Reversed compound agent theorem explained

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]). The theorem shows that product form solutions in Jackson's theorem, 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.

Further reading

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

Notes and References

1. Harrison . P. G. . Peter G. Harrison. Turning back time in Markovian process algebra . 10.1016/S0304-3975(02)00375-4 . Theoretical Computer Science . 290 . 3 . 1947–2013 . 2003 . free .
2. Harrison . P. G. . Peter G. Harrison. Process Algebraic Non-product-forms . 10.1016/j.entcs.2006.03.012 . Electronic Notes in Theoretical Computer Science . 151 . 3 . 61–76 . 2006 . free .
3. Harrison . P. G. . Peter G. Harrison. 10.1016/j.laa.2004.02.020 . Reversed processes, product forms and a non-product form . Linear Algebra and Its Applications . 386 . 359–381. 2004 .
4. Book: Hillston . J. . Jane Hillston. Process Algebras for Quantitative Analysis . 10.1109/LICS.2005.35 . 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05) . 239–248 . 2005 . 0-7695-2266-1 . 1236394 . http://www.dcs.ed.ac.uk/pepa/quantitativeanalysis.pdf.