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This assumes that n0¹ 0 and hence C1 actually enters and leaves the server. If n0 = 0 then |
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as no item entered or left the server. We combine these as |
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where d0 is the probability that n0 = 0. d0 has only two values: d0 = 0 when n0¹ 0 and d0 = 1 when n0 = 1, so that n0d0 = 0 and  . |
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Now find E(d), which lies between 0 and 1: |
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by the stationarity assumption. |
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Now E(r) is the expected number of arrivals during a service time; i.e., |
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The expectation that the server is idle, E(d), is |
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Now suppose we generalize equation E.1 for time intervals i and i - 1 and we square both sides of equation E.1. |
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Taking the expcted value of both sides, |
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again by stationary  . Also, since ni-1, ri, di-1 are independent and E(ri) = E(r), etc., we have |
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