Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium
Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium
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DOI：
10.1016/j.trb.2021.01.007
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
T. Friesz;Ke Han;A. Bagherzadeh
中科院分区：
文献类型：
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作者：
T. Friesz;Ke Han;A. Bagherzadeh
在本文中，我们提出了收敛的充分条件的投影和不动点算法用于计算动态用户平衡与弹性出行需求（E-DUE）。不需要强单调增路径时滞算子的假设。在它的地方，我们假设路径延迟运营商只是弱单调递增，一个属性由Lipschitz连续性保证，而逆需求函数是强单调递减。路径时滞的Lipschitz连续性是一个非常温和的正则性条件。因此，非单调时滞算子可以是弱单调递增的，并且满足我们的收敛准则，只要逆需求函数是强单调递减的。我们通过一个数值例子说明了非单调路径时滞的收敛性。
In this paper we present sufficient conditions for convergence of projection and fixed-point algorithms used to compute dynamic user equilibrium with elastic travel demand (E-DUE). The assumption of strongly monotone increasing path delay operators is not needed. In its place, we assume path delay operators are merely weakly monotone increasing, a property assured by Lipschitz continuity, while inverse demand functions are strongly monotone decreasing. Lipschitz continuity of path delay is a very mild regularity condition. As such, nonmonotone delay operators may be weakly monotone increasing and satisfy our convergence criteria, provided inverse demand functions are strongly monotone decreasing. We illustrate convergence for nonmonotone path delays via a numerical example.