Review of probability, random variables and distributions, generating functions and transforms.

Stochastic processes, discrete and continuous-time Markov chains, renewal processes, Brownian motion.

Characteristics of queueing systems, Little's formula, Markovian and non-Markovian queueing systems, embedded Markov chain applications to M/G/1, G/M/1, and related queueing systems, queues with vacations, priority queues, queues with modulated arrival process, discrete-time queues, and matrix-geometric methods in queues.

Networks of queues, open and closed queueing networks, algorithms to compute the performance metrics.

Simulation of queues and queueing networks.

Application to manufacturing, computer and communication systems and networks.

Texts and References:
1. L. Kleinrock, Queueing Systems, Vol. 1: Theory, 1975, Vol. 2: Computer Applications, 1976, John Wiley and Sons.
2. J. Medhi, Stochastic Models in Queueing Theory, 2nd Edition, Academic Press, 2002.
3. S. Asmussen, Applied Probability and Queues, 2nd Edition, Springer, 2003.
4. D. Gross, and C.Harris, Fundamentals of Queueing Theory, 3rd Edition, John Wiley and Sons, 1998.
5. R.B. Cooper, Introduction to Queueing Theory, 2nd Edition, North-Holland, 1981.
6. R. Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modelling, Springer-Verlag, 1995.
7. E. Gelenbe, and G. Pujolle, Introduction to Queueing Networks, 2nd Edition, John Wiley, 1998.
8. S.M. Ross, Stochastic Processes, 2nd Edn., John Wiley, 1995.