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This can be rewritten by factoring e-r from both numerator and denominator, leaving: |
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Observe that for n = 1 (and m = 1): |
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For each of the preceding cases: |
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Outside the single-server, low-population cases, the asymptotic model is generally consistent with the exact Kobayashi model (error usually less than 10%). It offers the following advantages: |
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1. It is computationally easier, especially for large n. |
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2. It is based on M/G/1, not M/M/1, and allows appropriate use of c2 when known or estimated. |
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Figure 9.14 plots the error between the asymptotic model and the finite population model (both for c2 = 1). |
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For the remainder of the chapter, we generally use the asymptotic model except in the special cases (n = 1, or n = 2 and c2 = 1) where the exact (M/M/1) result is used. |
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