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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 setup 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 ”heavyduty” 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)....
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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.
 Spring '11
 Zhou

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