Course

Unit I

Basic structure of queueing models, Examples of real queueing systems, Role of Exponential distribution, Birth-Death processes, Queueing models based on birth –death processes- M/M/1, M/M/s, M/M/1/K, M/M/s/K

Unit II

Queueing models involving non exponential distribution,- M/G/1, G/M/1, M/D/1,M/Ek/1, M/Ek/s, Priority discipline queueing models and Queueing networks.

Unit III

Application of Queueing Theory, Examples, Decision making, formulation of waiting cost functions, Decision models

Unit IV

Inventory concept – Components of Inventory model, Deterministic continuous review models, EOQ formula, EOQ models with shortages, EOQ models with quantity discount, Deterministic periodic review models,

Unit V

Stochastic continuous review models, stochastic single period model for perishable products, stochastic multi-period models, Stochastic periodic review model, inventory systems in practice, Supply chain management.

CO1: Understand the principle concept of Continuous time Markov Chains.
CO2: Work with various distributions such as the negative exponential distribution and Erlang distribution.
CO3: Understand Markovian queues and their solutions
CO4: Apply Markov Chains to general queues, such as M/G/1 and GI/M/1.
CO5: Understand, model and analyze simple deterministic and stochastic inventory control systems.
CO6: Undertake simple cost analyses relating to the above models.

Textbooks/ References

• Frederick S Hiller and Gerald J Liberman, Introduction to operations research, 7th edition, McGraw-Hill series, 2001.
• Gross D. and Harris C. M, John,“Fundamentals of Queuing Theory”, Third Edition, Wiley & Sons Inc, 2004.

Reference Books:

1. J. Medhi, “Stochastic Models in Queuing Theory”, Second Edition, Academic Press, Elsevier, 2003.
2. D. Bartman and M. J. Beckmann, Inventory Control-Models and Methods, Springer Verlag, 1992
3. Ravindran , Phillips and Solberg, Operations research Principles and Practice, 2nd Edition, John Wiley & Sons