Vehicles on a highway arrive at a security checkpoint at a Poisson rate of 20 per hour. At the checkpoint, vehicles are inspected by a single security guard. The security guard can inspect vehicles at an exponential rate of 50 per hour. a. Find the probability that an incoming vehicle must wait in a security line. b. What is the average number of vehicles at the checkpoint? c. What is the average amount of time spent at the checkpoint?
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Vehicles on a highway arrive at a security checkpoint at a Poisson rate of 20 per hour. At the checkpoint, vehicles are inspected by a single security guard. The security guard can inspect vehicles at an exponential rate of 50 per hour.
a. Find the probability that an incoming vehicle must wait in a security line.
b. What is the average number of vehicles at the checkpoint?
c. What is the average amount of time spent at the checkpoint?
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How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?Granos, Inc. purchased new automated coffee vending machines, the Preso 2000. This Preso 2000 requires a constant 45 seconds to produce a coffee. It has been estimated that customers will arrive at the vending machine according to a Poisson distribution at an average of one every 50 seconds. To help determine the amount of space needed for the line in front of the vending machine, Granos, Inc. would like to know the expected average time in the system, the average line length (in costumers), and the average number of costumers in the system (both in line and at the vending machine).Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour.a. How many trucks would you expect to see at the weighing station, including those being inspected?
- At a border inspection station, vehicles arrive at the rate of 10 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 16 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 total time it takes for a vehicle 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.)You observe an average of 10 customers in the System. On average, you also observe customers are in the system for 50 minutes before they leave. What is the arrival rate into the system in customers per hour?The new accounts loan officer of the Millennium Commercial Bank interviews all customers for new accounts. The customers desiring to open new accounts arrive at the rate of 4 per hour, according to a Poisson distribution, and the accounts officer spends an average of 12 minutes with each customer, setting up a new account. Determine the operating characteristics (P0, L, Lq, W, Wq and Pw) for this system.
- given the following: A typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screeneach passenger that arrives at the security gate. During the day, a passenger arrives at the gate onaverage every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based onthis information and the assumption that only one screening line is open at the security gate, answer thefollowing questions with the given information: a) average number of passengers waiting in line to be screened is 7 b) average amount of time (in minutes) passengers spend waiting in line is .147 minutes c) average amount of time (in minutes) passengers spend in the screening system?.166 minutes 1. What is percent of the time does the typical TSA agent spend actively screening passengers? 2. Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45 minutes before a flight is expected to depart. If during this…Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 50 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 55 seconds. To help determine the amount of space needed for the line at the drive-up window, answer the following questions. a. What is the average waiting line length (in cars)? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Average line length cars b. What is the average number of cars in the system (both in line and at the window)? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Average number of cars carsBurrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 55 seconds. To help determine the amount of space needed for the line at the drive-up window, answer the following questions. a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the average number of cars in the system (both in line and at the window)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. What is the expected average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
- 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.At 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.)A drive-through at a Fast Food serves 424 customers over a 10-hour day. On average, a customer spends 3 minutes waiting in line, 7 minutes placing the order, and 4 minutes completing the order before leaving the drive-through. How many customers on average are "in" the drive-through (i.e., from the time they enter to the time they exit the drive-through) on a typical day? (Specify your answer in two decimal points)