The arrival rate of parts of a machinist is Poisson distributed with a mean of 8 per hour. A part can be machined in an average of 6 minutes, with a standard deviation of s = 8 minutes. Consideration is being given to replacing this with an automated machine that can machine each part in exactly 6 minutes. What will be reduction in the average number of parts in queue? The reduction in time in queue?
What would happen to be average number in the queue if, using the automated machinery, the Poisson arrival rate were increased to 10 per hour to match the constant service rate?