A set of equations balancing the expected, steady-state flow rates or “probability flux” between each pair of states or entities of a stochastic process (most typically a Markov chain or queueing problem), for example written as:
where πm is the probability that the state is m and q(m, n) is the “flow rate” from states m to n. The states may be broadly interpreted to be multi-dimensional, as in a network of queues, and the entities might be individual service centers or nodes. Contrast this with global balance equations, where the average flow into a single state is equated with the flow out. Markov chains; Networks of queues; Queueing theory.
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© 2001 Kluwer Academic Publishers
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Gass, S.I., Harris, C.M. (2001). DETAILED Balance equations . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_235
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DOI: https://doi.org/10.1007/1-4020-0611-X_235
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