This work is licensed under the Creative Commons Attribution License. Differential Ordinary Lumpability in Markovian Process Algebra

In Markovian process algebra, fluid semantics interpret a term with a system of coupled ordinary differ-ential equations (ODEs). This has proven useful in approximating the stochastic behaviour of models consisting of groups of many independent replicas of sequential components characterised by small local state spaces. The size of the underlying continuous-time Markov chain (CTMC) is well known to be at worst exponential in the population of such components. Instead, the fluid semantics defines a single ODE for each local state, independently from the multiplicities. The solution to each ODE estimates the time-course evolution of average population of components in that state (e.g., [6, 3, 9]). We are developing a theory of aggregation for ODE systems induced by a process algebra with fluid semantics [7]. To illustrate and put in context our contribution, let us draw a parallel with established results of aggregation of CTMCs obtained from a Markovian semantics (e.g., [2, 5, 4]). This has involved finding suitable process algebraic behavioural relations that induce a partition of the CTMC state space which satisfies the property of ordinary lumpability [8, 1]: a smaller CTMC can be constructed where each state (a macro-state) is the representative of the states in a partition block; the probability of being in a macro-state is equal to the sum of the probabilities of being in the block’s states