Some Badly Behaved Closed Queueing Networks
Some Badly Behaved Closed Queueing Networks
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In our eReader you can find the full English version of the book. Read Some Badly Behaved Closed Queueing Networks Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Some Badly Behaved Closed Queueing Networks
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Let us denote by 7r2 the stationary probability of those states q with 92 > 0, by ■K4 the stationary probability of those states q with 174 > 0, and by ttis the stationary probability of those q with q\ + q^ = n (that is, 92 = 94 = 0). From the path decomposition described above (an initial period of finite expected duration, followed by alternating idle and busy periods, each with finite expected duration) it follows that (3. 4) 7r2 + 7r4 + 7ri3 = 1.
Moreover, with aj = E{Ij) and bj = E{B-i) a...s in (3. 2) and (3. 3), we have that (3. 5) 7ri3 = lim En Of course, two equivalent expressions for the long-run throughput rate A are (here /x/t = ^/rrik) (3. 6) A = /i2'iT2 and \ = ^^n^, implying that A(m2+m4) = 7r2+7r4. With our convention that m2 + m4 = 1, this and (3. 4) together imply (3. 7) A = (1 - 7ri3)/(Tn2 +m4) = 1 - 7ri3.
Together, (3. 2), (3. 3) and (3. 5) imply that 7ri3 — » as n — > cx), so we have the following major conclusion.
Proposition 3. 1. A -^ 1 as n — ► oo.
Corollary 3.
What to read after Some Badly Behaved Closed Queueing Networks?
You can find similar books in the "Read Also" column, or choose other free books by J Michael Harrison to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Let us denote by 7r2 the stationary probability of those states q with 92 > 0, by ■K4 the stationary probability of those states q with 174 > 0, and by ttis the stationary probability of those q with q\ + q^ = n (that is, 92 = 94 = 0). From the path decomposition described above (an initial period of finite expected duration, followed by alternating idle and busy periods, each with finite expected duration) it follows that (3. 4) 7r2 + 7r4 + 7ri3 = 1.
Moreover, with aj = E{Ij) and bj = E{B-i) a...s in (3. 2) and (3. 3), we have that (3. 5) 7ri3 = lim En Of course, two equivalent expressions for the long-run throughput rate A are (here /x/t = ^/rrik) (3. 6) A = /i2'iT2 and \ = ^^n^, implying that A(m2+m4) = 7r2+7r4. With our convention that m2 + m4 = 1, this and (3. 4) together imply (3. 7) A = (1 - 7ri3)/(Tn2 +m4) = 1 - 7ri3.
Together, (3. 2), (3. 3) and (3. 5) imply that 7ri3 — » as n — > cx), so we have the following major conclusion.
Proposition 3. 1. A -^ 1 as n — ► oo.
Corollary 3.
What to read after Some Badly Behaved Closed Queueing Networks?
You can find similar books in the "Read Also" column, or choose other free books by J Michael Harrison to read onlineMoreLess
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