Question

The customer support hotline for Bitway Computers is currently staffed by a single technician. Calls arrive...

The customer support hotline for Bitway Computers is currently staffed by a single technician. Calls arrive randomly at a rate of five per hour and follow a Poisson distribution. The technician can service calls at an average rate of seven per hour, but the actual time required to handle a call is an exponential random variable. The president of Bitway has received numerous complaints from customers about the length of time they must wait “on hold” for service when calling the hotline. Find the following

Find the probability that the technician is servicing a call

The average number of callers put on hold.

Find the average time that a customer must wait before receiving service from the technician

Find the total time a caller spends waiting for service and being served under Bitway ‘s current hotline configuration.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Arrival rate, = 5 per hour

Service rate, = 7 per hour

Probability that the technician is servicing a call = = / = 5/7 = 0.7142857

The average number of callers put on hold = Lq =

= 0.71428572 / (1 - 0.7142857) = 1.785714

The average time that a customer must wait before receiving service from the technician =

Wq =  Lq / = 1.785714 / 5 = 0.3571428 hr = 21.42857 minutes

The total time a caller spends waiting for service and being served under Bitway ‘s current hotline configuration = W = Wq + (1/) = 0.3571428 + (1/7) = 0.5 hr = 30 min.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A customer service center has customers call with questions about the use of a product. The...
A customer service center has customers call with questions about the use of a product. The mean arrival rate of customer calls is 20 per hour and follows a Poisson distribution. The mean service rate (how long it takes the call center employee to answer the customer’s question) is 30 customers per hour (most customer questions can be answered rather quickly) and follows an Exponential distribution. What is the mean (average) time in hours that a customer spends in the...
Arrival Rate = 1/50 = 0.02 calls hour. Service Rate= 1 hour (travel time) + 1.5...
Arrival Rate = 1/50 = 0.02 calls hour. Service Rate= 1 hour (travel time) + 1.5 hour (repair time) =2.5 hours With m = 1/ 2.5 = 0.4 hours per customers ** PLEASE SHOW HOW TO DO EQUATION ** OEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information: (a) probability that no customers are in the system, (b) average number of customers in the waiting line,...
Scenario: Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana....
Scenario: Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem. Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling...
4. Phone calls arrive at the rate of 48 per hour at the reservation desk for...
4. Phone calls arrive at the rate of 48 per hour at the reservation desk for Varig Airlines. a. Find the probability of receiving three calls in a five-minute interval time. b. Find the probability of receiving exactly 10 calls in 15 minutes. c. Suppose no calls are currently on hold. If the agent takes five minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none...
I need a detailed explanation with a formula (show work) included on how to solve this...
I need a detailed explanation with a formula (show work) included on how to solve this question: Scenario Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer's business site within an average of 3 hours from the time that the customer notifies OEI of an...
Use QM for Windows to solve the following problems. Click on the Waiting Lines menu options,...
Use QM for Windows to solve the following problems. Click on the Waiting Lines menu options, and make sure to select the correct model (i.e. finite system size, finite population, etc, etc) A telephone system at a help desk has the capacity to put a maximum 5 callers on hold. Assume calls come on average every 6 minutes, and it takes on average 5 minutes to assist the customer. What is the average wait time in minutes that a customer...
Ocala Software Systems operates a technical support center for its software customers. If customers have installation...
Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told...
Suppose that the customers arrive at a hamburger stand at an average rate of 49 per...
Suppose that the customers arrive at a hamburger stand at an average rate of 49 per hour, and the arrivals follow a Poisson distribution. Joe, the stand owner, works alone and takes an average of 0.857 minutes to serve one customer. Assume that the service time is exponentially distributed. a) What is the average number of people waiting in queue and in the system? (2 points) b) What is the average time that a customer spends waiting in the queue...
Suppose that the customers arrive at a hamburger stand at an average rate of 49 per...
Suppose that the customers arrive at a hamburger stand at an average rate of 49 per hour, and the arrivals follow a Poisson distribution. Joe, the stand owner, works alone and takes an average of 0.857 minutes to serve one customer. Assume that the service time is exponentially distributed. a) What is the average number of people waiting in queue and in the system? (2 points) b) What is the average time that a customer spends waiting in the queue...
Problem 11-15 (Algorithmic) Ocala Software Systems operates a technical support center for its software customers. If...
Problem 11-15 (Algorithmic) Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT