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 Markov chain with state space S, transition rate from state i to j given by qij and equilibrium distribution given by, the global balance equations are given for every state i in S by
Here 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 the global balance equation is
Read more about this topic: Balance Equation
Famous quotes containing the words global and/or balance:
“Much of what Mr. Wallace calls his global thinking is, no matter how you slice it, still “globaloney.” Mr. Wallace’s warp of sense and his woof of nonsense is very tricky cloth out of which to cut the pattern of a post-war world.”
—Clare Boothe Luce (1903–1987)
“Partisanship should be kept out of the pulpit.... The blindest of partisans are preachers. All politicians expect and find more candor, fairness, and truth in politicians than in partisan preachers. They are not replied to—no chance to reply to them.... The balance wheel of free institutions is free discussion. The pulpit allows no free discussion.”
—Rutherford Birchard Hayes (1822–1893)