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Abstract

Impatience is a psychological factor that varies from person to person and constantly changes with the environment in real time. In this paper, a model based on cellular automaton is presented to investigate the dynamics of bi-directional flow, with considering individual impatient behaviors. Potential field is defined to represent pedestrian’s interest in available space, which provides an approach to the description of proactive mechanism in bi-directional flow. By formulating the dynamics with controllable parameters, individual impatience level is measured, recorded and updated to trigger off the personalized behaviors. Three different patterns of impatient behaviors are modeled and compared with each other. Simulation results demonstrate the different performances of impatient behavior patterns. Comparing with the situation without considering impatience, bidirectional flow is improved in terms of speed, flow rate and waiting time when impatience level is used to triggers off the sidestep behavior. However, the collective performance shows a deterioration at a most density level when impatience is regarded as a direct parameter to estimate the priority to a target cell among several competitors. The parameter sensitivity analysis of impatience intensity and decision threshold shows the flexibility of the model to present the impatience effect. Simulation experiments under different scenarios also reveal the effects of low proportion of slower pedestrians, walkway width and mixed behavior mode on the efficiency of pedestrian counter flow.

Keywords:

Authors and contacts

Zhang Qi,
Qu Jing

Corresponding author:Zhang Qi,qzhang6@bjtu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 62003027), the Natural Science Foundation of Beijing, China (Grant No. L201013), the Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, China (Grant No. K201904), and the Fundamental Research Fund for the Central Universities, China (Grant No. 2020JBZD007)

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Cited By

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符号	物理意义
$ U_{i, j}^d $	行走方向为d的行人向格子(i,j)移动的转移概率,d表示“右向左”或“左向右”
$ E_{i, j}^d $, $ E_{i, j}^{\bar d} $	取决于方向d或 $ \overline {\boldsymbol{d}} $ 行人的格子(i,j)的潜在势能场值, 当d表示“右向左”, 则$ \overline {\boldsymbol{d}} $表示“左向右”, 反之亦然
$ E_{i, j}^{\rm{l}} $, $ E_{i, j}^{\rm{r}} $	取决于“右向左”或“左向右”行人的格子(i,j)的潜在势能场值, $ E_{i, j}^{\rm{l}} $表示“左向右”, $ E_{i, j}^{\rm{r}} $表示“右向左”
T	时间步
k	行人前进方向上前方k个格子(即受影响格子)
β	潜在势能场值的衰减率, 0 ≤β≤ 1
i	行人的不耐烦水平
α	不耐烦水平增长率,α≥ 1
γ	不耐烦水平衰减率, 0 ≤γ≤ 1
δ	影响决策的不耐烦水平阈值,δ≥ 0

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Step 1: 比较$ {U_{{{ - 1, 0}}}} $, $ {U_{{{ - 1, 1}}}} $ 和 $ {U_{{{ - 1, - 1}}}} $, 具备最大$ {U_{i, j}} $ 值的空闲格子(i,j)被选为目标格子, 转Step 2; 如果3个格子均无空闲,
　　　跳转至Step 4;

Step 2: 将当前格子的$ {E^{\rm{r}}} $值$ E_{{{0, 0}}}^{\rm{r}} $ 设为 $ E_{0, 0}^{\rm{r}} $ + 1, 转Step 3;

Step 3: 移向目标格子, 转Step 5;

Step 4: 停留在当前格子, 将右前格子的$ E_{ - 1, 1}^{\rm{r}} $设为 $ E_{ - 1, 1}^{\rm{r}} $ + 1, 将左前格子的$ E_{ - 1, - 1}^{\rm{r}} $设为 $ E_{ - 1, - 1}^{\rm{r}} $ + 1, 转Step 6;

Step 5: 将走行方向上前k个格子的 $ E_{ - k, 0}^{\rm{r}} $设为$ E_{ - k, 0}^{\rm{r}} $ + 1, 转 Step 6;

Step 6: 将所有空闲格子的$ {E^{\rm{r}}} $设为$ {E^{\rm{r}}} $ ×β.

对于“左向右”行人, $ {E^{\rm{l}}} $的更新规则类似. 当多人选择同一目标格子时, 随机选择一人移动.

DownLoad: CSV

Step 1: 比较前进方向3个格子的$ {U_{{{ - 1, 0}}}} $, $ {U_{{{ - 1, 1}}}} $ 和 $ {U_{{{ - 1, - 1}}}} $, 具备最大$ {U_{i, j}} $的空闲格子 (i,j) 被选为目标格子, 转Step 2; 如果3个格子
　　　均非空且i>δ, 跳转Step 7; 否则, 跳转 Step 4;

Step 2—Step 6: 与表2规则中的Step 2—Step 6 相同;

Step 7: 比较左右横向格子的$ {U_{{{0, 1}}}} $ 和 $ {U_{{{0, - 1}}}} $, 具备最大$ {U_{i, j}} $的空闲格子 (i,j) 被选为目标格子, 转Step 2; 如果两个格子均非空, 跳转
　　　 Step 4.

DownLoad: CSV

Step 1: 比较前进方向3个格子的$ {U_{{{ - 1, 0}}}} $, $ {U_{{{ - 1, 1}}}} $ 和 $ {U_{{{ - 1, - 1}}}} $, 具备最大$ {U_{i, j}} $的空闲格子 (i,j) 被选为目标格子, 判断该行人是否在竞
　　　争者中具备最大i(i>δ), 是转Step 2, 否跳转Step 7; 如果3个格子均非空, 跳转 Step7;

Step 2—Step 6: 与表2规则中的 Step 2—Step 6 相同;

Step 7: 依次针对该行人周边的空闲格子判断该行人是否在竞争者中具备最大i(i>δ), 是则对应的格子选为目标格子, 转Step 2; 否跳
　　　转 Step 4.

DownLoad: CSV

Step 1: 比较前进方向3个格子的$ {U_{{{ - 1, 0}}}} $, $ {U_{{{ - 1, 1}}}} $和 $ {U_{{{ - 1, - 1}}}} $, 具备最大$ {U_{i, j}} $(i≤δ) 或 $ {U_{i, j}} \times i $(i>δ)的空闲格子 (i,j) 被选为目标格
　　　子, 判断该行人是否在竞争者中具备最大的$ {U_{i, j}} $(i≤δ) 或 $ {U_{i, j}} \times i $(i>δ), 是转Step 2, 否跳转Step 7; 如果3个格子均非空,
　　　跳转Step 7;

Step 2—Step 6: 与表2规则中的Step 2—Step 6 相同;

Step 7: 依次针对该行人周边的空闲格子判断该行人是否在竞争者中具备最大$ {U_{i, j}} $(i≤δ) 或 $ {U_{i, j}} \times i $ (i>δ), 是则对应的格子选为
　　　目标格子, 转Step 2; 否跳转 Step 4.

DownLoad: CSV

指标	含义	计算方法
Speed	速度	每一时间步向前进方向3个邻居格子(正前、左前、右前)移动的人数比总计人数
Flow rate	流率	每一时间步移动穿过右侧边界的“左向右”行人数量与移动穿过左侧边界的“右向左”行人数量之和
Waiting time	等待时间	行人原地停滞等待的时间步之和比总计人数

DownLoad: CSV

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Vol. 71, Issue 7 - 2022-04-05

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