One needs to estimate the number of cars waiting in a left-turn lane at a traffi

Question

One needs to estimate the number of cars waiting in a left-turn lane at a traffic light-controlled intersection. The occurrences of left-turning cars are assumed to have a Poisson distribution in time. The mean arrival rate of left-turning cars is 160 per hour and the red light is on for 50 seconds per light cycle.

(a) Assuming no cars are waiting to turn left from previous cycles, what is the expected number of vehicles waiting to turn left at the end of each red light period?

(b) What is the probability that 4 or more cars are waiting at the end of the red light period?

Explanation / Answer

a) 160 cars per hour

So, in 50/60 minutes:

160 * 50/60 = 133.33/60 = 2.22 cars per 50/60 minute red light period

b) Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is . Then, the Poisson probability is: P(x; ) = (e-) (x) / x! where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71

P(X > 4) = ?

P = 0.1846

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