probability theory Probability theory or probability calculus 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 expre ...

, 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 In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Sto ...

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 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 continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an expon ...

, from which the stationary distribution can be computed.

Notes

Further reading