Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 15 customers per hour or 0.25 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 21 customers per hour, or 0.35 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system (b) The average number of customers waiting (c) The average number of customers in the system
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How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive- up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process. (a) What is the mean or expected number of customers that will arrive in a six-minute period? (b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a six-minute period. (Round your answers to four decimal places.) X 0 1 2 3 P(x) (c) Delays are expected if more than three customers arrive during any six-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. What is the mean or expected number of customers that will arrive in a five-minute period?λ = fill in the blank 1 per five minute period Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. If required, round your answers to four decimal places. x P(x) 0 fill in the blank 2 1 fill in the blank 3 2 fill in the blank 4 3 fill in the blank 5 Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your…
- Customers arrive at a bank counter manned by a single cashier according to Poisson distribution with mean arrival rate 6 customers/hour. The cashier attends the customers on first come first serve basis at an average rate of 10 customers/hour with the service time exponentially distributed. Find The probability of the number of arrivals (0 through 5) during (i) 15-minute interval, (ii) 30-minute interval The probability that the queuing system is idle, The probability associated with the number of customers (0 through 5) in the queuing systemTony’s Barbershop is run, owned, and operated by Anthony Jones, who has been cutting hairfor more than 20 years. Anthony does not take appointments, so the arrival pattern of customers is essentially random. Traditionally, the arrival rate had been about one customer every50 minutes. Two months ago, the local paper ran an article about Anthony that improved business substantially. Currently, the arrival rate is closer to one customer every 35 minutes. Haircutsrequire an average of 25 minutes, but the times vary considerably depending on customerneeds. A trim might require as little as 5 minutes, but a shampoo and styling could take as longas an hour or more. For this reason, the exponential distribution seems to provide a reasonablygood fit of the service time distribution.Anthony’s customers have always been patient, but ever since business picked up, somehave complained that the wait is too long. Anthony is considering taking his cousin Marvin intothe business to improve customer…Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. What is the average number of cars in the system? What is the average time that a car waits for the oil and lubrication service to begin? What is the average time a car spends in the system? What is the probability that an arrival has to wait for service?
- Robert Olney's Barbershop is a popular haircutting and styling salon near the campus of the University of New Haven. 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. Arrivals tend to follow the Poisson distribution, and service times are negative exponentially distributed. The software described in this quantitative module may be used to answer the following questions. a) The probability that the shop is empty is b) The average number of customers in the barber shop is c) The average time spent in the shop is hours (round your response to three decimal places). d) The average time that a customer waits to be called to the barber chair is hours (round your response to three decimal places). e) The average number waiting to be served is customers (round your response to two decimal places). f) Robert is thinking of adding a fifth barber. The utilization rate of his shop will be (round your…a single-server waiting line system has an arrival pattern characterized by a poisson distribution with 24 customer per hour. on average 30 customer are served per hour the service times are distributed according to the negative exponential distributionCustomers arrive at a carwash on average once every 40 minutes. It seems likely that customer arrivals follow an exponential distribution. For each of these random numbers, calculate the simulated time between arrivals at the carwash. (Round your answers the nearest whole number.) Random Number Time Between Arrivals 0.27 0.84 0.23
- Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…Please try to solve in 30 minute A queueing system has an arrival rate of 45 visitors per hour (standard deviation of 24) and a service rate of 35 visitors per hour (standard deviation of 20). What is the cofficientvof variation of the service rate .Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 87 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following: a. The average time customers spend at the machine, including waiting in line and completing transactions b. The probability that a customer will not have to wait upon arriving at the automatic teller machine c. The average number waiting to use the machine