You are considering to invest in a franchise for a coffee shop in your neighborhood. To understand the revenue potential, you decide to visit a coffee shop from the same chain next to your neighborhood. In the next few months, you visit this coffee shop at random times between 6am and 9am. You observe that the line (queue) averages about 9 customers and it takes about 3 minutes to get in and out of the coffee shop. Assuming this is a typical experience and each customer spends about $5 per visit, what is the revenue potential per hour of this coffee shop? Hint: Calculate the number of customers arriving per minute (i.e., λ). Convert this to customers per hour. Then, calculate the revenue from these customers (each customer spends about $5, on average)

At rush hour, two people per second step onto an escalator. The escalator takes30 seconds to bring a person from the bottom to the top. How many people are on theescalator during rush hour?

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

In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle?       What is the probability of having exactly 4 customers in the system?       What is the probability of having 4 or fewer customers in the system?

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours

In a queueing system, customers arrive once every 3 hours (standard devlation = 4) and services take 2 hours (standard deviation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the system? customers

A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in…

Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is five trucks per hour. Use the Single Server Queue Excel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle?   What is the average number of trucks in the queue?   truck(s) What is the average number of trucks in the system?   truck(s) What is the average time a truck spends in the queue waiting for service?   hour(s) What is the average time a truck spends in the system?   hour(s) What is the probability that an arriving truck will have to wait?   What is the probability that more than two trucks are waiting for service?

In improving services to consumers, Limited Company Prima conducted a study of the queue time spent by consumers during the payment process with one available payment service.The average arrival of consumers in 1 hour is 8 consumers, while every hour the number of customers who can be served is 10 consumers. Count: a. The average length of time the customer is in the storeb. Average number of consumers who are being servedc. If the waiter fee is 500 and the subscription fee is waiting for 100, calculate the hourly amount

A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour, with a Poisson distribution. The washing and drying process has a mean of 12 minutes, M= exponentially distributed, and a car cannot enter the lane until the car in front of it is finished drying (there can only be one car in the lane at one time). Due to the location, there is only space enough to hold 5 cars in line waiting to get washed. However, they rent space from the empty lot next door that is large enough to hold as many cars as needed. They decided to rent a section that will hold only 3 cars. a) If they decide to rent a section that will hold 3 cars, what will you solve for to determine the probability that they will still turn cars away? b) They promise each customer their money back ($10) if it takes longer than 30 minutes to get their car washed (from the time they enter). They are open 8 hours per day. How much money can they expect to give away per day?