Cars arrive on average 10 minutes apart at a single toll booth with a Poison arrival rate and an exponential service time averaging 1 minute. How often is this toll booth idle?

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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Cars arrive on average 10 minutes apart at a single toll booth with a Poison arrival rate and an exponential service time averaging 1 minute. How often is this toll booth idle?

Expert Solution
Step 1

Given that cars arrive on average 10 minutes apart .

That means 1 car arrives in every 10 minutes.

So, in 60 minutes , 60/10 = 6 cars will arrive

Therefore the arrival rate (\lambda) = 6 cars per hour

where \lambda is poison parameter.

The average service time is 1 minutes. Which means 1 car is served in one minute.

So in 60 minutes, 60 X 1 = 60 cars will be served

Therefore, Service rate (\mu) = 60 cars per hour

Utilization = \lambda / \mu = 6/60 = 0.1

Idle time = 1- utilization = 1 - 0.1 = 0.9 = 90%

 

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