Explain the system utilization rate and the probability, Operation Management

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Sid Das Brick Distributors currently employs 1 worker whose job is to load bricks on outgoing company trucks. An average of 24 trucks per day, or 3 per hour, arrive at the loading platform, according to a Poisson distribution. The worker loads them at a rate of 4 trucks per hour, following approximately the exponential distribution in his service times. Das believes that adding an additional brick loader will substantially improve the firm's productivity. He estimates that a two-person crew loading each truck will double the loading rate (µ) from 4 trucks per hour to 8 trucks per hour. Analyze the effect on the queue of such a change and compare the results to those achieved with one worker. Calculate the average number in the queue, average number in the system, average time in the queue, average time in the system, the system utilization rate, and the probability that the system is empty


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