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IE 618: Advanced Stochastic Processes for Operations Research

Prerequisites: IE 611 or equivalent and Instructor's consent.

Course contents

  1. Construction of Probability Measure, Integration, Convergence theorems, Law of large numbers and Central limit theorem. Lp spaces and Conditional expectation.

  2. Martingales : Super and Sub martingales, Doob's inequalities, Martingale convergence theorems.

  3. Analysis of M/G/1 and GI/M/1 queues. Derivation of Little's law and PASTA.

  4. Markov chains and stability (general state space, e.g., Rn): Introduction, \psi-irreducibility, Small sets, Transience and Recurrence. Drift criterion, SLLN, CLT.

  5. Random Walk Models, Analysis of G/G/1 queues using Ladder chains.


  • Jean Jacod, Philip E. Protter, 'Probability Essentials', Springer, 2003.

  • Sean Meyn and Richard L. Tweedie, 'Markov Chains and Stochastic Stability', Springer-Verlag London Ltd, 1993.

  • P. Billingsley, 'Probability and Measure', third ed., Wiley-Interscience, New York, 1995.

  • R. W. Wolff, 'Stochastic modelling and the theory of queues', Prentice Hall Inc., Englewood Cliffs, 1989.

  • Relevant Research papers.