"Time headway" in traffic flow is the elapsed time between the time that one car finishes...
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following.
f(x) =
| 0.16e−0.16(x − 0.5) | x ≥ 0.5 | |
| 0 | otherwise |
A) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.)
B) What is the probability that time headway is more than 6 sec? At least 6 sec? (Round your answers to three decimal places.)
more than 6s:
at least 6s:
C) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)
Homework Answers
a)
P(X<6) =(1-exp(-0.16*(6-0.5)))=0.585
b)
more than 6s:=1-0.585 =0.415
at least 6s =0.415
c) probability that time headway is between 5 and 6 sec =P(5<X<6)
=exp(-0.16*(5-0.5))-exp(-0.16*(6-0.5)) =0.072
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