Probability II WM-MA-S2-E2-RPII

1. Conception of stochastic process and Markov chain (MC).
2. Discrete time MC: basic definitions; Classification of states according to their mutual communications; classification of states according to asymptotic properties of transition probabilities; ergodic MC; stationary MC.
3. Continuous time MC: basic definitions and properties; systems of Kolmogorov differential equations for homogeneous MC; birth-death processes.
4. Introduction to queueing theory: preliminary (basic definitions); peculiarities of mathematical tools (generation functions, Laplace-Stieltjes transforms); Poisson arrival process and its properties; stationary arrival process; classification of basic queueing systems; stationary mode existence for queueing systems; Little’s formulae.
5. Markov queueing systems: preliminary; queueing system M/M/n/m; queueing system M/M/n/00; transient behavior of queueing system M/M/1/00; system M/M/00; closed Markov queueing system; Markov queueing system with stationary arrival process without aftereffects; one-server Markov queueing system in discrete time.