Question

Two mechanics are changing oil filters for the arriving customers. The service time has an Exponential...

Two mechanics are changing oil filters for the arriving customers.
The service time has an Exponential distribution with mean 12 minutes for the first mechanic,
and mean 3 minutes for the second mechanic. When you arrive to have your oil filter changed,
your probability of being served by the faster mechanic is 0.8.
Use simulation to generate 10000 service times and estimate the mean service time for you.

Using R code

Homework Answers

Answer #1

Let the service time for first mechanic be and the service time for first mechanic be .

Then

The resulting service time is with probability 0.8 and with probability 0.2.

The R code for simulating 10,000 resultant service times and finding the mean is given below.

set.seed(7657)
N <- 10000
X <- array(dim=N)
for(i in 1:N)
{
u <- runif(1)
if(u<0.8)
{
X[i] <- rexp(1,rate=1/3)
}
else
{
X[i] <- rexp(1,rate=1/12)
}
}
mean(X)

The mean service time is

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two mechanics are changing oil filters for the arriving customers. The service time has an Exponential...
Two mechanics are changing oil filters for the arriving customers. The service time has an Exponential distribution with mean 12 minutes for the first mechanic, and mean 3 minutes for the second mechanic. When you arrive to have your oil filter changed, your probability of being served by the faster mechanic is 0.8. Use simulation to generate 10000 service times and estimate the mean service time for you. Compare the simulated and the theoretical results. The theoretical mean can be...
Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate...
Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. A mechanic needs 15 minutes to serve one car. Assume Poisson arrivals and exponential service time (show steps) A) What is the average number of cars in the system (auto shop) B) What is the probability that an arrival has to wait for service C) What is the average time that a car waits for the oil and lubrication...
Customers arrive at random times, with an exponential distribution for the time between arrivals. Currently the...
Customers arrive at random times, with an exponential distribution for the time between arrivals. Currently the mean time between customers is 6.34 minutes. a. Since the last customer arrived, 3 minutes have gone by. Find the mean time until the next customer arrives. b. Since the last customer arrived, 10 minutes have gone by. Find the mean time until the next customer arrives.
Customers arrive at a two server system at an exponential rate 10 customers per hour. However,...
Customers arrive at a two server system at an exponential rate 10 customers per hour. However, customers will only enter the resturant for food if there are no more than three people (including the two currently being attended to). Suppose that the amount of time required to service is exponential with a mean of five minutes for each server. (a) Write its transition diagram and balance equations. (b) What proportion of customers enter the resturant? (c) What is the average...
The time required for Quick Changers to complete an oil change service on an automobile follows...
The time required for Quick Changers to complete an oil change service on an automobile follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. Quick Changers guarantees customers that the service will take no longer than 20 minutes, else the service is half-price. What percent of customers receive the service for half-price? (Write your answer as a percent, rounded to the nearest tenth of a percent.) The time required for Quick Changers...
Fast Auto Service provides oil and lube service for cars. It is known that the mean...
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this...
.A year-old study found that the service time for all drive-thru customers at the Stardust Coffee...
.A year-old study found that the service time for all drive-thru customers at the Stardust Coffee Shop is uniformly distributed between 3 and 6 minutes. Assuming the service time distribution has not changed, a random sample of 49 customers is taken and the service time for each is recorded. a. Calculate the mean and standard deviation of service times for all drive-thru customers at the Stardust Coffee Shop. (Hint: Review the uniform distribution from Chapter 6.) b. What is the...
State Bank always has two tellers on duty. Customers arrive to receive service from a teller...
State Bank always has two tellers on duty. Customers arrive to receive service from a teller at a mean rate of 40 per hour. A teller requires an average of 2 minutes to serve a customer. When both tellers are busy, an arriving customer joins a single line to wait for service. Experience has shown that customers wait in line an average of 1 minute before service begins. (a) Describe why this is a queueing system. (b) Determine the basic...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate...
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. A) What is the average number of cars in the system? If required, round your answer to two decimal places L = B) What is the average time that a car waits for the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT