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:
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)