Article · Wikipedia archive · Last revised Jun 16, 2026

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. The theorem shows that product form solutions in Jackson's theorem, the BCMP theorem and G-networks are based on the same fundamental mechanisms.

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Jun 16, 2026
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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 distribution1 (assuming that the process is stationary21). The theorem shows that product form solutions in Jackson's theorem,1 the BCMP theorem3 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

Notes

  1. 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.
  2. 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.
  3. 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.
  4. 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.
Further reading

Further reading

  • Bradley, Jeremy T. (28 February 2008). RCAT: From PEPA to product form (PDF) (Technical report DTR07-2). Imperial College Department of Computing. A short introduction to RCAT.