Postgraduate Course: Simulation (MATH11028)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Simulation is a decision-making tool which enables one to construct a model that replicates the real life behavior of a system on a computer and analyze/design/optimize the system using the result of this model, without actually going through the burden of experimenting with the real system. This course focuses on discrete event simulation and covers random variate generation methods to generate quantities from given probabilistic distributions. The course covers the use of statistical methods to convert available data to the necessary input to simulation models and analyse the output provided by these models as well as variance reduction techniques to apply these statistical methods more efficiently. The techniques learned in this class has very wide applicability, including but not limited to manufacturing and service systems, finance and communication networks. |
| Course description |
This course aims to provide comprehensive instruction on utilizing discrete-event simulation as a tool for analyzing real-world systems. We will begin by delving into the dynamic structure of discrete-event simulations, understanding their suitability for various problems. Subsequently, we will explore techniques for generating random quantities with specified distributions to accurately capture randomness within simulations. Given the reliance of discrete-event simulations on statistical techniques, we will thoroughly examine how statistical methods are employed in both input and output analysis, emphasizing their effective and efficient utilization.Additionally, we will briefly introduce other simulation techniques, such as Monte Carlo and agent-based simulation, to broaden
students' understanding. Throughout the course, we will utilize stateof-the-art simulation software like Simul8, Arena, and Simio, while also covering the coding of discrete-event simulation models in high level programming languages such as Python, C++, and R.
The course outline includes the following topics:
- Discrete-Event Simulation
- Random Number Generation
- Uniform Random Variate Generation
- Non-Uniform Random Number Generation (Inversion Method, Acceptance-Rejection Method, Composition and Convolution Methods, Special Cases)
- Input Analysis
- Output Analysis
- Terminating Simulations
- Comparing Different Systems
- Steady-State Simulations
- Variance Reduction
- Common Random Variates
- Antithetic Variates
- Control Variates
Upon covering these concepts and methods, students will engage extensively in applying them to case studies, serving as the primary assessment for the course.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
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| Academic year 2024/25, Not available to visiting students (SS1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 1.5,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
64 )
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| Assessment (Further Info) |
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %
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| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- ild discrete-event simulation models using a state-of-theart simulation software (e.g. Simul8, Arena or Simio) and simulation packages designed for high-level coding languages (e.g. SimPy for Python, R-simmer)
- Perform statistical analysis to convert available data to simulation input.
- Understand how uniform and non-uniform random generators work and design random variate generation methods for a given distribution.
- Demonstrate awareness of issues regarding the efficient design and analysis of simulation output.
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Reading List
1. Banks Jerry, ed. Discrete-Event System Simulation / Jerry
Banks [and Others]. Fourth edition / International edition.
Pearson Prentice Hall; 2005.
2. Law AM. Simulation Modeling and Analysis. Fifth edition,
International edition / Averill M. Law. McGraw-Hill Education;
2015. |
Additional Information
| Course URL |
http://student.maths.ed.ac.uk |
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
MSc Operational Research and Statistics students only. |
| Keywords | Discrete-event simulation,random variate generation,variance reduction techniques |
Contacts
| Course organiser | Dr Burak Buke
Tel: (0131 6)50 5086
Email: b.buke@ed.ac.uk |
Course secretary | Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk |
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