Question: Queueing Theory 2. (25 points) At a tool service center, machinists arrive according to a Poisson process with a rate of 2 per hour. The

Queueing Theory Queueing Theory 2. (25 points) At a tool service

2. (25 points) At a tool service center, machinists arrive according to a Poisson process with a rate of 2 per hour. The service time is exponentially distributed with mean 20 minutes. The hourly wage paid to the attendant at the service center is $15 per hour and the hourly cost of a machinist away from his work is $40. (a) (6 points) Calculate the average number of machinists in the system at any given time. (b) (6 points) Calculate the average time a machinist spends waiting for service. (c) (6 points) Calculate the total cost of operating the system for an 8-hour day. (d) (7 points) Calculate the cost of the system if there were two attendants working together as a team in effect acting together as a single server), each paid $15 per hour, and the mean service time of the new system is 15 minutes

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