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Equilibrium Distributions for an Open Migration Process
Journal of Applied Probability
Vol. 5, No. 3 (Dec., 1968), pp. 567-571
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3211921
Page Count: 5
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We consider a system of colonies in which migration, immigration and emigration take place according to a fairly general rule. Necessary and sufficient conditions for equilibrium are given in the theorem of Section (3). The equilibrium distribution of colony numbers is determined by Equations (7) and (9); the colony sizes are thus statistically independent in equilibrium. Attention is also paid to the case where one colony becomes a "bottleneck" to circulation, when equilibrium changes character.
Journal of Applied Probability © 1968 Applied Probability Trust