Question

In: Accounting

The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can...

The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can service 10 customers per hour. Cars arrive at the regular unleaded pump at a rate of 6 per hour. Determine the average queue length, the average time a car is in the system, and the average time a car must wait. If the arrival rate increases to 12 cars per hour, what will be the effect on the average queue length. Please put in excel format.

*Lq =*

*W =*

*Wq =*

If the arrival rate increases to 12 per hr., what would happen?

Solutions

Expert Solution

L_q = Average number of customer in the waiting line

W = Average time a customer will spend in the queue system

W_q = Average waiting time in the line per customer

Given data

6 Customer per hours

10 customers per hour

Use the following formula to calculate the average queue length :

L_q = ² /

= 6² / 10(10-6)

= 0.9

There are on an average 0.9 cars in the queue

Use the following formula to calculate the average time a car will spend in the total queue system

W = 1 /

= 1 / 10 - 6

= 0.25

The average waiting time in the entire system per car is 0.25 hours

Use the following to calculate how long each car must wait

W_q = /

= 6 /10(10 - 6)

= 0.15

The average waiting in line time per car is 0.15 hours

If the arrival rate is increase to 12 cars per hours, this is higher than the service rate therefore an infinite line would be formed.

Please Up -vote Thank You !!!

ekkarill92 answered 8 months ago

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