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:
“The local is a shabby thing. There’s nothing worse than bringing us back down to our own little corner, our own territory, the radiant promiscuity of the face to face. A culture which has taken the risk of the universal, must perish by the universal.”
—Jean Baudrillard (b. 1929)
“I am advised that there is an unexpended balance of about $45,000 of the fund appropriated for the relief of the sufferers by flood upon the Mississippi River and its tributaries, and I recommend that authority be given to use this fund to meet the most urgent necessities of the poorer people in Oklahoma.”
—Benjamin Harrison (1833–1901)