# queuing theory

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

#### Solution Preview

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.