Question (13-15): A Car service station owns one washing machine that serves 3.5 cars every 45 minutes. Moreover, 2.5 customers arrive at the station every 40 minutes. Answer the following questions: 13. Determine the expected waiting time in the car service: D D 3.021 D 4.621 C 14. Determine the expected number of customers in the queue: 0.9031 1.0909 C 3.872 B 0.3001 B 0.875 B 3.287 A 15. Determine the probability that customers are waiting more than 45 minutes in the queue: 0.4041 A 1.256 A 4.099 0.5981
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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 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 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 21 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…
- QUESTION 4 Assume that the UCC cafeteria has a single cashier. During peak hours, students arrive at a rate of 20 per hour. The average number of students that can be serviced by the cashier is 24 per hour. Calculate the following: The number of students in the cafeteria Number of students actively in the queue being served Waiting time in the cafeteria Waiting time for students in the queue What is the probability that there will be more than six students in the cafeteria or in the queue?Q4. A. Explain the concept of queue and queue theory or waiting line theory and its importance in business B. A bank has only one counter for its customers. Suppose that the customers to the bank arrive at random with exponential inter arrival time and their mean inter arrival time is 10 minutes. Suppose the counter takes on an average 15 minutes to serve the customer and this also follow an exponential distribution. a) What percentage of time the bank counter is busy? b) On the average, how many customers are in the system? c) On the average, how many customers are in the queue waiting for the service? d) How long a customer will take to be out of the service system after being served? e) How long a customer to wait before being served? f) What is the probability that there are at most three customers in the system?Question 6 Answer Question 8-10 based on the given information. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 18 customers per hour or 0.3 customers per minute. What is the mean or expected number of customers that will arrive in a ten-minute period? Question 7 Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 1, 2, and 3 customers will arrive during a ten-minute period. Note: The probabilities that exactly 0 customers will arrive during a ten-minute period is calculated for you as 0.0498. (Round your answers to four decimal places.) 1 Question 8 P(x) 0.0498 Delays are expected if more than three customers arrive during any ten-minute period. What is the probability…
- Q.2) Partially completed products arrive at a workstation in a manufacturing operation at a mean rate of 40 per hour (Poisson distributed). The processing time at the workstation averages 1.2 minutes per unit (exponentially distributed). The manufacturing company estimates that each unit of in process inventory at the workstation costs $31 per day (on the average). However, the company can add extra employees and reduce the processing time to 0.90 minute per unit at a cost of $52 per day. Determine whether the company should continue the present operation or add extra employees.Question An average of 17 cars per hour arrive at a single-server drive-in teller. Assume the average service time for each customer is 4 minutes, and both interarrival times and service times are exponential. Answer the following questions: 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.Question 3) Waiting Line Analysis Helen runs a small shop where she provides a service. She is able to process an average of 8 customers per hour. An average of 5 customers per hour seek this service at her shop. What is: a) the probability that Helen will not be working with a customer (no customers) when the shop phone rings? b) the probability of 4 customers in the system? c) the average time a customer spends waiting in line (in minutes)?
- Problem 2: Waiting to take-off a) At an airport, 125 planes took off during an 8-hour period. The control tower keeps a list on its computer of planes that it has released from the gates and that are waiting in queue to take off. Based on this inſormation, the average number of planes waiting to lake-off was 5, with the average taken over the same 8-hour period. How long did the average plane wait to take off? b) Suppose the air-traffic controller tells you that the next day there are 150 planes scheduled to take off (a 20% increase) during the same 8 hours of the day. He then predicts that there will be 6 planes waiting on average. How many would you predict were waiting on average: Circle one: about 6 planes less than 6 planes more than 6 planes? Assume that overall conditions (weather, number of runways open) are the same during the two days. Explain your reasoning. c) The airport authorities are worried about noise and pollution caused by the large queue of planes sitting waiting…Explain Structure of Waiting-Line Problems?Problem 15-31 (Algorithmic) Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour.