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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78 CHAPTER 7. CONTINUOUS-TIME PROCESSES<br />
4. We give a simulation <strong>for</strong> the proposed system.<br />
Let M = {1, 2, 3, 4} be as defined in Case 7.2.<br />
Define the following r<strong>and</strong>om variables:<br />
G ≡ time gap between regular calls<br />
H ≡ time gap between calls to the chair<br />
X ≡ time to answer regular calls<br />
Z ≡ time to answer chair’s calls<br />
Define the following system events.<br />
e 0 () (start of the day)<br />
S 0 ← 1<br />
C 1 ← FG<br />
−1 (r<strong>and</strong>om())<br />
C 2 ← FH<br />
−1 (r<strong>and</strong>om())<br />
C 3 ←∞<br />
C 4 ←∞<br />
e 1 () (regular call)<br />
if {S n =1} then<br />
S n+1 ← 2<br />
C 3 ← T n+1 + FX<br />
−1 (r<strong>and</strong>om())<br />
endif<br />
C 1 ← T n+1 + FG<br />
−1 (r<strong>and</strong>om())<br />
e 2 () (chair call)<br />
if {S n =1} then<br />
S n+1 ← 3<br />
C 4 ← T n+1 + FZ<br />
−1 (r<strong>and</strong>om())<br />
else<br />
if {S n =2} then<br />
S n+1 ← 4<br />
Z ← FZ<br />
−1 (r<strong>and</strong>om())<br />
C 4 ← T n+1 + Z<br />
C 3 ← C 3 + Z<br />
endif