Top Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. REQUIRED (e) What is the average number waiting to be served?
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Top Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed.
REQUIRED
(e) What is the average number waiting to be served?
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How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?Peter's International Barbershop is a popular haircutting and styling saloon near the campus of the Brooklyn College. One barber is available to work full time and spend an average of 3 minutes on each customer. Customers arrive all day long at an average rate of 2 customers every 10 minutes. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. Explain your results. What percentage of time the barber is busy? What is the average number of customers waiting to be served? What is the probability that there will be more than two customers in the shop?Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copierrepairs come in at a mean rate of three per eight-hour day (assume Poisson).A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?D) What is the average number of customers awaiting repairs?
- A branch office of a large engineering firm has one on-line terminal connected to a central computer system for 16 hours each day. Engineers drive to the branch office to use the terminal to make routine calculations with an average exponential distribution of 30 minutes per use. The daily arrival pattern of engineers is random (Poisson) with an average of 20 persons. The branch manager is starting to receive complaints from the engineers about the length of time many of them have to wait to use the terminal. Question: 1. What is and u measured in per hour intervals? 2. On the average, how many minutes does each engineer have to wait? 3. Using increments of 0.1 hours, what would be the least value of u so that the waiting time will be not exceed 30 minutes?Explain how waiting lines can develop even when the service time is a constant.[Queuing Theory - Operation research] The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following: (a) probability that the system is idle (b) average number of customers in the system (c) amount of time a customer should expect to wait before service (d) probability that a customer will have to spend more than 15 minutes in the queue
- The Hair Port is a hair-styling salon at Riverside Mall. Four stylists are always available to serve customers on a first-come, first-served basis. Customers arrive at an average rate of four per hour (Poisson distributed), and the stylists spendan average of 45 minutes (exponentially distributed) oneach customer.a. Determine the average number of customers in thesalon, the average time a customer must wait, and theaverage number waiting to be served.b. The salon manager is considering adding a fifth stylist.Would this have a significant impact on waiting time?Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from…