A certain highway with separate roadways

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At night, vehicles circulate on a certain highway with separate roadways according to a Poisson process with parameter λ = 2 per minute (in each direction). Due to an accident, traffic must be stopped in one direction. Suppose that 60% of the vehicles are cars, 30% are trucks, and 10% are semitrailers. Suppose also that the length of a car is equal to 5 m, that of a truck is equal to 10 m, and that of a semitrailer is equal to 20 m.

(a) From what moment is there a 10% probability that the length of the queue of stopped vehicles is greater than or equal to one kilometer?

(b) Give an exact formula for the distribution of the length of the queue of stopped vehicles after t minutes.

Indication, Neglect the distance between the stopped vehicles

Reference no: EM131130689

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