Question: 5. Let us consider a queueing system where a server processes the customers that arrive. Customers arrive according to a Poisson process with a rate

5. Let us consider a queueing system where a

5. Let us consider a queueing system where a server processes the customers that arrive. Customers arrive according to a Poisson process with a rate of 30 per hour and processing times are exponential with a mean of 1.2 minutes. Let's assume that the machine is turned off when the system is empty and it is turned on again when a new customer arrives. If the machine is turned on however, it requires a setup time that is exponential with mean 6 minutes. Assuming that the system capacity is 4 customers. a. What is the definition of the state in the rate diagram? (Hint: the state is 2-dimensional). (5 pts] b. Draw the rate diagram for the queueing system. (5 pts] Show the balance equations and compute for the probability distribution of each state (10 pts) d. What percentage of time will the machine be off? (5 pts) C. 5. Let us consider a queueing system where a server processes the customers that arrive. Customers arrive according to a Poisson process with a rate of 30 per hour and processing times are exponential with a mean of 1.2 minutes. Let's assume that the machine is turned off when the system is empty and it is turned on again when a new customer arrives. If the machine is turned on however, it requires a setup time that is exponential with mean 6 minutes. Assuming that the system capacity is 4 customers. a. What is the definition of the state in the rate diagram? (Hint: the state is 2-dimensional). (5 pts] b. Draw the rate diagram for the queueing system. (5 pts] Show the balance equations and compute for the probability distribution of each state (10 pts) d. What percentage of time will the machine be off? (5 pts) C

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