FIT5011 ASSIGNMENT 3
1. Assignment Task Definition (100 marks)
You task compromises the following.
(1) Produce a report on Traffic Modeling based on the papers
provided on Moodle, and other relevant papers you can find.
(2) Part 1 of this report shall compromise four sections (50
marks)
(a) Discuss the background and explain the main issues and
problems in network traffic modeling (not more than 400 words).
(b) Discuss the influence of traffic modeling on network
performance and design (not more than 800 words).
(c) Discuss the role of simulation in the analysis of
complex queueing systems (not more than 800 words).
(d) Explain simulation of random variables such as uniformly
distributed random variables, exponentially distributed random variables and
Pareto distributed random variables. Explain simulation of discrete random
variables.
(e) Add any other issues relevant to the topic
(f) Include references and use proper citation techniques.
(g) Your report need not be restricted to the material of
lecture notes. Please use books, information found on the web. Journal and
conference papers are very encouraged.
(3) Part 2 of this report shall compromise the simulation of
a queueing system and its analysis (50 marks). You need to provide the
following work for simulating an M/M/1 queueing system. (The value of traffic
parameter ? will be suggested individually for each student.)
(a) Simulate the sequence of interarrival times. For this
purpose you need first to simulate a sequence of uniformly distributed random
variables (denoted Un) in the interval (0,1). Then, the exponentially
distributed random variables are obtained by using the transform En = -?1 lnUn,
where ? is the parameter of the exponential distribution. The simulated number
of interarrival times is supposed to be not less than
10,000.
(b) Simulate the sequence of service times. It should be
done by the same way as before. You need first to simulate a sequence of
uniformly distributed random variables in the interval (0,1) (denoted by Vn)
and then to use the transform , where ยต is the reciprocal to the expected
service time. The simulated number of service times is supposed to be not less
than 10,000.
(c) On the basis of the two sequences {En} and {Sn} you need
to calculate the sequence of waiting times. For waiting times we have the
recurrence relation:
W1 = 0, Wn+1 = max{0,Wn- En + Sn}.
Here En is the time between the arrivals of the nth and n +
1st customers and Sn is the service time of the nth customer. Hint: We give
some details of the above recurrence relation. The first customer arrives in
the empty system, so its waiting time is set to zero. For the waiting time of
the second customer we have the relation
4 VYACHESLAV M. ABRAMOV AND COLIN ENTICOTT
W2 = max{0,S1 -E1}, which means that the waiting time of the
second customer is zero if the service time of the first customer is shorter
than interarrival time, i.e. second customer arrives in the empty system as
well. Otherwise, the waiting time is the difference between S1 and E1. For the
following calculations of W2, W3 etc. the students are to use the loop.
(d) After calculation of the sequence Wn, estimate the mean
waiting time,
EW, by the formula and variance
W)2 (Here N is the number of variables, say N = 10,000.)
Compare
the estimated value W with the theoretical value EW.
(e) Bonus question 1. Calculate the sequence for the number
of customers in the system:
Q1 = 0, Qn+1 = max{0,Qn + 1 - ?n},
where ?n is the number of served customers between the
arrivals of the nth and n + 1st customers. After calculation of the sequence
Qn, estimate the mean queue length, EQ, by the formula N , and the variance .
Compare the estimated value Q with the theoretical value EQ.
(f) Bonus question 2. On the basis of the calculated values
of Q and W check the validity of the Little’s formula. Estimate the error for
this formula compared to the theoretical result.
(4) Your answer must include source code and/or numerical
procedure. The choice of programming language is not restricted. It can be C,
Matlab or another language or even Microsoft Excel.
(5) Your final report should be 8-10 word processed pages.
This page limit excludes the title page, source code listing and references. No
additional marks will be given for reports that over the specified length. If
the report is more than 50% longer than specified, the total mark will be
decreased by 10% for every excess page in the report.
(6) Provide clear references for any theories, arguments,
claims, diagrams, equations and any related material that you get from
elsewhere.
(7) Each bonus question costs 5 additional marks. However,
the total mark must not exceed 100. That is, if you collected 92 marks for the
Assignment excluding the bonus questions, then your total mark will be 100, but
not 102.
(8) You will then submit a PDF format report in a single
file which includes your student number, name, the report and the references.
The format is A4 with wide margins from the left and right and 10 point sanf
serif font (e.g. Helvetica or Arial).
2. Submission Checklist
Submit an electronic copy of this work by 17:00, Friday,
Week 11 via the Moodle submission system.
Please submit your assignment via Moodle system or it will
not be marked.
The report must be in the PDF format, MS Word will not be
marked.
FIT5011 ASSIGNMENT 5
All files must be named using the convention
MyStudentNumber-5011-2015-Ass1.pdf, where MyStudentNumber is your actual
student number.
Late submission without a good reason agreed in advance of
submission due date will result in a penalty deduction of 10 marks per calendar
day or part thereof. If you believe that your assignment will be delayed
because of circumstances beyond your control such as illness you should apply
for extension before the due date. Medical certificates or certification
supporting your application may be required.
It is an academic requirement that your submitted work be
original. Zero marks will be awarded for the whole submission if there is any
evidence of copying, collaboration, pasting from web sites, or copying from
textbooks. Please ensure all referenced documents are properly cited, as per
Faculty policy on citations.
1. One PDF report as detailed above.
0 comments:
Post a Comment