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Balance equation : ウィキペディア英語版
Balance equation

In probability theory, a balance equation is an equation that describes the probability flux associated with a Markov chain in and out of states or set of states.
==Global balance==

The global balance equations (also known as full balance equations) are a set of equations that in principle can always be solved to give the equilibrium distribution of a Markov chain (when such a distribution exists).
For a continuous time Markov chain with state space ''S'', transition rate from state ''i'' to ''j'' given by ''q''''ij'' and equilibrium distribution given by \scriptstyle, the global balance equations are given for every state ''i'' in ''S'' by
::\sum_ = \sum_.
Here \pi_i q_ represents the probability flux from state ''i'' to state ''j''. In general it is computationally intractable to solve this system of equations for most queueing models.
For a discrete time Markov chain with transition matrix ''P'' and equilibrium distribution \pi the global balance equation is
::\sum_ = \sum_.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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