## OMA357 Syllabus - Queuing And Reliability Modelling - 2021 Regulation - Open Elective | Anna University

OMA357

QUEUEING AND RELIABILITY MODELLING

L T P C

3003

OBJECTIVES:
• To provide necessary basic concepts in probability and random processes for applications such as random signals, linear systems in communication engineering.
• To understand the concept of queueing models and apply in engineering.
• To provide the required mathematical support in real life problems and develop probabilistic models which can be used in several areas of science and engineering.
• To study the system reliability and hazard function for series and parallel systems.
• To implement Markovian Techniques for availability and maintainability which opens up new avenues for research.

UNIT I

RANDOM PROCESSES

9

Classification – Stationary process – Markov process - Poisson process – Discrete parameter Markov chain – Chapman Kolmogorov equations – Limiting distributions.

UNIT II

MARKOVIAN QUEUEING MODELS

9

Markovian queues – Birth and death processes – Single and multiple server queueing models – Little’s formula - Queues with finite waiting rooms.

UNIT III

9

M/G/1 queue – Pollaczek Khinchin formula - M/D/1 and M/EK/1 as special cases – Series queues – Open Jackson networks.

UNIT IV

SYSTEM RELIABILITY

9

Reliability and hazard functions- Exponential, Normal, Weibull and Gamma failure distribution – Time - dependent hazard models – Reliability of Series and Parallel Systems.

UNIT V

MAINTAINABILITY AND AVAILABILITY

9

Maintainability and Availability functions – Frequency of failures – Two Unit parallel system with repair – k out of m systems.

TOTAL: 45 PERIODS

OUTCOMES: Upon successful completion of the course, students should be able to:
• Enable the students to apply the concept of random processes in engineering disciplines.
• Students acquire skills in analyzing various queueing models.
• Students can understand and characterize phenomenon which evolve with respect to time in a probabilistic manner.
• Students can analyze reliability of the systems for various probability distributions.
• Students can be able to formulate problems using the maintainability and availability analyses by using theoretical approach.

TEXT BOOKS:
1. Shortle J.F, Gross D, Thompson J.M,Harris C.M., “Fundamentals of Queueing Theory”, John Wiley and Sons, New York,2018.
2. Balagurusamy E., “Reliability Engineering”, Tata McGraw Hill Publishing Company Ltd., New Delhi,2010.

REFERENCES:
1. Medhi J, ”Stochastic models of Queueing Theory”, Academic Press, Elsevier, Amsterdam, 2003.
2. Taha, H.A., "Operations Research", 9th Edition, Pearson India Education Services, Delhi, 2016.
3. Trivedi, K.S., "Probability and Statistics with Reliability, Queueing and Computer Science Applications", 2nd Edition, John Wiley and Sons, 2002.
4. Govil A.K., “Reliability Engineering”, Tata-McGraw Hill Publishing Company Ltd., New Delhi,1983.