Homework Fall 2011
Homework due Sept. 14
1.To study a modification of a system , indicate whether you would use a simulation or not and if
a simulation, whether the model would be physical or mathematical
a. a small section of an existing factory
b. a freeway interchange
c. an emergency room
d. a pizza-delivery operation
e. The shuttle bus operation for a rental car agency at an airport
f. a battlefield communications network.
g. The chemical composition of an optical fiber
2. For the above situations assume they would be studied using a simulation model- would the
simulation be static or dynamic, deterministic or stochastic, and continuous or discrete.
3. For the above situations name several entities and events
4Go to http://www.mathworks.com/academia/ View the matlab tutorial under learn and follow
along with the simulink tutorial doing your own bungee jumping simulation:
http://www.mathworks.com/products/demos/simulink/SimulinkEDU/simulinkedu/Viewlet/simuli
nkedu_viewlet_swf.html
.For the bungee problem hand in your diagram adding your name to some box.
Make a table for cord constant k= 5, 40, 500 and m( the mass in kilos) = 25(small child), 90,
and 250( 2 people jumping together) indicating an approximate lowest altitude and highest
altitude after the fall. for each of the 9 combinations. Put an “X” if the lowest point is under
ground. The company running the jump is thinking of adding a high platform for security. For
each “X” in the table, indicate how high above the 50 ft. mark would this platform have to be so
that the person would not hit the ground
Sept. 19:
Project 1: Do Problem 2, page 68 of Barrodale- the 2 missile problem-print the time of the
explosion and which object exploded. Plot the trajectories of the three moving bodies. You may
do this in any language you wish .like C++ and excel(x-y plot), C++ with your own plotting
tools, or Matlab by adding a few line to the single missile problem on the class home page. Hand
in source code + output
Homework due Sept. 21:
1.Assume one has the following service times
time (in minutes)
Probability
1
.25
2
.4
3
.2
4
.15
What are the cumulative probabilities?
How would you generate them?
2.a.Generate the arrival Service table for the following data
Interarrival : 3 6 1 2 4 6 5 1
Service times: 2 1 8 5 4 3 2 5 6
b. When are the events
c. Find the following statistics
1. Utilization
2. Average wait time
3. Average time in system
4. average service time
5.expected service time
6. average no. of customers waiting
Homework due Sept. 26
Read section 4.3 of Barrodale:
Project 2- Do problem 9, page 75 of Barrodale the baseball problem- print the time and position
of the ball hitting the ground. Plot the trajectory of the baseball
You may do this in any language you wish .like C++ and excel(x-y plot), C++ with your own
plotting tools, or Matlab. Hand in source code + output.
Produce the trajectory of the baseball using simulink.
Oct. 3:
Quiz
Homework for Oct. 3:
Project 3:
In Simulink solve the following problems
1.A damped pendulum with a one kg weight and string of length 1m.
x’’ =- cx’ .9.8*sin(x)
from time 0 to 50 and set c = 9 and 10
start with x=1.
2.Spread of disease where P represents the percentage of affected population.
P’ = 2P*(2000-P)
P(0)=10
3.Bank balance B with interest at 5%
B’ =0.05B
B(0) =1000
4. The depth Y of water in a bucket
with a whole in it.
Y’ = -Asqrt(2)g sqrt(y)
With g = gravity =32 and A is cross sectional area. Set A to pi.
Homework for Oct .5:
Project 4- : Program a specific probabilistic simulation model, the 2-pump gas station problem in
Barrodale. Cars arrive at a rate of 20 per hour to a gas station with two pumps & a single queue.
If both pumps are busy, put the car in the queue. Service time = 5 minutes per car. Run the
simulation for 10,000,000 hours. Determine and print as output: average queue length, the
average waiting time for a car, the percent of the time the pumps are busy (both pumps, one
pump, or idle time). Hand in source code and the
output it produces, Use an event driven mode.
Oct. 12: Project 5: Queues- On the Unix machine implement the queuing data type using a C++
class with a linked list, a straight array and a circular array( see the notes on my website) First
show it works with 5 items to be queued and then time with 10,000 items. Try 3 situations: all
enqueued and then all dequeued, enqueue followed by dequeue so that queue is never longer than
1, randomly enqueue and dequeue(if possible) with each equally likely
Homework for Oct. 17:
Do one of the questions in the practice midterm.
Oct. 19 Midterm
Oct. 26:
Project 6- Produce phantom data for Positron Emission Tomography and produce images in
Matlab
Oct. 31
Project 7: Implement one of the event simulations on the form that will be given out.
Nov.7:
Random number generator worksheet
.
Nov. 9: 600 throws determine the frequency of the numbers on the dice for each of the ways the
random numbers were generated.
Nov. 14:Project 9- Use the results of project 7 to determine the chi square statistic for each generator
.Determine the gap frequencies and the Kolmogorov-Smirnov statistic
Nov. 21
Worksheet on queueing analysis
Nov. 28 take home quiz
Dec. 5 Project 9 Solving a large queueing problem using SOR