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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112 CHAPTER 8. QUEUEING PROCESSES<br />
(d) We now have a network of 3 queues, with queue 3 being the rework station <strong>for</strong><br />
station 1.<br />
R =<br />
⎛<br />
⎜<br />
⎝<br />
0 0.9 0.1<br />
0 0 0<br />
0 0.5 0<br />
λ (1) =20<br />
λ (2) =0.9 λ (1) +0.5λ (3)<br />
λ (3) =0.1 λ (1)<br />
There<strong>for</strong>e,<br />
λ (1) =20<br />
λ (2) =18+1=19<br />
λ (3) =2<br />
For station 1 nothing changes. For station 2<br />
⎞<br />
⎟<br />
⎠<br />
ρ 2 = 19/30 ≈ 0.63<br />
c = 6<br />
(<br />
l (2) = λ (2)<br />
ρ 2 2<br />
λ (2) (1 − ρ 2 ) + 1 )<br />
µ (2)<br />
= 19/11 ≈ 1.7 jobs<br />
(e) This change has no impact on the results from part (d), but would change the<br />
per<strong>for</strong>mance of the rework stations.<br />
28. Model as a Jackson network of infinite-server queues, with a queue corresponding to<br />
each type of transaction.<br />
transaction i a 0j µ (j) per hour<br />
log on 1 1000 or 1500 20<br />
fetch 2 0 20<br />
read 3 0 5<br />
log off 4 0 100<br />
⎛<br />
R = ⎜<br />
⎝<br />
0 0.79 0.01 0.2<br />
0 0.17 0.63 0.2<br />
0 0.16 0.4 0.44<br />
0 0 0 0<br />
⎞<br />
⎟<br />
⎠