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

Lq = Average number of customer in the waiting line

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

Wq = 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 :

Lq = 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

Wq = /

= 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 1 year ago
Next > < Previous

Related Solutions

17. At a certain gas station 40% of the customers request regular gas, 35% request unleaded...
17. At a certain gas station 40% of the customers request regular gas, 35% request unleaded gas, and 25% request premium gas. Of those customers requesting regular gas, only 30% fill their tanks all the way up, while the remaining 70% only fill up part of their tank. Of those customers requesting unleaded gas, 60% fill their tanks all the way up, while of those requesting premium, 50% fill their tanks all the way up. If the next customer does...
A new gas station has only one pump for gasoline. Cars take on an average 5...
A new gas station has only one pump for gasoline. Cars take on an average 5 minutes to fuel up. The gas station manager calculated that the pump has an average of 8 cars visiting it every hour. On an average, how many cars will be waiting in the queue for refueling? (3 decimals)
A one-pump gas station is always open and has two types of customers. A police car...
A one-pump gas station is always open and has two types of customers. A police car arrives every 30 minutes (exactly), with the first police car arriving at time 15 minutes. Regular (nonpolice) cars have exponential interarrival times with mean 5.6 minutes, with the first regular car arriving at time 0. Service times at the pump for all cars are exponential with mean 4.8 minutes. A car arriving to find the pump idle goes right into service, and regular cars...
) The most recent 30 days of the price per gallon of regular unleaded gas is...
) The most recent 30 days of the price per gallon of regular unleaded gas is in the file. Using R code Please answer the following questions. a. Compute a forecast for the next day’s prices using a 3-day Moving Average model. What is the forecast? What is the MSE for the last five observations? b. Can you reduce the MSE for the last five observations by changing the movingaverage window? (Hint: Try 4-10 day windows) c. Compute a forecast...
Suppose that the daily demand for regular gasoline at a gas station is normally distributed with...
Suppose that the daily demand for regular gasoline at a gas station is normally distributed with a mean of 1,000 gallons and a standard deviation of 100 gallons. The next delivery of gasoline is scheduled later today at the close of business. What is the minimum amount of regular gasoline that the station must have in storage so that there is a 90% chance it will have enough to satisfy today’s demand? Select one: a. 836 b. 872 c. 1,128...
At one point the average price of regular unleaded gasoline was ​$3.543.54 per gallon. Assume that...
At one point the average price of regular unleaded gasoline was ​$3.543.54 per gallon. Assume that the standard deviation price per gallon is ​$0.080.08 per gallon and use​ Chebyshev's inequality to answer the following. ​(a) What percentage of gasoline stations had prices within 33 standard deviations of the​ mean? ​(b) What percentage of gasoline stations had prices within 2.52.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.52.5 standard deviations of the​ mean? ​(c) What...
At one point the average price of regular unleaded gasoline was $3.53 per gallon. Assume that...
At one point the average price of regular unleaded gasoline was $3.53 per gallon. Assume that the standard deviation price per gallon is ​$0.07 per gallon and use​ Chebyshev's inequality to answer the following. ​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean? ​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean? ​(c) What...
A gas station has a 7% chance of running out of gas. What is the probability...
A gas station has a 7% chance of running out of gas. What is the probability the gas station will run out of gas one day in the next week? What is the probability the gas station will run out of gas at least two days in the next week? What is the expected number of times the gas station will run out of gas?
A service station has both self-service and full-service islands. On each island, there is a single...
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.05 0.02 1...
A service station has both self-service and full-service islands. On each island, there is a single...
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y)      0 1 2 x 0     0.10     0.03     0.01  ...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT