Pathway Analysis for IMC

We present the ongoing work on the pathway analysis of a stochastic calculus. Firstly we present a particular stochastic calculus that we have chosen for our modeling the Interactive Markov Chains calculus, IMC for short. After that we specify a few restrictions that we have introduced into the syntax of IMC in order to make our analysis feasible. Finally we describe the analysis itself together with several theoretical results that we have proved for it. The IMC calculus has been introduced by Holger Hermanns in the 90’s as an orthogonal extension of Continuous Time Markov Chains (CTMC) and a process algebra (see [BH01]). We have adopted the syntax of IMC with a few minor changes (see Table 1). Small Latin letters denote actions that IMC processes are able to execute, capital Latin letters indicate process identifiers and Greek letters correspond to positive real numbers standing for delays during which IMC processes are stuck, i.e. do nothing. Delay durations are not fixed but are exponentially distributed with rates equal to the corresponding numbers. If the rate of some delay is equal to λ, then it’s average duration will be 1/λ and it’s variation 1/λ. One difference with respect to [BH01] is that all summands in the sum construct are ”guarded” either by actions or delay rates (see rule (2) in the Table 1). This is why we use the name guarded IMC or IMC. Another difference is that all actions and delay rates are decorated with labels from a predefined label set. Labels do not have any semantic meaning but are useful for our analysis.