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Ryan Izard

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Thus, the average number of customers in the system during the interval [0, t] is:

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Consider all customers in system at time t (i.e. N(t) customers). Let RN(t) denote the total time after t that those N(t) customers spend in the system. The average time spent in the system by all customers arriving in the interval [0, t] is:

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So:

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and:

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For the stable system we are concerned with, the following limits hold:

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