Quantitative Method Questions

Burger Dome sells hamburgers, cheeseburgers, French fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Suppose that Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 45 customers per hour and 1 customer processed per minute. 

Compare a multiple-server waiting line system with a shared queue to a multiple-server waiting line system with a dedicated queue for each server. Suppose Burger Dome establishes two servers but arranges the restaurant layout so that an arriving customer must decide which server's queue to join. Assume that this system equally splits the customer arrivals so that each server sees half of the customers. How does this system compare with the two-server waiting line system with a shared queue? Compare the average number of customers waiting, average number of customers in the system, average waiting time, and average time in the system. If required, round your answers to four decimal places.

	Shared single queue	Dedicated queues
Number of customers waiting	fill in the blank	fill in the blank
Average number of customers in the system	fill in the blank	fill in the blank
Average waiting time	fill in the blank minutes	fill in the blank minutes
Average time in the system	fill in the blank minutes	fill in the blank minutes

Comparing these numbers, it is clear that the (shared single or two dedicated?)  results in better process performance than the (shared single or two dedicated ?) .

Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of one job per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 5.5 hours and a standard deviation of 2 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs:

1. What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places. fill in the blank 1 per hour

2. What is the mean service rate in jobs per hour? If required, round your answer to four decimal places. fill in the blank 2 per hour

3. What is the average number of jobs waiting for service? If required, round your answer to three decimal places. fill in the blank 3

4. What is the average time a job waits before the welder can begin working on it? If required, round your answer to one decimal place. fill in the blank 4 hours

5. What is the average number of hours between when a job is received and when it is completed? If required, round your answer to one decimal place. fill in the blank 5 hours

6. What percentage of the time is Gubser's welder busy? fill in the blank 6% of the time the welder is busy.