随机路网配流及广义网络设计研究
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摘要
随着经济社会的快速发展,城市交通供需矛盾日益突出。要有效解决城市交通拥堵问题,必须科学管理和利用交通基础设施,合理调节交通流量时空分布。这要求交通管理者和理论研究者首先掌握交通流量分配理论。在实际的城市道路交通网络中,存在诸多随机事件(如恶劣天气、交通事故以及道路维护等)的影响,这些随机事件很多是无法避免的。因此,研究随机路网环境下的城市道路交通分配问题并将其研究成果应用于解决城市道路交通拥挤问题具有重要的理论价值和现实意义。
在已有研究的基础上,论文主要完成了以下研究工作：
1.建立了随机超预算期望用户均衡模型。在模型中,出行者以理解超预算期望行程时间作为选择路径的依据。超预算期望行程时间定义为路径行程时间超过行程时间预算时的条件期望,反映了行程时间随机变化条件下出行者在选择路径时对可靠性和不可靠性两方面的关注。此外,模型还明确考虑了出行者对行程时间的估计误差、路网服务水平对出行需求的影响以及路网的拓扑关系。推导了OD需求服从对数正态分布和路段通行能力服从贝塔分布条件下超预算期望行程时间的计算公式,建立了用等价变分不等式表示的用户均衡模型,并利用自适应投影收缩算法求解提出的模型。
2.建立了考虑出行目的差异的随机超预算期望用户平衡模型。将路网中的出行者分为通勤者和非通勤者。其中,通勤者需求量是确定的,非通勤者需求量是随机的。通勤者与非通勤者均采用理解超预算期望行程时间作为择路依据,但二者具有不同的行程时间估计误差和需求灵敏度。推导了通勤者需求量服从对数正态分布、路段通行能力服从贝塔分布条件下超预算期望行程时间计算公式,建立了用等价变分不等式表示的用户均衡模型。
3.建立了考虑出行者风险取向差异的混合用户均衡模型。按风险取向不同将出行者分为中立型、冒险型、保守型和超保守型,4类出行者分别采用理解期望行程时间、理解行程时间预算(可靠度低于0.5)、理解行程时间预算(可靠度高于0.5)和理解超预算期望行程时间作为择路依据。推导了随机供需条件下4类出行者出行成本计算公式,建立了用等价变分不等式表示的用户均衡模型。
4.分别建立了基于混合用户均衡的单目标和多目标广义网络设计模型。在单目标双层规划模型中,其上层目标为同时实施路段能力扩展与拥挤收费条件下的路网用户盈余最大化,下层模型为混合用户均衡模型；在多目标双层规划模型中,上层模型包含2个目标函数,分别为实施路段能力扩展条件下路网用户盈余最大化和网络设计投资费用最小化,下层模型为混合用户均衡模型。
With the rapid development of economics and society, the conflict of urban traffic supply and demand becomes more serious. In order to solve this problem effectively, the transportation infrastructure must be managed and utilized more scientifically, and the time and space distribution of traffic flow must be regulated more reasonably. Thus, the managers and researchers need to understand the theory of traffic assignment firstly. In the real road transportation network, there are many stochastic events (such as bad weather, traffic accidents, road maintenance, etc.) that disrupt the road conditions, and many of these stochastic events are unavoidable. As a result, it is significant both in theory and reality fields to study the road traffic assignment problem under stochastic circumstances and apply the research results to solve urban traffic congestion.
Based on the existed research, the main contents contained in this dissertation are as follows.
Firstly, a new traffic assignment model named stochastic mean-excess user equilibrium model is proposed. In the model, perceived mean-excess travel time is served as travelers' route choice criterion. Mean-excess travel time is defined as the conditional expectation of route travel time beyond travel time budget, which reflects travelers'attention to both reliability and unreliability aspects of travel time variability in the route choice decision process. In addition, travelers'perception errors on travel time, the effects on traffic demand caused by the road network service level, and the road network's topological relationship are taken into account. The calculation formula of mean-excess travel time is derived from conditions when the OD (Origin-Destination) demand follows a Log-normal distribution and the link capacity follows a Beta distribution, the user equilibrium model is built and formulated as an equivalent variational inequality problem, and a heuristic solution algorithm called self-adaptive projection and contraction algorithm is used to solve the proposed model.
Secondly, a stochastic mean-excess user equilibrium model taking the differences in travel purposes into account is presented. In the road network, the travelers of the road network are divided into commuters and non-commuters, in which the traffic volume of commuters is deterministic while the traffic volume of non-commuters is stochastic. Both commuters and non-commuters take own perceived mean-excess travel time as separate route choice criteria, but they have different perception errors on travel time and different demand sensitivities. The calculation formula of mean-excess travel time is derived when the commuters'demand follows a Log-normal distribution and the link capacity follows a Beta distribution, and the user equilibrium model is set up and formulated as an equivalent variational inequality problem.
Thirdly, considering travelers'heterogeneity in risk taking behaviors, a mixed user equilibrium model is founded. From the perspective of risk taking behaviors, the travelers are classified as risk-neutral travelers, risk-prone travelers, risk-averse travelers, and extremely risk-averse travelers, who take perceived expected travel time, perceived travel time budget (the reliability is less than0.5), perceived travel time budget (the reliability is more than0.5), and perceived mean-excess travel time as their route choice criteria, respectively. The calculation formulas of the travel cost for four types of travelers in the environment with stochastic supply and demand are derived, the user equilibrium model is founded and formulated as an equivalent variational inequality problem.
Finally, the single-objective and multi-objective generalized network design models based on mixed user equilibrium are proposed respectively. In the single-objective bilevel programming model, the upper objective is to maximize the consumer surplus of the road network in which both link capacity enhancement and road congestion pricing are put into effect at the same time, while the lower model is a mixed user equilibrium model. In the multi-objective bilevel programming model, the upper objective includes two target functions, that is to maximize the consumer surplus of the road network and minimize the total construction cost in the situations where link capacity enhancement is implemented, while the lower model is a mixed user equilibrium model.
在已有研究的基础上,论文主要完成了以下研究工作：
1.建立了随机超预算期望用户均衡模型。在模型中,出行者以理解超预算期望行程时间作为选择路径的依据。超预算期望行程时间定义为路径行程时间超过行程时间预算时的条件期望,反映了行程时间随机变化条件下出行者在选择路径时对可靠性和不可靠性两方面的关注。此外,模型还明确考虑了出行者对行程时间的估计误差、路网服务水平对出行需求的影响以及路网的拓扑关系。推导了OD需求服从对数正态分布和路段通行能力服从贝塔分布条件下超预算期望行程时间的计算公式,建立了用等价变分不等式表示的用户均衡模型,并利用自适应投影收缩算法求解提出的模型。
2.建立了考虑出行目的差异的随机超预算期望用户平衡模型。将路网中的出行者分为通勤者和非通勤者。其中,通勤者需求量是确定的,非通勤者需求量是随机的。通勤者与非通勤者均采用理解超预算期望行程时间作为择路依据,但二者具有不同的行程时间估计误差和需求灵敏度。推导了通勤者需求量服从对数正态分布、路段通行能力服从贝塔分布条件下超预算期望行程时间计算公式,建立了用等价变分不等式表示的用户均衡模型。
3.建立了考虑出行者风险取向差异的混合用户均衡模型。按风险取向不同将出行者分为中立型、冒险型、保守型和超保守型,4类出行者分别采用理解期望行程时间、理解行程时间预算(可靠度低于0.5)、理解行程时间预算(可靠度高于0.5)和理解超预算期望行程时间作为择路依据。推导了随机供需条件下4类出行者出行成本计算公式,建立了用等价变分不等式表示的用户均衡模型。
4.分别建立了基于混合用户均衡的单目标和多目标广义网络设计模型。在单目标双层规划模型中,其上层目标为同时实施路段能力扩展与拥挤收费条件下的路网用户盈余最大化,下层模型为混合用户均衡模型；在多目标双层规划模型中,上层模型包含2个目标函数,分别为实施路段能力扩展条件下路网用户盈余最大化和网络设计投资费用最小化,下层模型为混合用户均衡模型。
With the rapid development of economics and society, the conflict of urban traffic supply and demand becomes more serious. In order to solve this problem effectively, the transportation infrastructure must be managed and utilized more scientifically, and the time and space distribution of traffic flow must be regulated more reasonably. Thus, the managers and researchers need to understand the theory of traffic assignment firstly. In the real road transportation network, there are many stochastic events (such as bad weather, traffic accidents, road maintenance, etc.) that disrupt the road conditions, and many of these stochastic events are unavoidable. As a result, it is significant both in theory and reality fields to study the road traffic assignment problem under stochastic circumstances and apply the research results to solve urban traffic congestion.
Based on the existed research, the main contents contained in this dissertation are as follows.
Firstly, a new traffic assignment model named stochastic mean-excess user equilibrium model is proposed. In the model, perceived mean-excess travel time is served as travelers' route choice criterion. Mean-excess travel time is defined as the conditional expectation of route travel time beyond travel time budget, which reflects travelers'attention to both reliability and unreliability aspects of travel time variability in the route choice decision process. In addition, travelers'perception errors on travel time, the effects on traffic demand caused by the road network service level, and the road network's topological relationship are taken into account. The calculation formula of mean-excess travel time is derived from conditions when the OD (Origin-Destination) demand follows a Log-normal distribution and the link capacity follows a Beta distribution, the user equilibrium model is built and formulated as an equivalent variational inequality problem, and a heuristic solution algorithm called self-adaptive projection and contraction algorithm is used to solve the proposed model.
Secondly, a stochastic mean-excess user equilibrium model taking the differences in travel purposes into account is presented. In the road network, the travelers of the road network are divided into commuters and non-commuters, in which the traffic volume of commuters is deterministic while the traffic volume of non-commuters is stochastic. Both commuters and non-commuters take own perceived mean-excess travel time as separate route choice criteria, but they have different perception errors on travel time and different demand sensitivities. The calculation formula of mean-excess travel time is derived when the commuters'demand follows a Log-normal distribution and the link capacity follows a Beta distribution, and the user equilibrium model is set up and formulated as an equivalent variational inequality problem.
Thirdly, considering travelers'heterogeneity in risk taking behaviors, a mixed user equilibrium model is founded. From the perspective of risk taking behaviors, the travelers are classified as risk-neutral travelers, risk-prone travelers, risk-averse travelers, and extremely risk-averse travelers, who take perceived expected travel time, perceived travel time budget (the reliability is less than0.5), perceived travel time budget (the reliability is more than0.5), and perceived mean-excess travel time as their route choice criteria, respectively. The calculation formulas of the travel cost for four types of travelers in the environment with stochastic supply and demand are derived, the user equilibrium model is founded and formulated as an equivalent variational inequality problem.
Finally, the single-objective and multi-objective generalized network design models based on mixed user equilibrium are proposed respectively. In the single-objective bilevel programming model, the upper objective is to maximize the consumer surplus of the road network in which both link capacity enhancement and road congestion pricing are put into effect at the same time, while the lower model is a mixed user equilibrium model. In the multi-objective bilevel programming model, the upper objective includes two target functions, that is to maximize the consumer surplus of the road network and minimize the total construction cost in the situations where link capacity enhancement is implemented, while the lower model is a mixed user equilibrium model.
引文
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