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?
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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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 () = 6 cars per hour
where 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 () = 60 cars per hour
Utilization = /
= 6/60 = 0.1
Idle time = 1- utilization = 1 - 0.1 = 0.9 = 90%
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