MOC6163 Capacity Analysis and Reliability

1 Brief description of aims and content

 The course focuses on modelling and analysing communication networks, network protocols and applications, using mathematical tools. Special emphasis is put on the construction of tractable models of complex networking problems and attack performance problems with analytical methods or simulation.

The course is primarily focused on stationary random processes from a probability point of view, analysed both in the time- and the frequency domain.It addresses performance issues in current and future Internet architectures. Applications include multi-access communication schemes (CSMA) and reservation techniques (token and polling) for packet radio networks (WLANs); routing in data networks (shortest path routing, optimal routing and topology design); flow control (TCP); quality of service (QoS) in IP networks requirements for multimedia transmission and network support: scheduling, shaping, forward error correction.

2  Learning Outcomes

A. Knowledge and Understanding

 At the end of the programme students should be able to demonstrate knowledge and understanding of

1.The performance issues in current and future Internet architectures and packet radio networks. (A4)

2. The techniques needed to analyze algorithms and computer systems. (A2)

B. Cognitive/ Intellectual Skills/ Application of Knowledge

 At the end of the programme students should be able to:

1.  To construct tractable models of complex networking problems and attack performance problems with analytical methods or simulation. (B3)

2.  Describe how a problem involving random processes can be identified and solved. (B2)

C. Communication/ICT/Numeracy/Analytic Techniques/Practical Skills

At the end of the programme students should be able to:

1. Discuss and apply computation methods for random processes in linear systems. (C5)

2. Know the most important applications of random processes, especially in electrical engineering, mechanics and economy. (C8)

D. General transferable skills

At the end of the programme students should be able to:

1. Have the capacity to analyse and solve problems related to specific technologies and the success or failure of new trends. (D7)

2.Use the usual English vocabulary concerning random processes(D6)

3  Indicative Content

        i.            Probability &Combinatorics:

Provides the fundamental concepts of set-based probability and the probability axioms. Conditional probability and independence are stressed, as are the laws of total probability and Bayes’ rule. Introduces combinatorics (the art of counting) which is so important for the correct evaluation of probabilities.

        i.            Random variables and distribution functions:

Introduces the concepts of random variables and distribution functions including functions of a random variable and conditioned random variables. Joint and conditional distributions are treated with expectations and higher moments.

      ii.            Discrete and continuous distribution functions

Discrete distribution functions as well as their continuous counterparts, continuous distribution functions, are discussed in this unit. Particular attention is paid to phase-type distributions due to the important role they play in modeling scenarios and the chapter also includes a section on fitting phase-type distributions to given means and variances.

      iii.            Discrete- and Continuous-Time Markov Chains

Contains theoretical aspects of Markov chains, and their numerical solution. The basic concepts of discrete and continuous-time Markov chains and their underlying equations and properties are discussed. Special attention is paid to irreducible Markov chains and to the potential, fundamental, and reachability matrices in reducible Markov chains. It also contains sections on random walk problems and their applications, the property of reversibility in Markov chains, and renewal processes.

      iv.            Numerical solution of Markov Chains

It deals with numerical solutions, from Gaussian elimination and basic iterative-type methods for stationary solutions to ordinary differential equation solvers for transient solutions. Block methods and iterative aggregation-disaggregation methods for nearly completely decomposable Markov chains are considered.

      v.            Elementary queueing:

Introduction to the basic terminology and definitions is followed by an analysis of the simplest of all queueing models, the M/M/1 queue. This is then generalized to birth-death processes, which are queueing systems in which the underlying Markov chain matrix is tridiagonal. It deals with queues in which the arrival process need no longer be Poisson and the service time need not be exponentially distributed. Instead, interarrival times and service times can be represented by phase-type distributions and the underlying Markov chain is now block tridiagonal.

    vi.            The M/G/1 and G/M/1 Queues

Presents the M/G/1 and G/M/1 queues. The approach used is that of the embedded Markov chain. The Pollaczek-Khintchine mean value and transform equations are derived and a detailed discussion of residual time and busy period follows. A thorough discussion of nonpreemptive and preempt-resume scheduling policies as well as shortest- processing-time-first scheduling is presented. An analysis is also provided for the case in which only a limited number of customers can be accommodated in both the M/G/1 and G/M/1 queues.

4 Learning and Teaching Strategy

 A course handbook will be provided in advance and this will contain in depth information relating to the course content. This will give an opportunity to the students to prepare the course. The lecture materials will be posted on the web page that will also contain comprehensive web links for further relevant information. The module will be delivered through lectures, tutorial/practice sessions and group discussions. In addition to the taught element, students will be expected to undertake a range of self-directed learning activities.

By the end of the course students will be able to construct tractable models of complex networking problems and attack performance problems with analytical methods or simulation. These abilities are necessary for everyone working on technical fields - to understand the capabilities of specific technologies and the success or failure of new trends.

5 Assessment Strategy

 100% based on individual assessment.

As this is a Theoretical and Practical module: The Final assessment shall include 50% of continuous and 50% of End of Module assessment.

The assessments shall be made 50% each for practical and theoretical aspects.

For Example:

one quiz (5%), one/two practical assignment (10%), one mini project for presentation (10%), one tutorial session (5%), short practical test (10%) and a short written test (10%) followed by final assessment (50%) of End of Module Examination divided equally into practical viva-voce and theoretical examination.

6 Assessment Criteria:

For the assignment, criteria will be drawn up appropriate to the topic, based on the learning outcomes.