SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...

Chapter 4
Simulation
1. An estimate of the probability of system failure within 5 days should be about 0.082.
2. No answer provided.
3. Let G 1 ,G 2 ,... represent the interarrival-time gaps between the arrival of jobs. Let
B n represent the type of the nth job; 0 for a job without collating, 1 for a job with
collating.
Let X n represent the time to complete the nth job that does not require collating.
Let Z n represent the time to complete the nth job that does require collating.
We model all of these random variables as mutually independent.
Let S n represent the number of jobs in progress or waiting to start.
Define the following system events with associated clocks:
e 0 () (initialization)
S 0 ← 0
C 1 ← FG
−1 (random())
C 2 ←∞
e 1 () (arrival of a job)
S n+1 ← S n +1
if {S n+1 =1} then
B n ← FB
−1 (random())
if {B n =0} then
C 2 ← T n+1 + FX
−1 (random())
else
25