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# queuing theory

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4. Tom Smith's Jiffy Lube is able to serve customers in an average time of 12 minutes (negative exponential distribution). Customers arrive at the shop at an average of 3 per hour (Poisson distribution). The queue discipline is first-in, first-out and the calling population can be considered infinite.

a. What is the average number of vehicles in the system?
b. What is the average time a vehicle waits in the queue?
c. What is the probability that the shop is idle?

Please show all the steps taken.

The Jiffy Lube now only has room for 5 vehicles to wait for service.

d. What is the probability that the parking area is full when a customer arrives?
e. What is the probability that exactly 6 cars arrive in any given hour?

https://brainmass.com/statistics/probability/solution-queuing-theory-409689

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4. Tom Smith's Jiffy Lube is able to serve customers in an average time of 12 minutes (negative exponential distribution). Customers arrive at the shop at an average of 3 per hour (poisson distribution). The queue discipline is first-in, first-out and the calling population can be considered infinite.

What is the average number of vehicles in the system?
What is the average time ...

#### Solution Summary

Detailed solutions to queuing theory are provided.

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