Quick Lube operates a fast lube and oil change garage. On a typical day, custome
ID: 449371 • Letter: Q
Question
Quick Lube operates a fast lube and oil change garage. On a typical day, customers arrive at the rate of three per hour and lube jobs are performed at an average rate of one every 15 minutes. The mechanics operate as a team on one car at a time. Assume Poisson arrivals and Exponential service rates. What is the utilization of the lube team? What is the average number of cars in line? What is the average time a car waits before it is lubed? What is the total time it takes to get through the system?
Quick Lube’s manager want to make sure that with a 95% level of confidence, that no more than four cars will be in the system at any time. Given the present level of service, what is the probability that there are more than four cars in the system? What utilization and rate of lube service must be attained to achieve a 95% confidence level? Please list all step by step how to do?
******JUST NEED SECOND PART OF QUESTION
Explanation / Answer
1. What is the utilization of the lube team?
Arrival rate ()
3
Service rate ()
4
Utilization rate of server ()
= /
75.0%
2. What is the average number of cars in line?
Average number of customers in system (L)
=/(1-)
3
3. What is the average time a car waits before it is lubed?
Average time in system (W)
= L/
1
hour
Average time waiting in line (Wq)
= W-1/
0.75
hour
4. What is the total time it takes to get through the system?
Average time in system (W)
= L/
1
hour
5. Quick Lube’s manager want to make sure that with a 95% level of confidence, that no more than four cars will be in the system at any time. Given the present level of service, what is the probability that there are more than four cars in the system? What utilization and rate of lube service must be attained to achieve a 95% confidence level? Please list all step by step how to do?
******JUST NEED SECOND PART OF QUESTION
Probability of n customers in system
Pn
=(1-)*n
= 7.9%
n =
4
Desired Service Rate for 95% confidence level is = 5 cars per hour
Utilisation rate = 3/5 = 60%
Calculate using goal seek function in excel or trial and error method by substituting values in above formula Pn= (1-)*n
Arrival rate ()
3
Service rate ()
4
Utilization rate of server ()
= /
75.0%
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