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 poet’s eye, in a fine frenzy rolling,
Doth glance from heaven to earth, from earth to heaven;
And as imagination bodies forth
The forms of things unknown, the poet’s pen
Turns them to shapes, and gives to airy nothing
A local habitation and a name.”
—William Shakespeare (1564–1616)
“Any balance we achieve between adult and parental identities, between children’s and our own needs, works only for a time—because, as one father says, “It’s a new ball game just about every week.” So we are always in the process of learning to be parents.”
—Joan Sheingold Ditzion, Dennie, and Palmer Wolf. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 2 (1978)