In
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
, the reversed compound agent theorem (RCAT) is a set of
sufficient
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ...
conditions for a
stochastic process expressed in any formalism to have a
product form stationary distribution
In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the ...
(assuming that the process is stationary
). The theorem shows that product form solutions in
Jackson's theorem,
the
BCMP theorem In queueing theory, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form equilibrium distribution exists. It is named after the authors of the paper where the network was ...
and
G-network
In queueing theory, a discipline within the mathematical theory of probability, a G-network (generalized queueing network, often called a Gelenbe network) is an open network of G-queues first introduced by Erol Gelenbe as a model for queueing syst ...
s are based on the same fundamental mechanisms.
The theorem identifies a reversed process using
Kelly's lemma In probability theory, Kelly's lemma states that for a stationary continuous-time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process. The theorem is named after Frank Kelly.
...
, from which the stationary distribution can be computed.
Notes
References
*
::A short introduction to RCAT.
Probability theorems
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