QuestionAn average of 17 cars per hour arrive at a single-server drive-in teller. Assume the average service time for eachcustomer is 4 minutes, and both interarrival times and service times are exponential. Answer the followingquestions:a. What is the mean arrival time?b. What is the mean service time?c. What is the probability that the teller is busy?d. What is the average number of cars waiting in line for the teller?e. What is the average amount of time a drive-in customer spends waiting in the parking lot?f. What is the average number of cars in the system?g. Describe the possible behavior of customer arrivals. Justify your answer.

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Problem 15-25 (Algorithmic) 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 51 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…
Problem 15-25 (Algorithmic) 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…
Problem#1: Arrivals of a customers to payment counter in a bank follow poisson distribution with an average of 10 per hour. The service time follows negative exponential distribution with an average of 4 minutes.(a) What is the average number of customers in the Queue?(b) The bank will open one or more counter when the waiting time of a customer is at least 10 minutes. By how much the flow of arrivals should increase in order to justify the second counter?
5. The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. d.) Because the state has received less than expected tax receipts, the DMV is thinking of cutting one position. Is this a good idea? Why?
Question The new accounts loan officer of the Millennium Commercial Bank interviews all customers for new accounts. The customers desiring to open new accounts arrive at the rate of 4 per hour, according to a Poisson distribution, and the accounts officer spends an average of 12 minutes with each customer, setting up a new account. Required 1. Determine the operating characteristics (P0, L, Lq, W, Wq and Pw) for this system. 2. Add an additional accounts officer to the system described in this problem so that it is now a multiple-server queuing system with two channels and determine the operating characteristics required in part A.
Question The new accounts loan officer of the Millennium Commercial Bank interviews all customers for new accounts. The customers desiring to open new accounts arrive at the rate of 4 per hour, according to a Poisson distribution, and the accounts officer spends an average of 12 minutes with each customer, setting up a new account. Required A. Determine the operating characteristics (P0, L, Lq, W, Wq and Pw) for this system. B. Add an additional accounts officer to the system described in this problem so that it is now a multiple-server queuing system with two channels and determine the operating characteristics required in part A.
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a. What is the mean arrival time? b. What is the mean service time? c. What is the probability that the teller is busy?