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.)
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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.)
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How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?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 11 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? b. What is the average time that a vehicle must wait to get through the system? c. What is the utilization of the inspector? d. What is the probability that when you arrive there will be three or more vehicles ahead of you?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.)At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there are only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.a. What is the average length of the waiting line?b. What is the average time that a vehicle must wait to get through the system?c. What is the utilization of the inspector?d. What is the probability that when you arrive there will be three or more vehicles ahead of you?27. Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is two per minute and the average service rate of a single server is five per minute, what portion of the time is there less than 3 people in line? Answer to three decimal points please and thank you
- One mechanic services 7 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 8 working days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of three repair jobs per day. Repairs follow a negative exponential distribution. a) On the average, how many machines are waiting for service? The average number of machines waiting for service is. Round your response to three decimal places.) B.) The average time in the system C.) The average number in lineTrucks 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?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 vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup andis constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poissondistributed.A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?A 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.)