At the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per hour. The post office estimates a cost of $0.10 for each minute a patron waits in line and believes that it costs $20 per hour to keep a window open. Interarrival times and service times are exponential.
Q: Students arrive randomly at the help desk of the computer lab. There is only one service agent, and…
A: A queueing system is a system that includes a service facility where units of some kind (commonly…
Q: Machinists who work at a tool-and-die plant must check out tools from a tool center. An average of…
A:
Q: Patients arrive to a small hospital emergency room according to a Poisson process withan average…
A: Formula:
Q: Many of a bank’s customers use its automatic teller machine to transact business after normal…
A: Given data is Customers arrival rate: λ=1 customer2 mins×60 mins/hrλ=30 customers/hr Service rate:…
Q: To ensure that waiting times are not too long, the organizers want to ensure that the utilization of…
A:
Q: Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an average of…
A: Given that, The average number of cars per hour = 10 units The service time = 3 minutes per units.…
Q: The computer laboratory at a State University has a help desk to assist students working on computer…
A:
Q: The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can…
A:
Q: In an M/MA queueing system, the arrival rate is 4 customers per hour and the service rate is 6…
A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…
Q: For each of the following queuing systems, indicate whether it is a single or multiple-server model,…
A: Hair salon: multiple server, first come first served or appointment, calling population can be…
Q: Two doctors work at a hospital emergency room, the inter-arrivals of patients follow a Poisson…
A: ANSWER: P0+P1+P2 =1-λμ+λμ1-λμ+λμ2 = 1-λμ1+λμ+λμ2
Q: Many of a bank’s customers use its automatic teller machine to transact business after normal…
A:
Q: In a system with 4 servers and a single queue, jobs arrive at a rate of 8 per hour following a…
A: λ = Arrival rate = 8 jobs per hourμ =Service rate= 3 jobs per hour
Q: The organizers of a conference in the Houston Convention Center are evaluating the possibility of…
A: Given data Arrival rate (λ) = 19 attendee per hour Service rate (μ) = 14 minutes Service rate…
Q: Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday.…
A: It's a M/M/1 queue system Arrival rate,( )= 20 cars per hour Service rate,( )= one car at every 2…
Q: Consider a base case where a customer arrives every 52 seconds and the Customer Service Champlon can…
A: Queuing theory is an area of mathematics concerned with how lines develop, function, and fail. 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: Assume that an average of 125 packets per second ofinformation arrive to a router and that it takes…
A: We have an M/M/1 system with λ = 125 andμ = 1/0.002 = 500 => ρ = λ/μ = 1/4.
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: At the Strathmore University Cafeteria, students seeking to have a meal are observed to arrive at a…
A: Arrival rate λ 16 per 20 min Service rate µ 19 per 20 min
Q: Patients arrive to a small hospital emergency room according to a Poisson process withan average…
A: Formula:
Q: The Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A…
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: Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station…
A: Given- Price of Gasoline if a customer will wait = Php 45 Price of Gasoline if a customer will not…
Q: A single-server queuing system with an infinite calling population and a first-come, first-served…
A:
Q: Assume that at a bank teller window the customers arrive in their cars at the average rate of twenty…
A: Queuing theory refers to the study used to determine the formation and waiting line of the…
Q: A crew of mechanics at the Transylvania Department of Motor Vehicles garage make minor repairs to…
A: Given Information: The arrival rate of vehicles (λ) = 4 vehicles per day The service rate of…
Q: n a coffee shop, there are 4 baristas serving customers standing in a single queue. Customers arrive…
A: Below is the solution:-
Q: Customers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per…
A: The correct solution of the given statement is in Step 2.
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: Imagine a small coffee shop with a single counter. On average, 16 customers arrive at the store…
A: Here; L - the average number of items in a queuing system λ - the average number of items arriving…
Q: At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution.…
A: Queuing theory is a mathematical theory of representing data, where the company has arrival rate,…
Q: Customers arrive at a barber shop according to the Poisson distribution. The average time between…
A: Note- Hi! Thank you for the question, As per the honour code, we are allowed to answer three…
Q: Students arrive randomly at the help desk of the computer lab. There is only one service agent, and…
A: Given, Arrival rate a = 12 students per hour Service rate s = 20 students per hour Utilization p =…
Q: purchase
A: The portion of time the ticket seller is busy
Q: At the Strathmore University Cafeteria, students seeking to have a meal are observed to arrive at a…
A: Given, Arrival rate, λ =16 per 20 minutes =0.8 per minute Service rate, μ =19 per 20 minutes =0.95…
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: In improving services to consumers, Limited Company Prima conducted a study of the queue time spent…
A: Introduction: The term Market refers to an exchange of goods and services between the buyer and the…
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: Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide…
A:
Q: Ships arrive at a port facility at an average rate of two ships every three days. On average, it…
A: Arrival Rate = λ = 23 ships per day Service Rate = μ = 1 ship per day Fixed cost = $1000 per day…
Q: The parts department of a large automobile dealership has a counter used exclusively for mechanics'…
A: The Poisson distribution is a function of discrete probability that means that the variable will…
Q: A teller works at a rural bank. Customers arrive to complete their banking transactions on average…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
Q: Automobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes.…
A: Note: I have answered for sub-parts (1) to (5). Kindly post the remaining sub-parts separately.
Q: A single server queuing system with a Poisson arrival rate and exponential service time has an…
A: Service rate is the rate at which the service is served or supply to the customers in the company.
Q: An ice cream truck is parked at a local beach and customers queue up to buy ice creams at a rate of…
A: Given - Customer Arrival Rate (λ) = 1 per minute Service Rate (μ) = 40 seconds Standard…
Q: A teller works at a rural bank. Customers arrive to complete their banking transactions on average…
A: Model ( Queue ) Inputs Units of time Hours Arrival time 6…
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 4 images
- 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 $60 billion and positioned itself for continued growth in the future. How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?Twelve customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 4 minutes to fill each order (following a negative exponential distribution). The Waiting La λ Line Table is provided below and also we know that W₁ = Table: Average Number of Customer in Waiting Line P .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .30 .55 60 .65 .70 .75 .80 .85 .90 .95 1.0 1.2 1.4 1.6 1.8 2.0 Poisson Arrivals, Exponential Service Times Number of Service Channels, M 2 3 4 1 .0111 .0264 .0500 .0833 .1285 .1884 .2666 .3681 .5000 .6722 3000 .6722 .9000 1.2071 1.6333 2.2500 3.2000 4.8166 8.1000 18.0500 .0008 .0020 .0039 .0069 .0110 .0166 .0239 .0333 .0449 0333 .0449 .0593 .0767 .0976 .1227 .1523 .1873 2285 .2767 .3333 .6748 1.3449 2.8444 7.6734 .0019 .0030 .0043 0030 .0043 .0061 .0084 .0112 .0147 .0189 0239 .0300 .0371 .0454 .0904 .1778 .3128 .5320 .8888 .0031 .0041 .0053 .0067 .0158 .0324…For Billys bank situation in problems 12.4 and 12.5, the salary and benefits for the teller would be 12 dollars per hour. The bank is open 8 hours each day. It has been estimated that the wait time cost is 25$ per hour in line. How many Customers would enter the bank on a typical day? How much total time would the customers spend waiting in line during the entire day if two tellers were used? What is the total Daily waiting cost? How much total time would customers spend waiting in line during the entire day if two tellers were used? What is the total daily waiting cost? If billy wishes to minimize the total waiting time and personal cost how many tellers should be used?
- A request for assistance at the reference desk at a library is submittedat an average rate of 9 per hour (Poisson distribution). At the reference desk, there is only one librarianand he can serve customers in 6 minutes on average (exponential distribution). Calculate according tothe queuing model M/M/1:1. Server utilization2. Expected number of customers in queue3. Expected waiting time of customer in queueC) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) +…A supermarket has four girls ringing sales at the counters. If the service time for each customer is exponential with mean 4 minutes, and if people arrive in a Poisson fashion at the rate of 10 per hour, calculate i. The average number of customers in the system. ii. The average time a customer spends in the system. iii. The average queue length iv. The average waiting time for customers. v. The expected percentage of idle time for each girl vi. The probability that at least a girl is waiting for the customer.
- Twenty-one customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 2 minutes to fill each order (following a negative exponential distribution). The Waiting Line Table is provided below and also we know that ... a) What is the average number of customers in the queue? Using the table, the average number of customers in the queue is ______ customers (round your response to four decimalplaces). b) How long will a person wait in line on average? The average time a person spends in the queue is ______ minutes(round your response to two decimal places). c) If Andy's wife joins him in serving meals (at the same speed as Andy), how will your answers to parts a and bchange? Using the table, the new average number of customers in the queue is _________ customers (round your response to four decimal places). The new average time a person spends in the…5.12. For each of the following queuing systems, indicate if it is a single- or multiple-server model, the queue discipline, and if its calling population is infinite or finite: Hair salon Bank Laundromat Doctor’s office Adviser’s office Airport runway Service station Copy center Team trainer Mainframe computer