Question 1
(Ex. 4 pg. 129, Papacostas and Prevedouros)
Given s = 0.30 / (60 - u), derive the relationships u-k, u-q, and q-k.
Estimate the maximum theoretical flow of the roadway.
Note: s - spacing in miles, u - speed in miles per hour (mph)
.
Question 2
(Ex. 8 pg. 129, Papacostas and Prevedouros)
A study of traffic using a bridge showed that the speed-concentration relationship is
u = 17.2 ln (228/k)
Find the a) free-flow speed (uf), b) the theoretical maximum flow on the bridge (qmax), c) the speed (um) and concentration (km) that correspond to the maximum flow, and d) the jam concentration (kj).
Note: k - concentration in veh/mi, u - speed in miles per hour (mph)
.
Question 3
(Ex. 16 pg. 131, Papacostas and Prevedouros)
A vehicle stream is interrupted and stopped by a flag-person. The traffic volume for the vehicle stream before the interruption is 1200 veh/hr and the concentration is 100 veh/mi. Assume that the jam concentration is 240 veh/mi. After five minutes the flag-person releases the traffic. The flow condition for the release is a traffic volume of 1600 veh/hr and a speed of 20 mph.
Determine the length of the queue and the number of vehicles in the queue after five minutes. Also calculate how long it will take for the queue to dissipate after the flag-person releases the the traffic.
Question 4
(Ex. 17 pg. 131, Papacostas and Prevedouros)
Traffic is traveling at 40 mph and a flow rate of 1000 veh/hr when a tractor going at 15 mph turns on to the road.
The platoon that develops behind the tractor has a density of 60 veh/mi. After 0.75 mile, the tractor turns off the main road. The release travel condition for the vehicles in the platoon is at a flow rate of 1200 veh/hr and a density of 40 veh/mi.
Calculate the length of the platoon that develops and the time that it will take for it to dissipate after the tractor leaves
Question 5
Draw a conceptual Time-Distance Diagram representing the traffic in Q3 and Q4 above. Show the general shape of the lines represent the flow of vehicles and the shock waves but the graph need not be to scale. Label key points on the distance and time axes using the information calculated above.