Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with ...

A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...

We supply some relations that establish intertwining from duality and give a probabilistic interpretation. This is carried out in the context of discrete Markov chains, fixing up the background of ...