Simulation of a single-server Queue
Estimation of steady-state waiting time in queue
Inter-arrive time
0
2.623
0.029
15.470
7.850
15.827
266.733
0.141
4.359
26.134
0.701
15.973
6.274
0.154
0.531
0.005
0.840
44.165
15.010
Service
Time
9.116
7.879
10.231
13
Spreadsheet to Determine Weibull Parameters
alpha-guess
1.000
mean-given info
100
Gamma(1+1/a)
1.000
stdev-given info
25
Gamma(1+2/a)
2.000
C^2+1
1.0625
ratio
2.00000
Difference
0.938
Difference (value in B6) should be zero
beta
100.000
Use GoalSeek found
First example from the Appendix to Chapter 3: confidence limit for the mean
Mean
100
St.Dev.
20
Data
66.0
106.5
112.3
95.4
116.5
128.0
68.9
102.1
114.3
81.7
91.8
94.4
72.8
82.4
61.4
75.3
71.2
98.6
103.5
112.0
106.1
107.0
110.6
95.7
83.1
85.0
100.5
133.0
9
Chapter 13
Advanced Queues
13.1.
(a) x6 = 2 29 + 12 = 70
10 2
(b) x10 = 42 1 + 2
4 1 2
10
= 2378
13.3. The parameters are = 1/hr and = 0.8284/hr. (There be some roundwill
off error for this problem. The mean rate should actually be 2( 2 1).
(a) The gene
Chapter 11
Replacement Theory
11.1. This problem is a repeat of the last problem of Chapter 1. It illustrates an
important concept so that if it was not assigned as homework for Chapter 1, it may
be worthwhile to assign as homework for this chapter.
T U(0
Chapter 10
Inventory Theory
10.1.
(a) Find the smallest n such that g(n) 0.
g(1) = 3
g(2) = 2
n = 2
(b) Find the smallest n such that g(n) 0.
1
1
25 64
1
1
g(2) =
4 25
1
g(3) = 1
4
1
g(4) =
1 < 0
16
g(1) =
n = 4
(c) Find the smallest n such that g
Chapter 9
Event-Driven Simulation and Output Analyses
The hand simulations need at least two charts: the future events list and the main
simulation chart. My guess is that the future events list should not prove difcult,
but the main chart may be more dif
Chapter 6
Markov Processes
6.1.
10
5
G=
1
3
3
0
7
12 4
3
0
6
5
2
9 14
6.3. The events cfw_U > u and cfw_T > u cfw_S > u are equal. To show this equality,
observe that
cfw_U > u cfw_T > u cfw_S > u and
cfw_T > u cfw_S > u cfw_U > u .
Since T and S are
Chapter 1
Basic Probability Review
1.1.
(a) For (n1 , n2, n3), let ni be the number of demands at ith distribution center
= cfw_(0, 0, 0), (1, 0, 0), (2, 0, 0), (0, 1, 0), , (2, 2, 2)
(b) 227
(c) cfw_ (0,1,2), (0,2,1), (1,1,1), (1,0,2), (1,2,0), (2,0,1),
Chapter 2
Basics of Monte Carlo Simulation
The difcult part of doing simulations by hand is establishing the column headings.
Of course such headings are not unique, but we give below suggestions for the
headings and some entries for the problems that do
First example from the Appendix of Chapter 4: simulation of a compound Poisson process
Note: theoretical value of arrival rate of axles is 2.48/1.2 = 2.0667
Inter-arrive
time
0.028
3.638
1.282
2.357
1.763
0.633
1.554
2.110
1.765
0.530
0.488
1.046
0.791
0.
Example of some matrix operations
This is slightly different than as shown in the appendix to give you another approach
I=
P=
mod. (I-P)=
RHS=
Pi=
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0.5
0.2
0
0
0.5
0.4
0.1
0
0
0.4
0.8
0.3
0
0
0.1
0.7
0.5
-0.2
0
0
-0.5
0.6
-0
First example from the Appendix to Chapter 2: simulation of a discrete random variable
To save space, only a limited number of rows were copied down. Note, every time you hit the F9 key, the random numbers are re-computed.
If you copy these numbers down,