Local Balance
In some situations, terms on either side of the global balance equations cancel. The global balance equations can then be partitioned to give a set of local balance equations (also known as partial balance equations, independent balance equations or individual balance equations). These balance equations were first considered by Peter Whittle. The resulting equations are somewhere between detailed balance and global balance equations. Any solution to the local balance equations is always a solution to the global balance equations (we can recover the global balance equations by summing the relevant local balance equations), but the converse it not always true. Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms.
During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution, but Gelenbe's G-network model showed this not to be the case.
Read more about this topic: Balance Equation
Famous quotes containing the words local and/or balance:
“America is the world’s living myth. There’s no sense of wrong when you kill an American or blame America for some local disaster. This is our function, to be character types, to embody recurring themes that people can use to comfort themselves, justify themselves and so on. We’re here to accommodate. Whatever people need, we provide. A myth is a useful thing.”
—Don Delillo (b. 1926)
“At last I feel the equal of my parents. Knowing you are going to have a child is like extending yourself in the world, setting up a tent and saying “Here I am, I am important.” Now that I’m going to have a child it’s like the balance is even. My hand is as rich as theirs, maybe for the first time. I am no longer just a child.”
—Anonymous Father. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)