## 4 Discussion and Conclusions

Table 3: ANOVA results for the multiple regression models for deceleration. variables are the key determinant of individual acceleration and deceleration behaviors. In particular, males are more likely to accelerate and decelerate than females when they are interacting with the opposite gender. Spacing was significant only for several models that indicated that the spacing was not a strong predictor of the acceleration or deceleration of a pedestrian in a single-file crowd of mixed genders. In this study, individual pedestrians' time-delayed instantaneous accelerations were used as the dependent variable as it is the commonly used predicted variable in microscopic behavior models, such as car-following models [52] and force-based pedestrian simulation models [45]. One key outcome of the current study was that relative speed is the main determinant of acceleration and deceleration behaviors. Spacing displayed a marginal influence on acceleration and deceleration behaviors. These findings are consistent with the findings by [PERSON] et al. [51], who modeled pedestrians' following behaviors using six car-following models. The outcomes of [PERSON] et al. [51] indicated that the speed matching model [53], which explained that if the follower is traveling slower than the leader, they should accelerate, and if they are traveling faster, they should decelerate, performed better as compared to distance-based models. The spacing between the leading and the following pedestrian had no influence on the follower's behavior. However, simplified versions of the social force model used the spacing or the distance between pedestrians to predict interactive repulsive forces or accelerations, and relative speed is used to estimate pushing force when simulated agents are physically contacting [54]. Nevertheless, recent specifications of the social force model consider relative speed to estimate repulsive forces more realistically [55]. The behavior model proposed by [PERSON] et al. [56] to simulate pedestrian following behaviors when they board an aircraft also considered the relative speed in addition to the optimal speed and the current walking speed of the pedestrian. The numerical results of this study indicated that the model that used the variables mentioned above could reasonably reproduce the dynamics of aircraft boarding behaviors. [PERSON] et al. [47] derived several linear regression models to predict change in speed, which can be considered a proxy for the acceleration and walking direction of a pedestrian. The outcomes of this study indicated that the absolute speed, distance headway (spacing), time headway, number of pedestrians located nearby, angle of sight, and angle of interaction are significant predictors of the change in speed and direction of a pedestrian. As can be noted, the result that the space headway or spacing is a significant predictor of the change in speed partially agrees with the outcomes of the current study. However, as we noted, spacing was not a strong predictor of acceleration behavior. Even though the absolute walking speed was not considered in the regression models presented in our study (as it had a high correlation with spacing), as shown in Figure 5, walking speed displayed a strong negative correlation with acceleration. This finding also agrees with the findings by [PERSON] et al. [47], who established that absolute speed is a strong predictor of the change in speed. There are several limitations to this study. Instead of a single model to predict acceleration behaviors, eight separate models were obtained in this study. As mentioned earlier, to avoid the averaging effect, acceleration and deceleration behaviors were considered separately. A single model should be able to predict pedestrian walking dynamics as most microscopic behavior models do. However, different density levels and acceleration and deceleration behaviors were considered separately to comprehensively explore the gender influence on walking dynamics.