## APP MTH 7056 - Random Processes

### North Terrace Campus - Semester 2 - 2024

This course introduces students to the fundamental concepts of random processes, particularly continuous-time Markov chains, and related structures. These are the essential building blocks of any random system, be it a telecommunications network, a hospital waiting list or a transport system. They also arise in many other environments, where you wish to capture the development of some element of random behaviour over time, such as the state of the surrounding environment. Topics covered are: Continuous-time Markov-chains: definition and basic properties, transient behaviour, the stationary distribution, hitting probabilities and expected hitting times, reversibility; Queueing Networks: Kendall's notation, Jackson networks, Loss Networks: truncated reversible processes, circuit-switched networks, reduced load approximations. Basic Queueing Theory: arrival processes, service time distributions, Little's Law; Point Processes: Poisson process, properties and generalisations; Renewal Processes: preliminaries, renewal function, renewal theory and applications, stationary and delayed renewal processes.

• General Course Information
##### Course Details
Course Code APP MTH 7056 Random Processes Mathematical Sciences Semester 2 Postgraduate Coursework North Terrace Campus 3 Up to 3 hours per week Y (MATHS 1012 and MATHS 2103) or (MATHS 2201 and MATHS 2202) or (MATHS 2106 and MATHS 2107); knowledge of Markov chains, such as would be obtained from MATHS 2103 Ongoing assessment, exam
##### Course Staff

Course Coordinator: Dylan Morris

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
1.     demonstrate understanding of the mathematical basis of continuous-time Markov chains

2.     demonstrate the ability to formulate continuous-time Markov chain models for relevant practical systems

3.     demonstrate the ability to apply the theory developed in the course to problems of an
appropriate level of difficulty

4.     develop an appreciation of the role of random processes in system modelling

5.     demonstrate skills in communicating mathematics orally and in writing

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

University Graduate Attribute Course Learning Outcome(s)

Attribute 1: Deep discipline knowledge and intellectual breadth

Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

all

Attribute 2: Creative and critical thinking, and problem solving

Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

all

Attribute 3: Teamwork and communication skills

Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.

all

Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.

1,3

Attribute 8: Self-awareness and emotional intelligence

Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

all
• Learning Resources
None.
##### Recommended Resources
Students may wish to consult any of the following books, available from the Library as eBooks.

Essentials of Stochastic Processes (third edition), Richard Durrett, Springer, 2016.
Introduction to Probability Models, (currently the 10th edition), Sheldon Ross, Academic Press, 2009
##### Online Learning
All course materials will be made available on MyUni.
• Learning & Teaching Activities
##### Learning & Teaching Modes
Each week's material is presented via a number of sources that complement each other: the textbook, course notes and lecture videos that are posted on MyUni at the beginning of the week. Having studied the material from all sources, students test their initial understanding with an online quiz.

Students deepen their understanding of the material and their skills in applying it by working on tutorial exercises and attending a tutorial (face to face or online). Assignments provide students with further opportunities to practise and get feedback on their work. Students interact with the lecturer and with each other on a MyUni discussion platform. In addition, the lecturer offers weekly consulting and a face to face workshop.

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

 Activity Quantity Workload hours Study of notes, textbook and videos 70 Tutorials 12 24 Quiz 12 Assignments 4 25 Project 25 Total 156
##### Learning Activities Summary
Topics

- Modelling with stochastic processes
- Poisson Processes
- Continuous-time Markov chains
- Renewal theory
- Queuing theory

Tutorials

Weekly tutorials cover the material of the previous few weeks.
• 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
 Component Task type Due Weighting Assignments Formative and summative Start of weeks 4,6,8 and 11 20% Quizzes Formative and summative Weekly 5% Project Summative Week 12 15% Exam Summative Exam period 60%

Note that the project contains additional assessed components for APP MTH 7056.
##### Assessment Related Requirements
An aggregate score of 50% is required to pass the course.
##### Assessment Detail

No information currently available.

##### Submission

No information currently available.

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

M10 (Coursework Mark Scheme)
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
• Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

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