(Solved): There are two major routes - Routes 1 and 2 - between the residential zone and the commercial zone. ...

There are two major routes - Routes 1 and 2 - between the residential zone and the commercial zone. These two routes do not overlap each other. The travellers in the residential zone take one of these two routes to reach the commercial zone. The travel time functions for these two routes are as follows: $t_1=22+2\left(\frac{V_1}{225}\right),t_2=12+\left(\frac{V_2}{100}\right)$ where $t_i=$ travel times on Route $\mathrm{i}$ (minutes) and $V_i=$ number of vehicles on Route i. Assume that the total number of vehicles from the residential zone to the commercial zone is 3,600 vehicles. (a) Compute the number of vehicles and travel time on each route at the user-equilibrium (UE) condition. Also compute the total vehicle travel time using the following equation: $T=V_1\left(\frac{t_1}{60}\right)+V_2\left(\frac{t_2}{60}\right)$ where $T=$ total vehicle travel time (vehicles-hour). (b) Compute the number of vehicles and travel time on each route at the system-optimal (SO) condition when the total vehicle travel time is minimized. Also, compute the total vehicle travel time in the SO condition. (c) Compare the total vehicle travel times between the UE and SO conditions. Discuss why they are different and how to manage travel demand to change the UE condition to the SO condition.