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Birth–death process

The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one. It was introduced by William Feller. The model's name comes from a common application, the use of such…

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Overview

Definition

Recurrence and transience

Stationary solution

Examples of birth-death processes

Use in phylodynamics

Use in queueing theory

Equilibrium

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Birth–death process

Nodes50
Edges49
Triples17
Avg. degree1.96
Density0.04
Components1

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Birth–death process

Top relations

related to Use in queueing theory · 7
Birth–death process → Despite, FIFO, In, Kendall's, M/M/C/K, Poisson, This
related to M/M/1 queue · 4
Birth–death process → In, M/M/1, The, The M/M/1
related to Use in phylodynamics · 4
Birth–death process → Birth, Notably, The, While
is a · 1
Birth–death process → most fundamental example of a queueing model
see also · 1
Birth–death process → Erlang

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Important terminology

displaystyle process birth death queue time processes queueing population birth-and-death equations state system transitions recurrence transience theory lambda mu differential

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Birth–death processis amost fundamental example of a queueing model0.90text
Birth–death processrelated to M/M/1 queueThe M/M/10.60section
Birth–death processrelated to M/M/1 queueIn0.60section
Birth–death processrelated to M/M/1 queueThe0.60section
Birth–death processrelated to M/M/1 queueM/M/10.60section
Birth–death processrelated to Use in phylodynamicsBirth0.60section
Birth–death processrelated to Use in phylodynamicsNotably0.60section
Birth–death processrelated to Use in phylodynamicsThe0.60section
Birth–death processrelated to Use in phylodynamicsWhile0.60section
Birth–death processrelated to Use in queueing theoryIn0.60section
Birth–death processrelated to Use in queueing theoryM/M/C/K0.60section
Birth–death processrelated to Use in queueing theoryFIFO0.60section

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