Results On a Transient Queue

Cover Results On a Transient Queue
Results On a Transient Queue
C Siegel
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n ' — Clearly, n-1 / N PfA^} = ^ -f^P^t) -u), n > 1, p=l and n-1 (p) PlBn-l^ = ^ ^n 1^^" ^^ ^ n > 2 . P=l Moreover^ by Lemma 4, A = B _-, , which completes the proof for n >^ 2. For n = 1 we note that for u j 2.
[0, b] It is convenient to write this equation in the form (16) P^(b) = J (^l)(0). [0, b] Lemma 6. P (b) and (b) are of bounded variation.
12 Proof. Let (17) '^n^^^ " P{serviclng at least n customers} Then Pn(b) = 7r^(b) - 7r^^^(b) .
H. Hanisch and W. Hirsch [5] have shown th
...at w (h) is n^ ^ non-decreasing in b. Hence P^(h) is of bounded variation.
To establish that 0, n > 2. [0, 00) Since p is of bounded variation, so is 2, (where "-x.


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