1. Al-Imam Mohammad Ibn Saud University
CS433 Modeling and Simulation Lecture 11
Birth-Death Process
Dr. Anis Koubâa
02 May 2009

2. Birth-Death Chain
The birth-death process is a special case of Continuous-time Markov process where the states represent the current size of a population and where the transitions are limited to births and deaths.
Birth-death processes have many application in demography, queueing theory, or in biology, for example to study the evolution of bacteria.

3. Birth-Death Chain
A pure birth process is a birth-death process where μi = 0 for all i≥0
A pure death process is a birth-death process where λi = 0 for all i≥0
A (homogeneous) Poisson process is a pure birth process where λi = λ for all
A M/M/1 queue is a birth-death process used to describe customers in an infinite queue.

4. Birth-Death Chain 1 i λ0 λ1 λi-1 λi μ1 μi μi+11 i λ1
λi-1 λi μ1 μi
μi+1
Find the steady state probabilities
Similarly to the previous example,
And we solve
and

5. Example The solution is obtained In general Making the sum equal to 1
Solution exists if

6. End of Chapter