202.
al
Transportation Research Part A: Policy and Practice, 85 (2016) 1-16. [8] W.S. Vickrey, Congestion theory and transport investment, The American Economic Review, 59 (1969) 251-260.
urn
[9] R. Arnott, A. De Palma, R. Lindsey, Economics of a bottleneck, Journal of urban economics, 27 (1990) 111-130. [10] R. Arnott, A. de Palma, R. Lindsey, Departure time and route choice for the morning commute, Transportation Research Part B: Methodological, 24 (1990) 209-228.
[11] C.-H. Laih, Queueing at a bottleneck with single-and multi-step tolls, Transportation Research Part A: Policy and Practice, 28 (1994) 197-208.
Jo
[12] L.-L. Xiao, H.-J. Huang, R. Liu, Congestion behavior and tolls in a bottleneck model with stochastic capacity,
[13] K. Gkritza, M.G. Karlaftis, F.L. Mannering, Estimating multimodal transit ridership with a varying fare structure, Transportation Research Part A: Policy and Practice, 45 (2011) 148-160. [14] A.J. Pel, N.H. Bel, M. Pieters, Including passengers’ response to crowding in the Dutch national train passenger assignment model, Transportation Research Part A: Policy and Practice, 66 (2014) 111-126. [15] V. van den Berg, E.T. Verhoef, Congestion tolling in the bottleneck model with heterogeneous values of time, Transportation Research Part B: Methodological, 45 (2011) 60-78.
14
Journal Pre-proof
228
[16] K. Martens, The bicycle as a feedering mode: experiences from three European countries, Transportation Research Part
229 230 231 232 233 234 235 236 237 238
D: Transport and Environment, 9 (2004) 281-294.
239
Transportation Research Part A: Policy and Practice, (2019).
240 241 242 243 244 245 246 247
[22] S.E. Vedel, J.B. Jacobsen, H. Skov-Petersen, Bicyclists’ preferences for route characteristics and crowding in
248 249 250 251 252 253 254 255 256
[26] A. Szolnoki, M. Perc, Evolutionary dynamics of cooperation in neutral populations, New Journal of Physics, 20 (2018)
257 258 259 260 261 262 263 264
Physica A: Statistical Mechanics and its Applications, 456 (2016) 281-287.
[17] S.A. Bagloee, M. Sarvi, M. Wallace, Bicycle lane priority: Promoting bicycle as a green mode even in congested urban area, Transportation Research Part A: Policy and Practice, 87 (2016) 102-121.
Intelligent Transportation Systems, 19 (2018) 2279-2289.
of
[18] G. Tang, S. Keshav, L. Golab, K. Wu, Bikeshare pool sizing for bike-and-ride multimodal transit, IEEE Transactions on
[19] H. Li, H. Ding, G. Ren, C. Xu, Effects of the London Cycle Superhighways on the usage of the London Cycle Hire, Transportation research part A: policy and practice, 111 (2018) 304-315.
p ro
[20] S. Céspedes, J. Salamanca, A. Yáñez, D. Vinasco, Group Cycling Meets Technology: A Cooperative Cycling CyberPhysical System, IEEE Transactions on Intelligent Transportation Systems, 99 (2018) 1-11. [21] A. Agarwal, D. Ziemke, K. Nagel, Bicycle superhighway: An environmentally sustainable policy for urban transport,
Pr e-
Copenhagen–A choice experiment study of commuters, Transportation research part A: policy and practice, 100 (2017) 53-64. [23] A. Szolnoki, M. Perc, A. Szolnoki, M. Perc, Conformity enhances network reciprocity in evolutionary social dilemmas, Journal of the Royal Society Interface, 12 (2015) 20141299-20141299.
[24] A. Szolnoki, X. Chen, Competition and partnership between conformity and payoff-based imitations in social dilemmas, New Journal of Physics, 20 (2018) 093008.
[25] N. He, X. Chen, A. Szolnoki, Central governance based on monitoring and reporting solves the collective-risk social
013031.
al
dilemma, Applied Mathematics and Computation, 347 (2019) 334-341.
[27] Y. Zhang, A. Liu, C. Sun, Impact of migration on the multi-strategy selection in finite group-structured populations,
urn
Scientific reports, 6 (2016) 35114.
[28] Y. Zhang, X. Chen, A. Liu, C. Sun, The effect of the stake size on the evolution of fairness, Applied Mathematics and Computation, 321 (2018) 641-653.
[29] F. Fu, M.A. Nowak, Global migration can lead to stronger spatial selection than local migration, Journal of statistical physics, 151 (2013) 637-653.
Jo
[30] J. Ma, W. Han, Q. Guo, Z. Wang, Traffic dynamics on two-layer complex networks with limited delivering capacity,
[31] X. Jiang, X. Wen, M. Wu, M. Song, C. Tu, A complex network analysis approach for identifying air traffic congestion based on independent component analysis, Physica A: Statistical Mechanics and its Applications, 523 (2019) 364-381. [32] M.A. Nowak, R.M. May, Evolutionary games and spatial chaos, Nature, 359 (1992) 826. [33] R. Cong, B. Wu, Y. Qiu, L. Wang, Evolution of Cooperation Driven by Reputation-Based Migration, Plos One, 7 (2012) e35776. [34] M. Perc, J. Gomez-Gardenes, A. Szolnoki, L.M. Floría, Y. Moreno, Evolutionary dynamics of group interactions on structured populations: a review, Journal of the royal society interface, 10 (2013) 20120997.
15
Journal Pre-proof
265
[35] K. Li, Z. Kang, L. Zhang, Group structures facilitate emergency evacuation, Europhysics Letters, 124 (2019) 68002.
266 267 268 269 270 271 272 273 274 275
[36] M. Perc, A. Szolnoki, Coevolutionary games—a mini review, BioSystems, 99 (2010) 109-125.
276
[42] K. Li, R. Cong, T. Wu, L. Wang, Bluffing promotes overconfidence on social networks, Scientific Reports, 4 (2014)
277 278 279 280 281 282 283 284
5491.
285 286 287 288 289 290 291 292 293
[47] H. Spiess, Conical Volume-Delay Functions, Transportation Science, 24 (1990) 153-158.
294 295 296 297 298 299 300 301
[52] A. Szolnoki, Z. Wang, M. Perc, Wisdom of groups promotes cooperation in evolutionary social dilemmas, Scientific
[37] K. Li, A. Szolnoki, R. Cong, L. Wang, The coevolution of overconfidence and bluffing in the resource competition game, Scientific reports, 6 (2016) 21104. [38] Y. Zhang, F. Fu, X. Chen, G. Xie, L. Wang, Cooperation in group-structured populations with two layers of interactions,
of
Scientific reports, 5 (2015) 17446.
[39] K. Li, R. Cong, T. Wu, L. Wang, Social exclusion in finite populations, Physical Review E, 91 (2015) 042810. [40] X. Chen, A. Szolnoki, Punishment and inspection for governing the commons in a feedback-evolving game, PLoS
p ro
computational biology, 14 (2018) e1006347.
[41] A. Szolnoki, M. Perc, Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment, Physical Review X, 7 (2017) 041027.
Pr e-
[43] F.J. Bahamonde-Birke, U. Kunert, H. Link, J. de Dios Ortúzar, About attitudes and perceptions: finding the proper way to consider latent variables in discrete choice models, Transportation, 44 (2017) 475-493. [44] D. Branston, Link capacity functions: A review, Transportation Research, 10 (1976) 223-236. [45] R. Akcelik, Travel time functions for transport planning purposes: Davidson's function, its time dependent form and alternative travel time function, Australian Road Research, 21 (1991) 3.
[46] E.T. Mtoi, R. Moses, Calibration and evaluation of link congestion functions, Journal of Transportation Technologies, 4 (2014) 2.
al
[48] G. Gould, A. Karner, Modeling bicycle facility operation: cellular automaton approach, Transportation research record, 2140 (2009) 157-164.
urn
[49] S. Zhang, G. Ren, R. Yang, Simulation model of speed–density characteristics for mixed bicycle flow—Comparison between cellular automata model and gas dynamics model, Physica A: Statistical Mechanics and its Applications, 392 (2013) 5110-5118.
[50] S. Jin, X. Qu, D. Zhou, C. Xu, D. Ma, D. Wang, Estimating cycleway capacity and bicycle equivalent unit for electric bicycles, Transportation Research Part A: Policy and Practice, 77 (2015) 225-248.
Jo
[51] K. He, Z. F. Zhu, Code for design of urban road engineering, China Architecture & Building Press, Beijing, 2012.
Reports, 2 (2012) 576.
[53] A. Szolnoki, M. Mobilia, L.-L. Jiang, B. Szczesny, A.M. Rucklidge, M. Perc, Cyclic dominance in evolutionary games: a review, Journal of the Royal Society Interface, 11 (2014) 20140735. [54] M. Perc, J.J. Jordan, D.G. Rand, Z. Wang, S. Boccaletti, A. Szolnoki, Statistical physics of human cooperation, Physics Reports, 687 (2017) 1-51. [55] Z. Kang, L. Zhang, K. Li, An improved social force model for pedestrian dynamics in shipwrecks, Applied Mathematics and Computation, 348 (2019) 355-362.
16
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Declaration of interests
☑The authors declare that they have no known competing financial interests or personal relationships
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that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered
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as potential competing interests: