## 4 Discussion and Conclusions  
The safety and efficiency of bicycle facilities can be greatly impacted by the interactions between cyclists. The behavior of each cyclist can have a significant impact on how they interact with others at a microscopic level, ultimately shaping the global patterns of motion. The behavior of riders may be studied using microscopic simulation models. In order to develop, calibrate, and validate microscopic behavior models, interactions between riders must be thoroughly studied. This study used the data collected from a controlled experiment to derive key microscopic variables of cyclists' riding behaviors, such as spacing, speed, and acceleration, which are commonly employed in microscopic behavior models. Relationships between these microscopic variables were explored in detail to understand the microscopic characteristics of cyclists' interactions when they are moving in a single file. Results of the reaction delay analysis explained that resembling car-following behaviors, cyclists adjust their behaviors after a specific characteristic delay time that may be defined as the'reaction time' or'sensory motor delay'. Such a parameter could be considered in microscopic simulation models to enhance the accuracy of such models. As reported in previous studies, the reaction time for cars generally varies between approximately 1.2 and 1.5 s [27, 28, 35]. It can be noted that, on average, these values are larger than the reaction times for bicycles estimated in this study. This is logical as cycling does not involve complex tasks, e.g., moving the leg from the accelerator to the brake paddle to press the brake, as in driving. Furthermore, under high density situation, riders are generally prepared to brake and stop or reduce the speed to avoid a potential collision. Previous studies on the simulation of bicycle traffic used larger values, e.g., 1.2 s, for the reaction time [12, 15]. Apparently, such studies have not used microscopic calibration methods that involve the comparison of trajectories. Nevertheless, the estimated reaction times were consistent with the reaction times reported in previous studies for micromobility vehicles such as the Segway. For example, as mentioned in [PERSON] et al. [33], the average reaction time when a Segway rider follows a cyclist can be 0.91 s (\(\pm\)0.35 s) and 0.50 s (\(\pm\)29 s) for general following and sudden brake conditions, respectively. According to the results of the multiple linear regression models used to model cyclists' time-delayed accelerations and decelerations as functions of relative speed and spacing, relative speed is a key predictor of the acceleration and deceleration behaviors of the cyclists. Spacing does not show a strong association; however, it was a significant predictor of the time delayed acceleration. In addition, relative speed and time delayed (by a reaction time) acceleration plots showed a strong correlation. These outcomes indicate that, with re-calibration, simple car-following models, e.g., [PERSON]'s model [22] and [PERSON]'s model [23], can be used to simulate bicycle traffic on narrow bike paths. [PERSON] et al. [12] also mentioned that complex models are not necessary and simpler models with a relatively smaller number of parameters are adequate to realistically capture cyclists' following behaviors. However, the findings of the study of [PERSON] et al. [12] mentioned that a velocity-based distance model, which mainly used the spacing between the following and leading cyclists, performed better than the speed matching model, which used speed difference and is equivalent to [PERSON]'s model [22]. It is important to note that there is a contradiction between this result and the findings of the current study. Stronger interactions, e.g., stop-and-go waves, were observed in the data used in [12] as compared to the current study. Experiment conditions might play a role in such differences and additional data, e.g., real world observations, might be necessary to verify such concerns.