This work has three important purposes: first it is the study of Markov Chains, second to show that chains have different applications and finally model a process this behaves. Throughout we will describe what chain is, these processes are for how classified. We Chain, analyze primary elements make up chain, among others.

we propose to use a mathematical method based on stochastic comparisons of markov chains in order to derive performance indice bounds‎. ‎the main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (fcfs) orbit and general retrial times using the stochastic ordering techniques‎.

1 Markov chains and Markov processes 4 1.1 Discrete-time Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Continuous-time Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 General definitions for Markov processes . . . . . . . . . . . . . . . . . . . . 10 1.4 Poisson processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 H...

I Markov Chains and Stochastic Sampling 2 1 Markov Chains and Random Walks on Graphs . . . . . . . . . . . 2 1.1 Structure of Finite Markov Chains . . . . . . . . . . . . . 2 1.2 Existence and Uniqueness of Stationary Distribution . . . 10 1.3 Convergence of Regular Markov Chains . . . . . . . . . . 14 1.4 Transient Behaviour of General Chains . . . . . . . . . . 17 1.5 Reversible Markov Chains...

[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...