Question

1. At a specified point on a highway, vehicles are known to arrive according to a Poisson distribution. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. It is noted that no cars arrive in 18 of these 120 intervals. Determine the number of these 120 intervals in which exactly three cars arrive. 2. For the data collected in previous problem, estimate the percentage of time headways that will be 10 seconds or greater and those that will be less than 6 seconds.

Answer 1

1 Zero Car interval Probability P (o) = 18 120 0.15 Average arrival time 8 (n) = (st) - At n! P (O) = (x20) :-*20 01 Incois) = -200 » x=0.095 venlfec - Probability of Three Can interval P =10.095x20,3 -0.015420 3 X 2X1 = 1.025/6 = 0.1707 No. of intervals = 0.17078120 = 20.484

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Answer 2

A section of highway has a speed-flow relationship of the form

q = au2 + bu

It is known that at capacity (which is 3100 veh/h) the space-mean speed of traffic is 28 mi/h. Determine the

speed when the flow is 1500 veh/h and the free-flow speed.