The Fore and Aft Marina is located on the Ohio River near Madison, Indiana. Fore and Aft currently operates a docking facility where only one boat at a time can stop for gas The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. A rate is 6 boats per hour and that the service rate for each server is 10 boats per hour. (Round your answers to four decimal places. Report time in hours.) (a) What is the probability that the boat dock will be idle? (b) What is the average number of boats that will be waiting for service? (c) What is the average time a boat will spend waiting for service? h (d) What is the average time a boat will spend at the dock? h

A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Calculate the percentage utilization of the graduate student. Note: Round your answer to 1 decimal place.   Calculate the average number of students in the system, including the graduate student service desk. Note: Round your answer to the nearest whole number.   Calculate the average time in the system. Note: Round your answer to the nearest whole number.   Calculate the probability of four or more students being in line or being served. Note: Round your intermediate calculations to 3…

4.) The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?

The utilization of baggers is Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the first 7 hours of each workday (Monday-Friday), 6 cashiers and 2 baggers serve approximately 25 customers per hour. A cashier and a bagger who require approximately 6 minutes at checkout and 4 minutes at bagging serve each customer. a. The utilization of cashiers is 41.7%. (Enter your response rounded to one decimal place.) %. (Enter your response rounded to one decimal place.) v an example Part 2 of 3 Get more help. O Points: 0 of 3 Clear all Check answer O

3 The M/M/1 Queue During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23 per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system: Waiting Service Calculate the marginal probability P (T > oT). a. O b. 0.25 O c. 0.63 O d. 0.75 Calculate the mean time a customer spends at the bank (waiting time plus service time) in minutes. O a. 30 minutes O b. 27.6 minutes O c. 2.4 minutes O d. 7 minutes

A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk?      1.143 minutes     3.429 minutes     1.929 minutes     0.643 minute