Reversed compound agent theorem

In probability theory, the reversed compound agent theorem (RCAT) is a set of sufficient conditions for a stochastic process expressed in any formalism to have a product form stationary distribution^[1] (assuming that the process is stationary^[2]^[1]). The theorem shows that product form solutions in Jackson's theorem,^[1] the BCMP theorem^[3] and G-networks are based on the same fundamental mechanisms.^[4]

The theorem identifies a reversed process using Kelly's lemma, from which the stationary distribution can be computed.^[1]

Notes