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:
“The Sage of Toronto ... spent several decades marveling at the numerous freedoms created by a “global village” instantly and effortlessly accessible to all. Villages, unlike towns, have always been ruled by conformism, isolation, petty surveillance, boredom and repetitive malicious gossip about the same families. Which is a precise enough description of the global spectacle’s present vulgarity.”
—Guy Debord (b. 1931)
“The hero is a mind of such balance that no disturbances can shake his will, but pleasantly, and, as it were, merrily, he advances to his own music, alike in frightful alarms and in the tipsy mirth of universal dissoluteness.”
—Ralph Waldo Emerson (1803–1882)