APP MTH 7087 - Applied Mathematics Topic E

North Terrace Campus - Semester 2 - 2014

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/students/honours

  • General Course Information
    Course Details
    Course Code APP MTH 7087
    Course Applied Mathematics Topic E
    Coordinating Unit Applied Mathematics
    Term Semester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Course Description 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/students/honours
    Course Staff

    Course Coordinator: Dr David Green

    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)
    Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4,5,6
    The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 3,5
    An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 3,4,5,6
    A proficiency in the appropriate use of contemporary technologies. 3,4,5
    A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5,6
  • Learning Resources
    Required 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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