## APP MTH 3016 - Random Processes III

### North Terrace Campus - Semester 2 - 2020

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, mean; 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 3016 Random Processes III School of Mathematical Sciences Semester 2 Undergraduate 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 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, mean; 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;
##### Course Staff

Course Coordinator: Dr Andrew Black

##### 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)
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
Teamwork and communication skills
• developed from, with, and via the SGDE
• honed through assessment and practice throughout the program of studies
• encouraged and valued in all aspects of learning
all
• technology savvy
• professional and, where relevant, fully accredited
• forward thinking and well informed
• tested and validated by work based experiences
1,3
Self-awareness and emotional intelligence
• a capacity for self-reflection and a willingness to engage in self-appraisal
• open to objective and constructive feedback from supervisors and peers
• able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
all
• Learning Resources
##### Required Resources
The textbook for the course is Essentials of Stochastic Processes (third edition), Richard Durrett, Springer, 2016. This is avaiable as a ebook from the library.
##### Recommended Resources
Students may wish to consult any of the following books, available in the Library.

Introduction to Probability Models, (currently the 10th edition), Sheldon Ross, Academic Press, 2009
Introduction to Stochastic Models (2nd edition), R. Goodman, Dover Publications, 2006
##### 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). Biweekly 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.

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 80 Tutorials 6 12 Quiz 11 22 Assignment 5 30 Test 2 12 Total 156
##### Learning Activities Summary
Topics

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

Tutorials

Tutorials in Weeks 3, 5, 7, 9, 11 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 Odd weeks 20% Quizzes and Piazza participation Formative and summative Weekly 10% Test 1 Summative Weeks 4-6 15% Test 2 Summative Weeks 8-10 15% Exam Summative Exam period 40%
##### 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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