# Queuing Questions

You have recently become the manager of the Patriot Airlines check in counter. Because Patriot Airlines has flights that leave frequently all day, customers arrive randomly (i.e., exponentially distributed) at the counter at the average rate of 3 per minute. There is only one employee at a time to staff the counter. Assume the employee takes on average 18 seconds to serve each customer. You may assume this is exponentially distributed.

a) Please fill in the following table. Please include the units.

λ

Average interarrival time

μ

Average service time

Utilization

b) What is the average number of customers in line?

c) What is the average number of customers in the system?

d) What is the average waiting time in line?

e) What is the average waiting time in the system?

f) When the employee is not serving customers, he answers complaint letters regarding service at the airport. If the employee works an 8 hour shift, how much time on average does he have to devote to this activity during the shift?

g) Suppose that, as a result of customer complaints, you decide you need two employees working at the same time. You hire someone so there are two employees but now on average, the service time has a mean of 25 seconds and the variability is 50 sec2.

Please fill in the following table. Please include the units.

μ

Average service time

Utilization

S

Ca

Cs

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#### Solution Preview

See the attached file. Thanks

Hope this will help.

You have recently become the manager of the Patriot Airlines check in counter. Because Patriot Airlines has flights that leave frequently all day, customers arrive randomly (i.e., exponentially distributed) at the counter at the average rate of 3 per minute. There is only one employee at a time to staff the counter. Assume the employee takes on average 18 seconds to serve each customer. You may assume this is exponentially distributed.

a) Please ...

#### Solution Summary

The exponentially distributed averages are determined.