Assuming that the whole DMV is only handled by one queue and one server and both the arrival rate (20 customer per hour) and the service rate (30 customers per hour) random variables are Markovian. (a) What is the mean queue length? [3 pts] (b) Percentage of Idle time of the server? [3 pts] (c) Average number in the queue? [3 pts] (d) Average number in the system? [3 pts] (e) The average wait time in the queue? [3 pts] (f) The average wait time in the system? [3 pts] (g) The probability that no one is in the system. [2 pts]

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: • • maximum trip completion rate gmax=100 [veh/min] critical accumulations ncr1=1000 [veh] and ncr2=1500 [veh] jam accumulation njam=4000 [veh]. gmax 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 q1=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…

Kindy explain the pie chart percentage and give some related study and references about Value of travel time connected to the pie chart

The Jeffersonville Transportation Study area has been divided into four traffic zones. The following data have been compiled. Travel Time (min) District Productions Attractions 1 2 3 4 1 3,000 3,000 5 8 12 15 2 1,000 400 8 5 10 8 3 2,000 4,500 12 10 5 7 4 2,500 600 15 8 7 5 Travel Time 1 5 6 7 8 10 12 15 Fij 2.00 1.30 1.10 1.00 0.95 0.85 0.80 0.65 After the first iteration, the trip table was as follows. District 1 2 3 4 Ps 1 1,415 138 2 367 67 1,306 141 493 73 3 522 4 641 74 125 As 2,945 404 1,478 256 4,550 601 3,000 1,000 1,273 131 2,000 2,500 Complete the second iteration. District 1 2 3 4 Computed A 1 2 3 4 Computed P