Question: 4. Consider a manufacturing system with a single station with two servers. Jobs arrive following an exponential distribution with a rate of 6 jobs per

4. Consider a manufacturing system with a single

4. Consider a manufacturing system with a single station with two servers. Jobs arrive following an exponential distribution with a rate of 6 jobs per hour, while the service rate of each of the two servers follows an exponential distribution with a rate of 8 jobs per hour. If the total number of jobs that can be in the system at any time is 3, use this information to answer the following questions. (25 points) a) Draw and label a state space diagram, showing all states and the rates of transition between states. b) Write a complete set of balance equations c) Solve your system of equations to determine the long run probability of the system being in each possible state d) What is the average number of jobs in the system at any point in time? 4. Consider a manufacturing system with a single station with two servers. Jobs arrive following an exponential distribution with a rate of 6 jobs per hour, while the service rate of each of the two servers follows an exponential distribution with a rate of 8 jobs per hour. If the total number of jobs that can be in the system at any time is 3, use this information to answer the following questions. (25 points) a) Draw and label a state space diagram, showing all states and the rates of transition between states. b) Write a complete set of balance equations c) Solve your system of equations to determine the long run probability of the system being in each possible state d) What is the average number of jobs in the system at any point in time

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