Customers approach Florence’s Fortune Telling booth at a rate of 8 people/ hour. (Arrival rate follows a Poisson distribution.) Customers wait, on average 20 minutes to have their fortunes told by Florence. On average, how many people are waiting in line? (Round to the nearest hundredth. Because this is an average, you can have a fraction of a person.)
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Customers approach Florence’s Fortune Telling booth at a rate of 8 people/ hour. (Arrival rate follows a Poisson distribution.) Customers wait, on average 20 minutes to have their fortunes told by Florence. On average, how many people are waiting in line? (Round to the nearest hundredth. Because this is an average, you can have a fraction of a person.)
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- A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 76 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customersA vending machine dispenses hot chocolate or coffee. Service time is 15 seconds per cup and is constant. Customers arrive at a mean rate of 55 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)Malcom Ghana is considering opening a drive-through window for customer service. Management estimates that customers will arrive at the rate of20 per hour. The teller who will staff the window can service customers at the rate of one every two minutes. Assuming Poisson arrivals and exponential service, find Average waiting time in line.
- Western National Bank wants to provide a drive-through window for its customers. Management estimates that customers will arrive in their cars at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of 20 per hour. Assuming Poisson arrivals and exponential service, find the following: Capacity utilization of the teller. Average number of cars in the waiting line Average number in the system. Average waiting time in line. Average waiting time in the system, including service.A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customers ?? b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes ??Drivers who come to get their licenses at the Department of Motor Vehicles have their photograph taken by an automated machine that develops the photograph onto the license card and laminates the complete license. The machine requires a constant time of 4 minutes to prepare a complete license. The interarrival time between two drivers is 6 minutes distributed exponential. a) What type of queuing model this system follow ? b) Determine the average length of the waiting line. c) Determine the average waiting time.
- Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ?customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places).Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average time that a vehicle must wait to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)
- 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?13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.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:a. The average number of customers waiting.b. The average time a customer waits.c. The average time a customer is in the shop.d. The average utilization of Benny’s time.