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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Chapter 9<br />
Topics in Simulation of <strong>Stochastic</strong><br />
Processes<br />
1. Solve ̂σ/ √ k ≤ 20 which gives k = (110/20) 2 ≈ 31 replications.<br />
2–7. No answer provided.<br />
8. To obtain a rough-cut model we will (a) use a 0.5 probability that an item joins the<br />
queue of each inspector, rather than selecting the shortest queue, <strong>and</strong> (b) treat all<br />
processing times as exponentially distributed (later we will refine (b)).<br />
• Current System<br />
Λ =<br />
station j name a 0j µ (j)<br />
1 repair 1 0.125 0.167<br />
2 repair 2 0.125 0.167<br />
3 inspect 0 0.333<br />
⎛<br />
⎜<br />
⎝<br />
R =<br />
λ (1) ⎞<br />
λ (2) ⎟<br />
λ (3)<br />
⎛<br />
⎜<br />
⎝<br />
A =<br />
0 0 1<br />
0 0 1<br />
0.1 0.1 0<br />
⎛<br />
⎜<br />
⎝<br />
0.125<br />
0.125<br />
0<br />
⎞<br />
⎟<br />
⎠<br />
⎞<br />
⎟<br />
⎠<br />
⎠ =[(I − R) ′ ] −1 A =<br />
119<br />
⎛<br />
⎜<br />
⎝<br />
0.156<br />
0.156<br />
0.313<br />
⎞<br />
⎟<br />
⎠