Assignment 3 Event driven simulator

Purpose:
To familiarize yourself with the event driven simulator provided
and generating statistical measures for such a system.
Questions:
1) The current single-server system provided with the Discrete Event Simulator (available on the
Moodle course site) computes the basic statistics: N, NW, WS, WQ, T0 and Tmax. Using these
values, create a function that produces the following derived statistics
• average wait time: wq = W
Q / N
• probability of waiting: # customers who wait / N
• probability of idle server: P0 = T0 / Tmax
• probability of busy server: 1 - P0
• average service time: ws = WS / N
• average service rate per minute: 1 / ws
• average service rate per hour
i.e. average number of customers served per hour
and stores them in ‘stats’ and finally returns ‘stats’ to be stored in a ‘results’ variable.
This function should be linked to the simulator through the ‘measure’ parameter of
new.discreteEventSystem(). In other words you should modify the first function in
singleServerSystem.R to read
new.singleServerSystem <- function(){
new.discreteEventSystem(firstEvent.name = "A",
measure = myDerivedStatsFn, ß-- your function goes here
state = new.state(...),
stats = new.stats(...),
updateFn.stats.default = base.statsUpdate,
updateFns = new.updateFns(...)))
}
Call the file with your modifications “sssWithDerivedStats.R”.
Run the system in verbose mode and your function as the system measure (instead of the default
‘identity’ function) for 100 simulated minutes to demonstrate that your function works.
Then run the system (silently) for 500 and 1000 and 5000 simulated minutes and compare the results.2) While T0 is the total idle time (i.e the T0 variable in ‘stats’) , it is denoted as T0 because it also is
the total time that there are no customers in the single server system.
T1 denotes the total amount of time where there is only a single customer in the system (no one
in the queue, but the server is busy).
T2 denotes the total amount of time where there is two customers in the system (one being
served, one in the queue), etc.
Modify the single-server system in singleServerSystem.R so that you
• Keep track of T0, T1, T2, … in the single server stats.
• Take the ‘stats’ returned by the simulator and report these times as well as the percentage
of time the system had no customers, one customer, two customers etc. (i.e. T0/Tmax,
T1/Tmax, T2/Tmax, …)
Call the file with your modifications “sssWithTL.R”
Run the system in verbose mode and your function as the system measure (instead of the default
‘identity’ function) for 100 simulated minutes to demonstrate that your function works.
Then run the system (silently) for 500, 1000 and 5000 simulated minutes and compare the results.
3) The file singleTiringServerSysterm.R contains a modified version of the single-server system.
In this system the service time of the single server is affected by the how long the previous
service event took. The server is more tired the longer the previous service time lasted; this is
directly related to the length of the previous task and not to the length of time the server has
been serving overall.
• Do the following:
o Run singleTiringServerSysterm.R in verbose mode with an endTime of 150 minutes.
o Take note of what happens to the service time (the ST variable) from event to event.
o Repeat this 15 times.
o Discuss what you observe. Include an explanation for what is happening.
§ Hint: the formula used to calculate service times was not well designed,
leading to undesirable results.
• Next:
o Modify how the service time is calculated in the update events to produce more
realistic behavior in the system.
o You must demonstrate that your system has the desired effect;
don’t just produce the code with no analysis.
o Compare the behavior of your system with the original single-server system using the
statistics you calculated in question 1
Call the file with your modifications “stssWithBetterST.R”
Important Note:
• If you have already loaded singleServerSysterm.R, you must reload the entire file
singleTiringServerSysterm.R, not just the function new.singleTiringServerSystem();
otherwise the simulator will not work properly.
• Similarly, if you want to run the original single-single system, you must reload
singleServerSysterm.R and not just run new.singleServerSystem()Mark Breakdown
Q1 Q2 Q3a Total
Correct Answer 3 3 3 9
Code 3 3 3 9
Testing 3 3 3 9
Discussion 3 3 5 11
Total 12 12 14 38
Instructions:
Code
• All code must be written in R
Statistics
• You do not need to perform any statistical tests for either question.
Just report and describe the behavior you see.
Documentation
• All questions must be answered in single document using output from your programs as
evidence.
o If only code is provided with no documentation actually answering the questions, you
will get a grade of zero for the assignment.
o Similarly if you only provide the answer document and don’t hand in your source
code and executable file, you will get a grade of zero for every question with missing
programs.
• All documentation must be provided in MS-Word, PDF or PS formats
• Source code must be in text form (of course)