Question

A 3-lane freeway drops a lane at location x=0 km. The maximum flow per lane is 1,800 vph, the jam density per lane is 108 veh/km, and the free flow speed is 100 km/hr. Assuming triangular flow-density relation, determine the trip time that will hold from x=-1 to x=+2 km under different types of traffic demand. Recognize that the section under consideration is inhomogeneous and assume that the bottleneck transition is much smaller than the length of the section (3km); i.e., you can assume that space needed for bottleneck transition can be ignored. Please have a comprehensive coverage of the potential types of demand. Clearly state your traffic demand levels in your solutions.

Answer 1

A 3-lane freeway drops a lane at location x=0 km. If the maximum flow per lane is 1,800 vph, the jam density per lane is 108 veh/km, and the free flow speed is 100 km/hr, then:

(a) Plot to a scale on a single set of axes the qvs .k relations for the 3-lane and 2- lane sections of the road, as well as the curve corresponding a single lane that the Q(k) curve(s) are smooth and explain in words the geometrical feature that relates the three curves.

(b)Plot the v(s) curves that correspond to the above Q(k), and again explain their relationship. (Note here that the spacing of cars in a given lane is not the same as 1/k, and that the sin the v(s) relation should be the latter.)