BIRTH - DEATH PROCESSES: FUNDAMENTAL PROPERTIES  AND THEIR APPLICATIONS

Nông Quỳnh Vân

doi:10.34238/tnu-jst.13092

BIRTH - DEATH PROCESSES: FUNDAMENTAL PROPERTIES AND THEIR APPLICATIONS

About this article

Received: 20/06/25 Revised: 14/11/25 Published: 18/11/25

Authors

Nong Quynh Van , TNU - University of Education

Abstract

Birth–death processes represent a fundamental class of Markov processes used to model dynamic systems in which states evolve only between adjacent levels via “birth” (an increase by one unit) or “death” (a decrease by one unit) events. This paper presents a systematic overview of birth-death processes, including: (1) the mathematical foundations with precise definitions of transition rates/probabilities; (2) a comprehensive classification based on time structure (discrete/ continuous) and process properties (linear, pure); and (3) multidisciplinary applications spanning from biomedical sciences to engineering and economics. The core focus of the paper lies in two key applications: (i) modeling red blood cell dynamics using the Fokker–Planck equation, illustrating the capacity to describe complex physiological processes; and (ii) analysis of the M/M/∞ queuing system in service environments, demonstrating efficient resource optimization. These examples highlight the strength of birth-death processes in bridging Markov process theory with real-world problems through a mathematically rigorous yet flexible modeling framework.

Keywords

Birth – death processes; Markov processes; Stochastic process; Homogeneous birth death process; Queuing model M/M/∞

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DOI: https://doi.org/10.34238/tnu-jst.13092

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