## APP MTH 7087 - Applied Mathematics Topic E

### North Terrace Campus - Semester 2 - 2017

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au

• General Course Information
##### Course Details
Course Code APP MTH 7087 Applied Mathematics Topic E Mathematical Sciences Semester 2 Postgraduate Coursework North Terrace Campus 3 Y Ongoing assessment 30%, Exam 70%
##### Course Staff

No information currently available.

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
In 2014 the topic of this course will be Matrix Analytic Methods in Stochastic Modelling.

Syllabus

Matrix-analytic methods are popular tools in stochastic modelling because they allow the construction and analysis, in a unified and algorithmically tractable manner, of a wide class of stochastic models. The methods have been applied in various areas, including health, finance and most notably performance analysis of communication systems.

This course presents the basic mathematical ideas and algorithms that are part of the matrix-analytic methods. The approach uses probabilistic arguments to the fullest extent and demonstrates the unity of the argument in the whole theory. It also reveals the stochastic process at work within the computational procedures.

The methods are presented in the framework of quasi-birth-and-death-processes (QBDs), which are Markov processes in two dimensions known as level and phase. The restriction to QBDs, which are processses that do not jump across several levels in any single transition, does not unduly limit the analysis, as the theory for more general classes of models such as the GI/M/1 and M/G/1-type Markov chains can be deduced from the QBD analysis.

Learning Outcomes

1. Understand the Phase-type distribution as a matrix generalisation of the exponential distribution and hence the Phase-type renewal process as the matrix generalisation of the Poisson process.
2. Understand the ideas of the Phase-type distribution and extension to the Markovian Arrival process and it's versatility in both discrete and continuous cases.
3. Recognise and understand the use of the Quasi-Birth-and-Death-Process (QBDs) and the structure of the stationary distribution.
4. Be able to understand and use probabilitic reasoning to explain and develop the algorithms used in the Matrix Analytic methodology for QBDs.
5. Be able to use the QBD to model real processes and establish performance measures of interest.
6. Understand how the more general GI/M/1 and M/G/1-type Markov chains may be viewed as special cases of QBDs.
##### University Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Deep discipline knowledge
• informed and infused by cutting edge research, scaffolded throughout their program of studies
• acquired from personal interaction with research active educators, from year 1
• accredited or validated against national or international standards (for relevant programs)
all
Critical thinking and problem solving
• steeped in research methods and rigor
• based on empirical evidence and the scientific approach to knowledge development
• demonstrated through appropriate and relevant assessment
all
• Learning Resources
None.
##### Recommended Resources
1. G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Models, ASA-SIAM Series on Statistics and Applied Probability, 1999.

2. Marcel F. Neuts, Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Dover Publications, 1981.
##### Online Learning
This course uses MyUni for providing electronic resources, such as assignments and handouts, and for making course announcements. It is recommended that students make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/
• Learning & Teaching Activities
##### Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Written assignments supplement the lectures by providing example problems to enhance the understanding obtained through lectures and provides assessment opportunities for students to gauge their progress and understanding.

##### Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload hours Lectures 30 90 Assignments 5 60 Total 150
##### Learning Activities Summary
Lecture outline

Introduction to Matrix Analytic Methods and example applications (2 Lectures).

Revision of Basic Probability, Discrete-time Markov chains, and Continuous-time Markov Chains (5 Lectures).

Phase-type distributions, renewal processes and Markovian Arrival Processes (10 Lectures).

The birth-and-death-process and Quasi-Birth-and-Death-process and the structure and derivation of the stationary distribution and other performance measures (13 Lectures).

The GI/M/1 and M/G/1-type Markov chains as QBDs (2 Lectures).

Summary (1 Lecture).
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Assessment task Task type When due Weighting Learning outcomes Examination Summative Examination period 70% All Assignments Formative and summative Weeks 3, 5, 7, 9 and 11 30% All

##### Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
##### Assessment Detail

No information currently available.

##### Submission
All written assignments are to be submitted to the lecturer with a signed cover sheet attached. There will be a maximum two week turn-around time on assignments for feedback to students.

Late assignments will not be accepted, but students may be excused from an assignment for medical or compassionate reasons. In such cases, documentation is required and the lecturer must be notified as soon as possible before the fact.
##### Course Grading

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
Grade Mark Description
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

• Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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