Consider a city center where the traffic conditions are described by a Macroscopic Fundamental Diagram (MFD) of network outflow (g- rate of trips finished) vs. accumulation (n- number of cars) with a trapezoidal shape, as shown in the figure below. The values of the parameters are: gmax maximum trip completion rate gmax=100 [veh/min] critical accumulations ner1=1000 [veh] and ncr2=1500 [veh] jam accumulation njam=4000 [veh]. ncr1 ncr2 njam There are two types of demands in the morning peak hour (7-8am): trips generated from outside the city center with rate q-80 [veh/min], and trips generated from within the city center with rate q2-50 [veh/min]. In addition, a perimeter traffic control, u, is available that only restricts vehicles entering the city from outside. If at 7am there are already no-500 [veh] in the city center: a. Write the dynamic equations (mass conservation equation) in a continuous form for the center of the city. b. Convert the continuous dynamic into the discrete form. Use a time unit of 5min. c. What would the accumulation of the system be at 7:30am, if the perimeter control is inactive, i.e. u=1? d. Choose a perimeter control value (u) which starts after 7:30am, so that the network outflow (g) remains at its maximum value at 8:00am. Explain your choice. Hint: You can choose a constant or a time-dependent perimeter control. Both solutions will be considered correct. e. How many vehicles will be queued outside the city center at 8am, when the control restriction, chosen in part d, stops?