Statistics and Probability The Fast Shop Market checkout counter is a single-server queuing system with the following characteristics: (1) An infinite calling population (2) A FIFO queue discipline (3) Poisson arrival rate (4) Exponential service times By past experience, we know that 24 customers arrive the checkout counter per hour and 30 customers can be checked out per hour. Determine the following items. If a new employee is hired, customers can be served in less time, 40 customers can be served per hour. Assume the arrival rate remain unchanged. Determine the following items. (c) On average, how many customers are there in queue? (d) Average time in the system per customer. (e) Probability that the server will be busy and the customer must be wait.
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How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?no handwritten solution Question The management of a busy petrol station is concerned that customers are being lost because of long waiting times sometimes required at their petrol pump. Over a two weeks period a careful study has been taken of the arrival of cars and the length of time taken to serve customers at the petrol station. The tables below show the arrival rates and the service time distribution: Inter arrival time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <2 1 60 60 00 - 59 2 - <4 3 25 85 60 - 84 4 - <6 5 10 95 85 - 94 6 - <8 7 5 100 95 - 99 Service time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <4 2 20 20 00 – 19 4 - <6 5 30 50 20 – 49 6 - <8 7 20 70 50 - 69 8 - <10 9 15 85 70 – 84…The following data has been collected on the number of customers seen to arriveto a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1,5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. Ifthis data was known to come from a Poisson process, what would be your estimateof l, the rate of customer arrivals?
- The common measures of a queuing system's performance include: O probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration. average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue. average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system. average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system. maximum queue length, maximum time a customer may spend in the queue, and average queue length.13. Movie Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evening, customers arrive at Movies Tonight at the average rate of 1.25 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times.What is the probability that no customers are in the system?What is the average number of customers waiting services?What is the average time a customer waits for service to begin?Do the operating characteristics indicate that the one-clerk check out system provides an acceptable level of service?Identify 10 real-life examples of queuing systems withwhich you are familiar.
- What is queuing model in the service operations? Explain different configurations of the service system?Explain The Queuing System with an example?Angkut Deras Hauling Company has two long-trip cars rental servicesinclusive with a driver at Kota Kinabalu International Airport. The companyhas determine during the late-evening hours on weekend, customersrequest driver for cars rental at a rate that follows the Poisson distributionwith a mean of 0.8 per hour. Travel and assistance time is exponential witha mean of 1 request per hour. Find each of the performance measures ofthis waiting line system. a) What is the system utilization rate for Angkut Deras Hauling Company?b) Probability that both drivers will be busy when a customer request.c) The average number of customer waiting in line.d) The average time customers wait for a driver.e) What is the customers average waiting time on arrival?
- a. Customers queue at the express aisle of a supermarket checkout at the rate of 16 per hour. Employees can serve one customer every three minutes. Assuming the number of anivals follows a Poisson distribution: i. Calculate the average number of customers in the waiting line. ii. Calculate the average time a customer spends in the waiting line. b. An investment firm is considering whether to invest in the mining sector, property, or fixed interest in the coming year. The research division has provided modelling under various scenarios and estimated the expected profit for each choice depending on whether economic growth is moderate, low, or in recession. It has also estimated the probability for each economic growth scenario, as summarised in the table below: Economic growth Moderate Low Recession Profit for each Mining 100 55 -25 choice (Smillions) 46 25 15 Property Fixed 20 20 20 Probability 0.2 0.35 0.45 i Calculate the expected profit for each choice and state which investment the…Describe a situation in your daily life that could be improved by waiting line analysis. Explain how the design of a waiting system can negatively affect customers. Visit your local bank and observe the waiting line system. Describe the system in terms of number of lines, number of facilities, and number of phases.Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a.Compute the average number of cars in line. b.Calculate the value of probability that there are no car in the system. c.Compute the average time that a car spends in the system.