en 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

^ ^a ^b ^c ^d Harrison, P. G. (2003). "Turning back time in Markovian process algebra". Theoretical Computer Science. 290 (3): 1947–2013. doi:10.1016/S0304-3975(02)00375-4.
^ Harrison, P. G. (2006). "Process Algebraic Non-product-forms". Electronic Notes in Theoretical Computer Science. 151 (3): 61–76. doi:10.1016/j.entcs.2006.03.012.
^ Harrison, P. G. (2004). "Reversed processes, product forms and a non-product form". Linear Algebra and Its Applications. 386: 359–381. doi:10.1016/j.laa.2004.02.020.
^ Hillston, J. (2005). "Process Algebras for Quantitative Analysis" (PDF). 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05). pp. 239–248. doi:10.1109/LICS.2005.35. ISBN 0-7695-2266-1. S2CID 1236394.