## 4 Results
with an interval of 5 min (i.e., 5 min, 10 min, 15 min, etc.). The number of active carpoolers quickly rises during the warm-up period of the simulation and the shortest carpooling period continues up to 30 days. Note that the warm-up period is 30 days where the individuals are only joining the carpool groups. After the warm-up period, the increase rate is lower because of the joining and leaving the carpool groups, respectively. The curves show the decrease of the number of active carpoolers after the warm-up period because the rate of joining by the new carpoolers is lower compared to the rate of leaving the carpool periods by the existing carpoolers. The share of carpooling individuals appears to have become saturated after 100 simulated working days. The results show that when the length of the time window is larger, the chances for negotiation success are greater than when using the smaller one and the behavior of the carpoolers evolves over time due to their carpooling periods and the car capacity parameters. The graph in the Figure 7 illustrates the average carpool group size as a function of time. The carpool size gradually increases during the warm-up period up to 30 days of the simulation. After the warm-up period, the carpool group size curve almost shows spikes. This is enlightened  
Figure 5: Number of active carpool groups (cars/drivers) over the simulated period. Figure 6: Number of active carpoolers over the simulated period. as follows: when the carpooling period of the carpoolers expires and they leave the existing carpool group, there is an enhanced likelihood that they will join another (existing or the same) carpool group instead of creating a new one. After a few days (nearly 80-days), the carpool group size increases at an aggregate level because the rate of the passengers joining groups is higher than the new drivers joined. During this period, the passengers join the existing carpool groups rather than create new ones. The measurement of the computation time of the agent-based simulation is also one of the goals of this study. This is done to analyze the effect of the interaction between individuals. In addition, it aims to determine whether optimization is required to iterate reality and precisely predict carpooling negotiation consequences for the whole population of the study area. The graph in Figure 8 indicates the average computation time of the presented simulation. The experiment was conducted on an Intel(r) Xeon(r) CPU E5-2643 [EMAIL_ADDRESS] GHz 3.50 GHz (2-processors) machine, with 128 GB of RAM and 64-bits operating system. The population scale is achieved by taking 1000 to 10,000 agents (i.e., 1000, 2000, 3000, up to 10,000) for various simulation runs. Each time, the simulation is executed for 150 work-days. To perform this experiment, a constant time window of 30 min is used for each run. The rest of the constraints are the same as shown in the Table 1 except the number of agents. The curve in the graph shows that the processing time increases in a nearly polynomial way with different numbers of agents. It happens due a greater execution of the interaction and the negotiation mechanisms. Figure 8: Computation time in minutes by running different numbers of agents. Figure 7: Carpool groups and carpoolers over the simulated period. The model presented in this paper requires that all carpooling individuals share the source _travel analysis zone_, as well as the destination _travel analysis zone_. This constraint will be considered in future research, which will allow the route of one participant to be a subpath of the route of another participant. The car trip depends on the selection of the _driver_ and the pick-up and drop-off orders of the passengers. This information is used to select the optimal driver.