1 / 6

Birth-Death Processes: Modeling and Applications in Population Dynamics

Explore birth-death processes in this lecture, studying population size changes, applications in demography, queueing theory, biology, and more. Learn about pure birth and pure death processes, Poisson processes, and M/M/1 queues.

lalley
Télécharger la présentation

Birth-Death Processes: Modeling and Applications in Population Dynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Al-Imam Mohammad Ibn Saud University CS433Modeling and SimulationLecture 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 = λfor all • A M/M/1 queue is a birth-death process used to describe customers in an infinite queue.

  4. Birth-Death Chain λ0 λ1 λi-1 λi 0 1 i μi μi+1 μ1 • Find the steady state probabilities • Similarly to the previous example, • And we solve and

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

  6. End of Chapter

More Related