Question

4 The following 15-minute volumes were obtained on an eastbound lane of a highway. (a) If the capacity of the lane in that direction is 1820 vehicles per hour, would there be queuing delay? Show all the steps to the solution of the problem. (b) Compute the peak hour factor Time period Volume (vehicles) 7:00-7:15 7:15-7:30 7:30-7:45 7:45-8:00 410 459 289 5. A section of highway has the following flow-density relationship in metric units (that is, density is in vehicles per kilometer and speed is in kilometers per hour 9-80k-0.4k2 a) What is the capacity of the highway section in vehicles per hour? b) What is the speed at capacity in kilometers per hour? c) What is the density in vehicles per kilometer when the highway is at a half of its capacity?

Answer 1

Solution:

5.

Maximum capacity can be determined by differentiating the equation and then equating it to 0

thus,

q = capacity

q = v*k

where, v = velocity

(dq/dk ) = 80 - 0.8*k

equating it to 0, we get,

0.8*k = 80

or, k = 80/0.8 = 100

at, k =100,

q = 80*100 - 0.4*100^2

= 4000 veh / hr

b. we know,

q = v*k

or, 4000 = v* 100

v = 40 km/h

this is when capacity is maximum,

but in general, v= q/k

v= 80 - 0.4*k

c. q(max) = 4000

half its capacity = 2000 veh/hr

putting the value in the original equation we get,

2000 = 80*k - 0.4*k^2

k = 29.29 or 170.7

thus, k = 29.29 veh / km as it cannot exceed k =100 which was for maximum.