CoSc 4350/5350
Spring 2001
2/18/2016 2:50 AM
page 1 of 6
notes
17 jan 01
message buffer system. interested in length of first message that
overflows the buffer. model message lengths as equally likely 0, 1, .. 9.
use buffer length of 20.
conjecture that overflow message lengths have same distribution as input
message lengths.
handout: list of random digits. each student makes twenty buffer fill runs
and reports distribution of overflow message lengths. (almost) all sets of
20 runs have median > 4.5.
describe use of z-score to test hypothesis that mean of 20 runs is a sample
from distribution of mean of 20 runs. my simulation resulted in z about
+2.5.
relate this scenario to general simulation. emphasize complexity if this
message buffer is one part of a more complex system.
handout: assignments. read chapter one and report on 7, 8, .., or 11. design a
problem similar to message buffer overflow, simulate, and report.
CoSc 4350/5350
Spring 2001
2/18/2016 2:50 AM
page 2 of 6
notes
19 jan 01
The message buffer system results can be expressed theoretically with a
recursive system. The key observation is the importance of the
probability that a sum of message lengths has a given value. For the
equally likely message lengths 1, 2, …, n the probability that message
length i overflows the buffer at limit lim is the sum of the message
length sum probabilities lim-i+1 to lim divided by n.
The message length sum probability for sum x is the sum of the message
length sum probabilities lim-n to lim-1.
These recursively defined probabilities can be used to calculate the
overflow message probability distribution for any n and any lim.
For large lim all the message length sum probabilities become equal. There
probability is 2/(n+1). The overflow message probability distribution
becomes triangular, prob = 2i/n/(n+1).
handouts: distributions for n=4 obtained using Excel
handouts: code for a simulation of a related problem, input is a continuous
uniform(0, n) distribution of message lengths. uses a tally sheet class, a
random generator class, and a message buffer class.
handouts: output for n=4.0, lim = 2.0, 4.0, and 8.0.
The results for the continuous case closely follow the predicted results for
the discrete case.
CoSc 4350/5350
Spring 2001
2/18/2016 2:50 AM
page 3 of 6
notes
22 jan 01
Discrete event simulation terms:
System state – the collection of current values of all variables for the state.
Event – something that changes the state of the system.
Simulation clock – a variable that keeps track of the current simulated time.
Calculation time passes as the code processes an event. No simulation
time passes during this processing. Simulation time passes between
events. No calculation time is used between events.
Event list – a list of all the currently scheduled events. The simulation
system processes the events on the list. Processing an event may include
scheduling new events.
With only four students in the class, the format has got to change. I will
try to redesign the course around one or more major projects. We will
use the Wednesday reports to suggest projects that are potentially
publishable.
Perhaps Swarm and Arena can be used as the implementation engines.
Perhaps some AI or hardware or networking problems can be simulated.
Perhaps one of these systems can be extended.
Perhaps one of these systems can be implemented with a Design Pattern
paradigm.
CoSc 4350/5350
Spring 2001
2/18/2016 2:50 AM
page 4 of 6
notes
24 jan 01
Anton: Simulation to determine the price of options.
Scott: Simulation to
Eric: Simulation to determine the effect of small finite buffers on
FlowShop problems. Are solutions that assume infinite buffers usable?
CoSc 4350/5350
Spring 2001
2/18/2016 2:50 AM
page 5 of 6
notes
26 jan 01
Joel: Report on the education web site of the Winter Simulation
Conference.
Discussion of class organization. We will select one or more problems and
produce a simulation study for possible publication.
For Monday: find a potential problem
CoSc 4350/5350
Spring 2001
2/18/2016 2:50 AM
page 6 of 6
notes
29 jan 01
Suggested Problems:
Anton: Sugar cane harvest transportation from field to mill. In Arena.
Scott: Something about primitive evolution from soup to cell.
Eric: Elevator control.
Joel: Effect of protocol changes on network traffic loads.
We selected the elevator control study.
We can observe the input distributions.
We have a good grasp of the expected behavior.
We can try several different implementations: Arena, Swarm, C++.
We can compare several control algorithms.
We can try several adaptive algorithms.
For Wednesday:
Write down a description of the customer arrival process.
Write down a description of the elevator control process.