Turning back time in Markovian process algebra

Analysis of stochastic Petri nets with signals

“…Several examples of nets, with or without rate-dependent product-form conditions, have been presented to support these claims. We derived the product-form solutions by means of RCAT [28] and the strength of this approach is twofold. First, we do not need to work with complicated systems of global balance equations, as most other approaches do.…”

“…For these states the ERCAT Condition 2 is trivially satisfied since P (k,0)→ = A (k,0)← = P (k,k)→ = A (k,k)← = L. In fact, every passive action and every reversed action corresponding to an active action are always enabled, so that for these states the original RCAT structural conditions are satisfied [28].…”

“…Then RCAT's conditions apply to irreducible subsets of the composition (the third condition holds by Lemma 1), which thereby has product-form [28].…”

Product-Form in G-Networks

“…However, the most interesting aspect of this approach is that the product-form of G-networks can be studied modularly, that is, by considering the isolated components instead of the whole queueing network. In this paper, we apply RCAT introduced by Harrison in [46] and then extended in [49,58] which gives a process algebraic characterization of a class of product-form models that includes the quasi-reversible queues [9,52]. In this way, the process algebraic modular description of the components is projected to the modular product-form analysis of the G-networks.…”

“…In this survey we focus on the analysis of the product-form in G-networks, starting from the original model proposed by Gelenbe in 1989 [19] and then showing how (and why) more recent behaviors maintain the product-form property. We explore the connections between the product-form characterizations such as the quasi reversibility [52] and its extended formulation [9], the Reversed Compound Agent Theorem (RCAT) [46,49]. This paper is structured as follows.…”