AMS 553: Program Set 1
We wish to analyze the following two single-server queueing systems: (i) An M/M/1 queue, where the interarrival times and service times are independent exponentially distributed random variables (ii) An M/D/1 queue, where the intera
AMS 553: Homework 3
1. (L&K 8.7) For a < b, the right-triangular distribution has density function fR (x) =
2(xa) (ba)2
if a x b otherwise.
0
2(bx) (ba)2
(1)
and the left-triangular distribution has density function fL (x) = if a x b otherwise. 0 (2)
Thes
AMS 553: Homework 1
1. (L&K 4.2) Let X be a continuous random variable with pdf 2 1 f (x) = x2 + x + for 0 x c 3 3 (a) Find the value of c; (b) Plot the pdf f (x); (c) Compute and plot the cdf F (x); (d) Compute P ( 1 X 2 ), E [X ], and V ar(X ). 3 3 2. (
AMS 553: Homework 5 (Due November 30th)
1. (L&K 9.1) Argue heuristically that comparable output random variables from replications using different random numbers should be independent. 2. (L&K 9.3) In Example 9.9, suppose that the condition (b) is violate
Solutions to Problems in Chapter 4 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
(Problem 4.4, continued from previous page)
4.28. Let N = number of keys required to open the door (a random variable).
1
k 1 1
Solutions to Problems in Chapter 10 of
Simulation Modeling and Analysis, 4th ed., 2006, McGraw-Hill, New York
by Averill M. Law
10.3. We modified the code of Sec. 2.5 to block registering a response time if its number (called
num_responses in the code) wa
Solutions to Problems in Chapter 7 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
7.15. The first 36 Wi ' s are (every tenth Wi is in boldface)
15, 8, 13, 13, 4, 2, 5, 9, 15, 1, 11, 10, 8, 4, 11, 3, 14, 3, 7, 5
Solutions to Problems in Chapter 5 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
5.7. If the queue of the first machine in the second submodel becomes full, then the last machine
in the first submodel may beco
Solutions to Problems in Chapter 13 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
13.1.
The arrival rate is = 1 / 1.25 = 0.8 and the processing rate is
factor is = 0.8 / 0.9 = 0.889 < 1 .
= 0.9 .
Therefore, t
Solutions to Problems in Chapter 6 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
6.20. Service times
Data Characteristic
Source File
Observation type
Number of observations
Minimum observation
Maximum observat
Solutions to Problems in Chapter 12 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
12.4. To be consistent with Example 9.29, we use a run length of 65 seconds and a warmup
period of 5 seconds. We also use a con
Solutions to Problems in Chapter 11 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
(Problem 11.11, continued from previous page)
11.17. Only seven streams are required if we use stream 1 for interdemand times a
Solutions to Problems in Chapter 9 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
9.32. Assume that p will not change appreciably as we make more replications. Let n be the
required number of replications, whic
Solutions to Problems in Chapter 8 of
Simulation Modeling and Analysis, 4th ed., 2007, McGraw-Hill, New York
by Averill M. Law
(Problem 8.11, continued from previous page)
8.19. Suppose that u ( z ) = u , where z = v / u for 0 < z < . Then from the defini
AMS 553: Homework 6
1. (L&K 11.2) In Section 11.2.2 and specically in gure 11.1, We consider the question of whether CRN
would induce the desired positive correlation for a given pair of alternative congurations, or whether
it might backre. Consider the f
AMS 553: Homework 2
1. (L&K 7.1) Consider the LCG Zi = (5Zi + 3)(mod16) and Z0 = 7. Find Z500 , using only pencil and paper. 2. (L&K 7.2) For the following multiplicative LCGs, compute Zi for enough values of i 1 to cover an entire cycle: (a) Zi = (11Zi1
AMS 553: Homework 6
1. (L&K 11.2) In Section 11.2.2 and specically in gure 11.1, We consider the question of whether CRN would induce the desired positive correlation for a given pair of alternative congurations, or whether it might backre. Consider the f
AMS 553: Program Set 2 Due December 2 (Thursday)
Consider a single commodity inventory system, where times between successive demands are i.i.d. U (0, 1) days, demands are i.i.d. exponentially distributed with mean 10 tons. Assume all demands that cannot
AMS 553: Homework 2
1. (L&K 7.1) Consider the LCG Zi = (5Zi1 + 3)(mod16) and Z0 = 7. Find Z500 , using only pencil and
paper.
2. (L&K 7.2) For the following multiplicative LCGs, compute Zi for enough values of i 1 to cover an
entire cycle:
(a) Zi = (11Zi1
AMS 553: Homework 3
1. (L&K 8.7) For a < b, the right-triangular distribution has density function
fR (x) =
2(xa)
(ba)2
if a x b
0
otherwise.
(1)
and the left-triangular distribution has density function
fL (x) =
2(bx)
(ba)2
if a x b
0
otherwise.
(2)
Thes
AMS 553: Homework 4
1. Consider an inventory system with the following daily demand:
n : 1 2 3 4 5 6 7 8 9 10
Dn : 13 27 33 5 43 17 52 33 15 19
An (s, S) ordering policy is used to manage the inventory system. At the beginning of each day, assume
that the
AMS 553: Homework 5
1. (L&K 9.1) Argue heuristically that comparable output random variables from replications using different random numbers should be independent.
2. (L&K 9.3) In Example 9.9, suppose that the condition (b) is violated. In particular, su