Question

A vehicle pulls out onto a single-lane highway that has a flow rate of 300 veh/h (Poisson distributed). The driver of the vehicle does not look for oncoming traffic. Road conditions and vehicle speeds on the highway are such that it takes 1.7 seconds for an oncoming vehicle to stop once the brakes are applied. Assuming a standard driver reaction time of 2.5 seconds, what is the probability that the vehicle pulling out will get in an accident with oncoming traffic?

Answer 1

Answer:

Pr(N < 4.2) = 0.295

Explanation:

given data

flow rate q =  300 veh/h

reaction time = 2.5 s

oncoming vehicle to stop = 1.7 s

solution

we know here that ongoing  vehicle head way between successive vehicles is here greater than (1.5 + 2.5) = 4.2 second

so that driver pulling out will not be in an accident

and if head way is less than 4.2 seconds then driver pulling out will be  accident

here q is 300 vehicles/hour,

then λ= 0.0833 vehicles/second

than probability will be

Pr(N < 4.2) = 1 - $e^{- \lambda t}$  ................ 1

put here value

Pr(N < 4.2) = 1 - $e^{-0.08333*4.2}$

Pr(N < 4.2) = 0.295