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IE3xx : Stochastic Processes & Queueing Systems

Prerequisites topics
IE1xx Probability & Statistics 


Models and techniques to deal with randomness that underlie many industrial and social systems. Emphasis on models, their properties and their applications.

  • Elementary stochastic processes: random walks,
  • Markov chains: first step analysis, state classifications, invariant distributions, Finite state Markov chains, Chapman-Kolmogorov equations, Recurrent Markov Chains, positive & null recurrence, limiting state probabilities, Stationary distributions. 
  • Gambler’s ruin, Random walk, Birth death chain
  • Memory-less property of exponential random variables and related models & examples, Poisson processes. 
  • Queueing systems, Little law, PASTA
  • Introduction to renewal processes, Machine repair problems, replacement problems.


  • Sheldon Ross, Probability Models,10th Edition, Academic Press, 2010
  •  S. M. Ross, Stochastic processes, 2nd Edition, 1996, John Wiley, New York
  • D.P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2002
  • R. W. Wolff, Stochastic modeling and the theory of queues, 1989, Prentice Hall Inc., Engle-woodCliffs
  • Hoel, Port, Stone, Introduction to Stochastic Processes
  • Jean Jacod and Philip Protter, Probability Essentials, Springer, 2004.
  •  James Norris, Markov Chains, CUP, 1998