(Applied Stochastic Methods) 1st Edition
by Bruno Sericola (Author)
Markov chains are a fundamental
class of stochastic processes. They are widely used to solve problems in
a large number of domains such as operational research, computer
science, communication networks and manufacturing systems. The success
of Markov chains is mainly due to their simplicity of use, the large
number of available theoretical results and the quality of algorithms
developed for the numerical evaluation of many metrics of interest.
The author presents the theory of both discrete-time and continuous-time
homogeneous Markov chains. He carefully examines the explosion
phenomenon, the Kolmogorov equations, the convergence to equilibrium and
the passage time distributions to a state and to a subset of states.
These results are applied to birth-and-death processes. He then proposes
a detailed study of the uniformization technique by means of Banach
algebra. This technique is used for the transient analysis of several
queuing systems.
Contents
1. Discrete-Time Markov Chains
2. Continuous-Time Markov Chains
3. Birth-and-Death Processes
4. Uniformization
5. Queues
About the Authors
Bruno
Sericola is a Senior Research Scientist at Inria Rennes – Bretagne
Atlantique in France. His main research activity is in performance
evaluation of computer and communication systems, dependability analysis
of fault-tolerant systems and stochastic models.
