Microscopic modeling of attention-based movement behaviors

Abstract

For transportation hubs, leveraging pedestrian flows for commercial activities presents an effective strategy for funding maintenance and infrastructure improvements. However, this introduces new challenges, as consumer behaviors can disrupt pedestrian flow and efficiency. To optimize both retail potential and pedestrian efficiency, careful strategic planning in store layout and facility dimensions was done by expert judgement due to the complexity in pedestrian dynamics in the retail areas of transportation hubs. This paper introduces an attention-based movement model to simulate these dynamics. By simulating retail potential of an area through the duration of visual attention it receives, and pedestrian efficiency via speed loss in pedestrian walking behaviors, the study further explores how design features can influence the retail potential and pedestrian efficiency in a bi-directional corridor inside a transportation hub.

Keywords: Architectural design; Pedestrian dynamics; Retail environment; Transportation hubs; Visual attention.

Fig. 1.. Model Architecture:

The simulation framework is a loop composed of two modules: visual attention and locomotion. The loop begins with a position ${\overrightarrow{r}}_T$ and a visual attention state $s_T$ at time step T. Based on them, the probability of initiating or terminating the attention is calculated. From the probability, we get the attention state at the next time step $s_{T+1}$. Then the new attention state determines the desired speed of a pedestrian, which is fed into a Social Force Model to get a new position ${\overrightarrow{r}}_{T+1}$.

Fig. 2.. Field observation site and the camera installation.

The study area covers the front of a convenience store. And the origin of the x-axis is set to the middle point of the corridor section line.

Fig. 3.. Input variables in prior and our work.

Generally, our model combines the observation angle $\varphi$ in Zhou et al. (2022). with the angular separation $\phi$ in Xie et al. (2007), resulting in a representation that can deal with varying environmental object sizes and orientations.

Fig. 4.. Walking direction change (lateral positional deviation) for pedestrians with visual attention.

(a) The illustration of walking direction change (lateral positional deviation) Δx. (b) The distribution of visual attention duration, shown in a histogram. Pedestrians without visual attention are not shown here. (c) The average deviation of lateral position after the initiation of attention. The gray solid line represents the deviation of pedestrians without visual attention after entering the camera.

Fig. 5.. Angular speed ω to store display.

(a) The illustration of angular speed ω and tangential velocity ${\overrightarrow{v}}_{\mathit{\text{tangent}}}$. (b) How average angular speed $\omega$ varies with lateral position (x coordinate). x = 0 represents the middle of the corridor section. x = 270 represents the wall boundary of the corridor on the store side and x = −270 represents the opposite boundary. The gray dotted line represents the angular speed of pedestrians without visual attention to the store. And the shaded areas represent 95% CIs of the metrics. (c) The average walking speed change after the initiation of attention. The gray solid line represents the speed change of pedestrians without visual attention after entering the camera. The shaded areas represent 95% CIs of the metrics.

Fig. 6.. Boundary conditions:

(a) and (b) shows the probability distributions of the time gaps between pedestrians in two directions. The dots are empirical measurements. The dashed lines are exponential fitting results. The y-axes are shown in log scales. (c) shows how the average walking speed varies with lateral coordinates for pedestrians without visual attention, suggesting that pedestrians close to walls tend to walk more slowly. (d) shows the density distributions of pedestrians as a function of lateral coordinates. The two distributions in two colors represent the pedestrian flows in two directions. The shaded areas represent the 95% CIs for the metrics.

Fig. 7.. AUC scores of visual attention predictions with different representations.

Boxplots are drawn based on 100 trials with randomized samplings of our dataset. An AUC score equal to 1 indicates the model is always correct in the test dataset. And a score close to 0.5 indicates that the model performance is the same as random choices. The red boxes denote the performance of our representation. The gray boxes are representation performances that have significantly different mean values from ours. The x-axis labels are abbreviations of representations, where a single letter means a uni-variate linear logistic regression. And two letters connected by a plus (such as $\varphi +\omega$) mean a bi-variate linear logistic regression. A squared letter means the logistic regression is polynomial up to 2 degrees. It should be noted that we only display the top five results and all uni-variate linear fitting results here.

Fig. 8.. Compare our visual attention module with prior work.

(a) and (b) are ROC curves with regard to attention initiation and termination predictions. When the curve gets closer to the top-left corner, the model achieves a higher true positive rate when the false positive rate is fixed. Shaded areas represent the standard errors of true positive rates. Our model is on par with Zhou et al. (2022) in attention initiation modeling, shown by their overlapping curves. The model names with asterisks (e.g., *Wang et al.) refer to the modified models fitted by gradient descent. (c) compares the attention duration distributions of model results and empirical data by probability density functions. For visualization quality, the lines are smoothed by a Gaussian kernel. In the legend, the numbers in the parenthesis are the Wasserstein distances to the empirical distribution. (d) shows the differences between the attention duration distribution of model simulation and that of empirical data, represented in the residuals of cumulative distribution function. When the line is closer to y=0, the simulation result is closer to empirical data. The legend is the same as the previous sub-figure, and lines are also smoothed by a Gaussian kernel.

Fig. 9.. Simulation results compared to empirical data.

To better visualize the contribution of our model, we split all pedestrians in the empirical dataset into 3 disjoint groups: (1) commuters; (2) pedestrians with attention-based movement behaviors; (3) consumers. (see definitions in Section 3.3.4) (a) Mean walking speed υ as a function of x coordinate in empirical data. The error bars represent the 95% CIs for the metrics. We compare the slowing effects when different groups are included in the population. (b) The proportion of long-attention pedestrians P_long as a function of x coordinate. (c) Mean walking speed υ as a function of x coordinate for commuters (group 1). Green: empirical measurement. Magenta: simulation data with visual attention module disabled (simulation of group 1). (d) Mean walking speed υ as a function of x coordinate for commuters and pedestrians with attention-based movement (group 1+2). Blue: empirical measurement. Red: simulation data with visual attention module enabled (simulation of group 1+2).

Fig. 10.. Design settings with varying features in isometric views.

White floors represent the corridor segment. Light red floors are store areas. And the red volumes represent store displays. Corridor width L_c , store width L_s, and store depth L_d are all in the unit of meter here.

Fig. 11.. Simulations with varying design features

Refer to Fig. 10 for corresponding 3D representation. (a) The distribution map of P_long, which means the probability of observing a pedestrian with long-time visual attention to the store; (b) The distribution map of Δυ, which means the average speed loss compared to the same corridor without a store. Maps are top-down views of the corridor in real-world dimensions. The gray boxes represent the dimensions of the store width and display depth.

Fig. 12.. Design settings with varying corridor width in isometric views.

White floors represent the corridor segment. Light red floors are store areas. And the red volumes represent store displays.

Fig. 13.. Simulations with varying corridor widths.

The proportion of long-attention pedestrians and average walking speed for all pedestrians are plotted in the same diagram with different scales. There are two scenarios where (a) store display depth is 0.5 m, and (b) depth is 5 m. The error bars represent the 95% CIs for the metrics.