ECI 161, Fall 2015

HW #1 Problems Assigned 9:30PM, 9/30/2015, Due 5PM, 10/7/2015

Textbook (5th edition) problems (15 pt each)

5.2, 5.3, 5.6

[Yellow light dilemma] [15pt]

A driver is cruising along an arterial street at the speed limit v=30 mph, and sees the

traffic light ahead of him turns yellow when he is 150 ft away from an intersection. The

intersection is 20 ft wide, the yellow light lasts 3 seconds and is followed by the red light,

and the maximum deceleration rate of his car is 6 ft/sec/sec . Suppose the driver cannot

speed up (otherwise he would get a speeding ticket),

a. what would happen should the driver proceed to pass the intersection? [5]

b. what would happen if he applies on his brakes immediately (i.e. 0 reaction time)

to decelerate at the maximum rate after he sees the yellow light? [5]

c. what can a traffic engineer do to eliminate this dilemma faced by this motorist

(show your calculations to verify your solution)? [5]

[Critical and Jam Density] [20pt]

The flow and density of a highway were observed to follow the triangular model as given

below:

𝑞 = {50𝑘, 𝑘 ≤ 𝑘𝑐

10(𝑘𝑗 − 𝑘), 𝑘 ≥ 𝑘𝑐

where 𝑘𝑗is the jam density and 𝑘𝑐 is the critical density at which the traffic reaches

maximum flow (the units of flow, density, and speed in the above equations are veh/hour,

veh/mile and mile/hour). In order to find the values of the jam and critical densities, a

traffic engineer took a measurement of the time headway when traffic density is at 140

veh/mile and found that it was 3.6 seconds (round all your calculations to integer values):

a. What is the speed of traffic when the headway measurement was taken? [5pt]

b. What is the jam and critical densities for this highway? [10pt]

c. What is the maximum flow that can be reached on this highway? [5pt]

Note:

1) Please submit your homework on time

2) Number each page and write your name on the front page

3) Write cleanly and clearly, do not miss key steps