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Cars arrive at a highway toll booth according to a Poisson distribution with a mean of 90 cars per hour. The service rate for passing through the booth is also Poisson distributed with an average 100 cars per hour. The drivers complain of the long waiting time, and authorities are willing to increase the average passing rate by installing automatic toll collecting device. However, before they incur the expenses, they would like you to calculate the average time in system. It will be closest to:

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Answer: Average time in the system = 0.1

Step-by-step explanation:

Given that :

Mean arrival rate ( λ) = 90 cars per Hour

Service rate for passing (mean Numner of people passed per time) (u) = 100 cars per hour

Average time in system (Ws) is given by;

Ws = 1 / (u - λ)

Ws = 1 / ( 100 - 90)

Ws = 1 / 10

Ws = 0.1

Hence, the average time in the system is 0.1

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