SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...
SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...
SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...
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107<br />
(b) For the M/M/1<br />
For the M/D/1<br />
w q (λ, µ, 1) =<br />
ρ 2<br />
λ(1 − p)<br />
w q (λ, 1,µ,0, 1) =<br />
ρ 2<br />
2λ(1 − ρ) = 1 2 w q(λ, µ, 1)<br />
20. No answer provided.<br />
21. Let osu.edu be station 1, <strong>and</strong> eng.ohio-state.edu be station 2 in a network of<br />
queues. Then<br />
j =1 j =2<br />
a 0j 2 1<br />
µ (j) 3 2<br />
s (j) 1 1<br />
( 0<br />
R =<br />
0<br />
There<strong>for</strong>e,<br />
λ (1) = a 01 =2/second<br />
λ (2) = a 02 +0.2 λ (1) =1.4/second<br />
We approximate it as a Jackson network.<br />
)<br />
0.2<br />
0<br />
(a) l (1)<br />
q = ρ2 1<br />
1−ρ 1<br />
= (2/3)2 =4/3 messages<br />
1−2/3<br />
w (1)<br />
q<br />
= l(1) q<br />
λ (1)<br />
=2/3 second<br />
(b) l (2)<br />
q = ρ2 2<br />
1−ρ 2<br />
= (1.4/2)2 ≈ 1.63 messages<br />
1−(1.4/2)<br />
w q<br />
(2) = l(2) q<br />
≈ 1.2 seconds<br />
λ (2)<br />
(c) (12 K/message) (1.63 messages) = 19.56K<br />
(d) Let h be the inflation factor, so that<br />
λ (1) = ha 01 =2h<br />
λ (2) = ha 02 +0.2λ (1)<br />
= h +0.2(2h)<br />
= 1.4h