Nonlinear pricing in linear cities with elastic demands
Nonlinear pricing in linear cities with elastic demands
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具有弹性需求的线性城市的非线性定价
DOI：
10.1016/j.trc.2018.08.005
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发表时间：
2018-10
期刊：
影响因子：
--
通讯作者：
Fang He
中科院分区：
文献类型：
--
作者：
Xi Lin;Meng Li;Fang He
非线性道路收费是根据每个出行者的出行所对应的特定属性等级来收费的。为了帮助当局在战略层面上设计道路收费系统，本文试图解决两个基本问题：(i)定价的非线性对缓解交通拥堵的价值是什么？（ii）若采用非线性收费函数，它是凸形、凹形还是其他形状？具体来说，我们考虑线性城市中基于距离的定价。对于具有异质出行者的线性单中心城市，我们证明了系统最优距离定价确实表现出非线性。证明了：(1)基于费用的系统最优收费函数对行驶距离是单调递增的凹函数；(2)基于时间的系统最优收费函数总是存在且是唯一的。如果走廊上每个出行者群体的初始比例不变，且需求函数为指数型，则基于时间的系统最优收费函数使远离城市中心的出行者单位距离的收费水平更低。对于线性多中心城市，我们证明：(1)总存在系统最优微分收费函数（就城市中心而言）；(2)系统最优非微分收费函数极有可能不存在。因此，我们进一步提出了一个最优收费设计模型，证明了其目标的Lipschitz连续性，并采用全局优化算法求解该模型。
Nonlinear road pricing charges each traveler based on his/her trip’s corresponding particular attribute level. In order to help authorities in designing road pricing systems at a strategic level, this paper attempts to address two fundamental questions: (i) what is the value of pricing’s nonlinearity for mitigating traffic congestion? (ii) if a nonlinear toll function is implemented, should it be convex, concave or other shape? Specifically, we consider distance-based pricing in linear cities. For linear monocentric cities with heterogeneous travelers, we show that the system optimal distance-based pricing indeed exhibits nonlinearity. It is proved that: (i) the cost-based system optimal toll function is monotonically increasing and concave with respect to the traveled distance; (ii) the time-based system optimal toll function always exists and is unique. If the initial proportion of each traveler group is invariant along a corridor and the demand function is of exponential type, then the time-based system optimal toll function enables the travelers, living further away from a city center, to face a lower toll level per unit distance. For a linear polycentric city, we demonstrate: (i) there always exists the system optimal differentiated (in terms of city centers) toll functions; (ii) it is highly possible that the system optimal non-differentiated toll function does not exist. Hence, we further propose an optimal toll design model, prove the Lipschitz continuity of its objective and adopt a global-optimization algorithm to solve it.
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发表时间：
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影响因子：
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影响因子：
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