lec19 - Birth and Death Processes Review: What is a...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Birth and Death Processes Review: What is a stochastic process? What is a Poisson Process? Motivation: Birth and Death process ( B + D ) is a generalization of Poisson process, and it provides for modeling of queues, i.e. we assume that arrivals stay some time in the system and leave after that. More motivation: The concept of memoryless property is further formalized by the Markov property. Definition: A B+D process X ( t ) is a stochastic process that monitors the number of people in a system. Remarks: 1. X ( t ) = k , implies that at time t there are k people/objects in the system. 2. X ( t ) is still called the state at time t . X ( t ) is in { , 1 , 2 ,... } for all t . 1 B+D Process: Examples Visualization: ♥ One can visualize the set-up for a B+D process in a state diagram as movements between consecutive states. ♥ Conditional on X ( t ) = k , we either move to state k + 1 or to k- 1 , depending on whether a birth or a death occurs first. ♠ This process sometimes is referred as Random walk, used more in material science, physics, chemistry and biology. Figure 1: State diagram of B+D process 2 B+D Process: Examples (Cont’d) Stat Printer: The ”heavy-duty” printer in the Stats department gets 3 jobs per hour. On average, it takes 15 min to complete printing. The printer queue is monitored for a day (8h total time).queue is monitored for a day (8h total time)....
View Full Document

This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

Page1 / 11

lec19 - Birth and Death Processes Review: What is a...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online