A crew of mechanics at the Transylvania Department of Motor Vehicles garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. Approximately how many vehicles are in the garage, waiting for or being repaired?
Q: A small bank is trying to determine how many tellers to employ. The total cost of employing a teller…
A: The theory used for the formation, congestion, function in the waiting lines is known as the queue…
Q: A large industrial pier has two cranes that load container ships. Trucks arrive in a single line and…
A: Given data The arrival rate of the vehicle is Poisson distributed Arrival rate (λ) = 20 trucks per…
Q: Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an…
A: Hello thank you for the question. As per guidelines, we would provide first three sub parts of a…
Q: A post office has a single line for customers waiting for the next available postal clerk. There are…
A: Given: λ = 13×60= 20/hourμ = 12×60=30/hour c = number of servers = 2 Multiple server queues model…
Q: The Acme Machine Shop has five machines that periodically break down and require service.The average…
A: Given data: Number of machines (N) = 5 Now, the average number of machines will be calculated by…
Q: An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential),…
A: a). M/M/5 system with λ = 90 customers/hr and μ = 20 customers/hour. P(j≥5) = .76. Then Wq =…
Q: An office employs several clerks who create documents, and one operator who enters the document…
A: Therefore M/M/1 model fits. Arrival rate, λ = 22 customers per hour Service rate, μ = 1 / service…
Q: CT Commercial Bank is the only bank in the town of Kuching, Sarawak. On a typical Friday, an average…
A:
Q: Students arrive randomly at the counter of the CIT Library. There is only one library assistant,…
A: Given data: Average arrival rate λ= 12 students per hour Average service rate μ = 20 students per…
Q: A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18…
A: A normal of 18 clients show up every hour at the general store and the normal look at time for a…
Q: The computer laboratory at a State University has a help desk to assist students working on computer…
A:
Q: All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a…
A:
Q: The Escargot is a small French restaurant with six waiters and waitresses. The average service time…
A: λ=Arrival rate at in whole at restaurant =6018=3.33Current Arrival rate at each table =3.336=0.56…
Q: Wingard Credit Union is interested in understanding how long customers spend in front of the ATMs.…
A: Ans 1: The probability that the client will take less than half a time will be calculated by the…
Q: A small grocery store has a single cashier lane where groceries line up to pay for their purchases.…
A: Interarrival time (a) = 3 minutes Arrival rate λ = 1a = 13×60=20 customers per hour Service time (b)…
Q: A mechanic at johnsons shop is able to install new mufflers at an average rate of 3 per…
A: Service rate is the rate at which the customers are being served in the organizational system by the…
Q: One mechanic services 6 drilling machines for a steel plate manufacturer. Machines break down on an…
A: Given data The number of the machines breakdowns or the arrival rate λ= 1 breakdown every 3rd…
Q: Patients arrive to a small hospital emergency room according to a Poisson process withan average…
A: Formula:
Q: Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is…
A: A)Identify the queueing model:The queueing model identified using the given situation is M/M/1…
Q: Juhn and Sons Wholesale Fruit Distributors employ one worker whose job is to load fruit on outgoing…
A:
Q: When customers arrive at Gilley’s Ice Cream Shop, theytake a number and wait to be called to…
A: Given data Total number of service = 3 The following formula will calculate the average…
Q: The Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A…
A:
Q: An office employs several clerks who create documents and has one operator who enters the document…
A:
Q: The Seaboard Shipping Company has a warehouse terminalin Spartanburg, South Carolina. The capacity…
A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available toserve…
A: Average customers in wait is 175.
Q: The local Burger Doodle fast-food restaurant has a drive-through window. Customers in cars arriveat…
A: Given data , Customers arrive the rate = 10 per hour (Poisson distributed) Time taken = 4 minutes…
Q: The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and…
A: λ =7.5 cabs/hrμ= 7.05 cabs/hrIn finite que system the guest are service providers and cabs are…
Q: Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an average of…
A: THE ANSWER IS AS BELOW:
Q: At the Franklin Post Office, patrons wait in a single line for the first open window. On average,…
A: Please refer the next step for answer
Q: A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average…
A: Given- Vehicles repaired at an average of λ = 7.5 vehicles per day Service at an average of μ = 10…
Q: 12-19 Juhn and Sons Wholesale Fruit Distributors employs one worker whose job is to load fruit on…
A: Given data: Arrival rate = an average of 24 per day or 3 per hour Service rate = 4 per hrs
Q: An ofi ce employs several clerks who create documents and one operator who entersthe document…
A: Documentation rate = 25 per hour Service Rate= 1 in 2 min = 30 per hr
Q: State University has decided to increase the number of computer assignments in its curriculum and is…
A: This question is of waiting line model in that model it is of Multi-server model. In this model, the…
Q: . The DMV Licensing office has a single line for customers waiting for the next available clerk.…
A: We have s = number of clerks in the system = 2 The arrival rate λ = 8 customers per minute Service…
Q: epair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is…
A: Given: Mean repair = 2hrs per call Mean arrival rate (λ) = 3per eight hour day i.e. 0.375 call per…
Q: Patients arrive to a small hospital emergency room according to a Poisson process with an average…
A: Given Rate of arrival λ = 1.5 patients/hour Service rate μ = 2.3 patients/hour (60/26)
Q: Marty's Barber Shop has one barber. Customers have an arrival rate of 1.1 customers per hour, and…
A: 1) Compute the probability that one customer is receiving a haircut and two customers are waiting:…
Q: Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more…
A: From. the above given information, The customers arrive at 5 per hour and, Each technician takes 5…
Q: A computer processes jobs on a first-come, first served basis in a time-sharing environment. The…
A: Data given: Arrival rate(λ)= 605= 12j/hr Time in system(w)= 8 minutes No. of server=1 M1/M1 queuing…
Q: The First American Bank of Rapid City has one outside drive-up teller. It takes the teller an…
A:
Q: The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur…
A:
Q: Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide…
A:
Q: The Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A…
A: Arrival rate and service rate are distributed poison and in exponential form. When they are poison…
Q: The office has a single line for customers waiting for the next available clerk. There are two…
A: Queuing theory is a mathematical study of the formation, function, and congestion of waiting lines…
Q: Wingard Credit Union (from Problem 1) is also interested in understanding how long customers spend…
A: m = 1/average service time = 1/(3/2) = 2/3 minutes P(x<X) = 1-EXP(-mX)
Q: A small bank is trying to determine how many tellers toemploy. The total cost of employing a teller…
A:
A crew of mechanics at the Transylvania Department of Motor Vehicles garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. Approximately how many vehicles are in the garage, waiting for or being repaired?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- During nearly four decades of business operations, Memphis-based FedEx has earned a reputation for reliable, on-time delivery of packages to homes and offices around the country. Founder Fred Smith originally focused on overnight deliveries, choosing Memphis as the company’s headquarters because the airport rarely closes due to bad weather. With FedEx’s planes departing and arriving on schedule nearly all the time, its express shipments usually remained on schedule, then and now. To reassure customers that delivery will take place when and where promised, the firm offers a money-back guarantee on time-sensitive express shipments, among other services. FedEx has steadily expanded its portfolio of services since the 1970s. Its original overnight express delivery is currently available to U.S. customers in various forms, including “first-overnight” delivery, next-morning delivery, next-afternoon delivery, and budget-pleasing two- or three-day delivery. The company’s services also include cost-effective ground delivery for parcels and extra-speedy same-day delivery for urgent deliveries within 1,800 cities. Over the years, FedEx has widened its delivery network to more than 220 countries. It has purchased more cargo jets and acquired specialized shipping firms, including Tiger International, Roberts Express, RPS, and TNT Express, to support global growth. For international business customers needing products, parts, or raw materials shipped across countries or continents, the company now offers time-saving services such as commercial freight forwarding and cross-border logistical support. To add the convenience of local drop-off and pickup points for U.S. consumers and small businesses, FedEx acquired the Kinko’s office services company in 2004 and later rebranded it as FedEx Office. This acquisition also added printing and copying to the menu of services offered. Then the company arranged for large U.S. retailers such as Walgreens, Albertsons, Kroger, and Safeway to accept packages for shipment and receive package delivery for customer pickup in thousands of store locations. This means people who want to send a package can head to a nearby retailer and ship where they shop, rather than making a separate trip to the FedEx location. It’s also a safe alternative for packages to be picked up by people who don’t want FedEx shipments left by the front door. Another service FedEx offers to small and mid-sized businesses, including retailers, is FedEx Fulfillment. The purpose is to expedite order fulfillment by having each business store its products in a FedEx warehouse. Then, when the business’s customers place orders, FedEx puts the products into boxes bearing the business’s own logo and ships directly to those customers. The business doesn’t need a separate warehouse or staff for fulfillment, and packages are on their way to customers more quickly because the products were in FedEx’s warehouse, ready to be packed and shipped. This service puts FedEx into direct competition with Amazon.com, which offers a similar service to merchants that sell through the online Amazon Marketplace. But it also gives businesses that don’t sell via Amazon a fast and professional fulfillment alternative. FedEx is careful to let customers know, through media and social-media announcements, when it anticipates that extreme weather or other conditions will cause delays or force it to halt pickups and deliveries. For the duration of Hurricane Irma, for example, FedEx said it would suspend deliveries in Florida. Some Florida customers who had ordered generators to be delivered via FedEx were unhappy, because they worried about being without power during and after the storm. But one FedEx employee loaded several generator orders into his car and took them to customers himself. When a customer posted a grateful compliment to FedEx on Facebook, the message generated thousands of likes, shares, and positive comments. The company also received positive comments for its donations of cash and transportation services to areas devastated by Hurricanes Irma, Harvey, and Maria. According to the American Customer Satisfaction Index (ACSI), FedEx often tops the list of U.S. shipping companies as ranked by customers surveyed. Every day, the company delivers 13 million packages—and during the busy year-end holiday season, it delivers many more. By meeting customers’ expectations for on-time deliveries, FedEx has increased annual revenues beyond $60 billion and positioned itself for continued growth in the future. How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?A mechanic at the Department of Maintenance makes minor repairs to faulty golf electric carts. The carts break down at an average rate of 4 carts per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 6 carts per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. a- What is the utilization rate for the mechanic? b- What is the average time in hours that a cart is out of service?A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 10 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. On average, how long does a plow wait before the mechanic begins the repair? Group of answer choices 0.17 days 0.53 hours 53 minutes 1.33 hours
- The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes.A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained?C. How many trucks are lined up in front of the station on the average?D. How long on the average does a truck driver have to wait in line for the truck to beinspected?A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What are the chances that 3 vehicles are in the service system? Group of answer choices 9% 38% 63% 19%Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 3 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 10machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system? b) The average downtime for a broken machine? c) Average number of machines waiting to be serviced at any given time? d) The probability that more than 1 machine is in the system? The probability that more than 2 machine is in the system? The probability that more than 3 machine is in the system? The probability that more than 4 machine is in the system?
- Pasquist Water Company (PWC) operates a 24-hour facil-ity designed to efficiently fill water-hauling tanker trucks.Trucks arrive randomly to the facility and wait in line to ac-cess a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the timeto fill a truck is also random.a. If the manager of PWC uses the multiple-server modelto calculate the operating characteristics of the facility’swaiting line, list three assumptions she must make regard-ing the behavior of waiting trucks and the truck arrivalprocess.b. Suppose an average of 336 trucks arrive each day, thereare four wellhead pumps, and each pump can serve anaverage of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrivebetween 1:00 p.m. and 2:00 p.m. on any given day?▪ How likely is it that once a truck is in position at a well-head, the filling time will be less than 15 minutes?c. Contrast and comment on the performance differencesbetween:▪…A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? 5 1.04 1.67 8