30: Continuous-Time Markov Chains

"It is a mistake to look too far ahead. Only one link in the chain of destiny can be handled at a time." — Winston Churchill.Lecture outline: How to model computer systems/ networks using Markov Models?

1. Solving general CTMCs

Transition rate diagram of a CTMC

Time evolution of a CTMC

Steady-state solution of a CTMC

Transforming a CTMC into a DTMC (uniformization)

2. Solving a birth-death-process

What is a birth-death-process (BDP)?

Poisson process

Transition rate matrix of a BDP

Time evolution of a BDP

Steady state solution of a BDP

General equilibrium solution of a BDP

Primary reference for this lecture:

1. “Performance Modeling of Communication Networks with Markov Chains” by Jeonghoon Mo.

2. “Performance analysis of the IEEE 802.11 distributed coordination function” by G. Bianchi published in IEEE Journal on Selected Areas in Communication (JSAC).