birth-death process


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birth-death process

[¦bərth ¦deth ‚prä‚səs]
(industrial engineering)
A simple queuing model in which units to be served arrive (birth) and depart (death) in a completely random manner.
(statistics)
A method for describing the size of a population in which the population increases or decreases by one unit or remains constant over short time periods.
References in periodicals archive ?
Furthermore, motivated from our previous work with the spatial Cox process application in [10], we elected to incorporate the birth-death process to statistically determine the number of clusters.
Sampling parameter estimates from their posterior distributions can be achieved via Gibbs sampler, in which the statistical inference on the number of clusters is modeled using the birth-death process. The birth-death process is one type of continuous-time Markov chain originally introduced in [13].
A stochastic birth-death process models the size of a single population, altered by events in which the size either increases by one or decreases by one.
Trajectories of this system do not correspond to realizations of the stochastic birth-death process but rather trace out curves along the surface of u versus x and t, which can be used to analyze the behavior of u over time.
It is easy to be proved that {N(t),t [greater than or equal to] 0} is birth-death process [12-16].
If the number of data packets C1 is i and the number of data packets C2 is j, it is easy to prove that {N(t), t [greater than or equal to] 0} is the birth-death process [12-16].
Stochastic threats to persistence include demographic stochasticity (i.e., probabilistic birth-death process), environmental stochasticity (i.e., climatic variability), genetic stochasticity (e.g., genetic drift and inbreeding), and environmental catastrophes (e.g.
On the assumption that the underlying reality is a continuous-time, birth-death process with constant parameters [Lambda] and [Mu], the probability that a lineage that arose at time t in the past has some descendants today is the same as the probability that a birth-death process has not gone extinct at a time T - t after its origin.
The [z.sub.i] are known for both a constant birth-death process (Kendall 1948a) and a process in which birth and death rates vary through time (Kendall 1948b), the former being a special case of the latter, of course.
[10] Kyriakidis, E.G., 1994, "Stationary probabilities for a simple immigration birth-death process under the influence of total catastrophes," Stat.
al [7] obtained the transient analysis of immigration birth-death processes with total catastrophe.
of Budapest, this reference discusses such research topics as hardware and software models for system analysis and architecture, stochastic petri nets and quasy birth-death processes. Tutorials are also provided for simulation and hypothesis testing for model checking and petri net analysis using decision diagrams.