Extended Differential Aggregations in Process Algebra for Performance and Biology

TL;DR

This paper introduces approximate fluid lumpability for Markovian process algebra, enabling aggregation of heterogeneous processes with minimal error by perturbing parameters, thus simplifying performance and biological models.

Contribution

It presents a novel approach to approximate aggregation in differential equations for process algebra, relaxing symmetry requirements and proving robustness to parameter perturbations.

Findings

Small parameter perturbations lead to similar differential trajectories.

Many heterogeneous processes can be aggregated with negligible errors.

Approximate lumpability broadens the applicability of fluid semantics.

Abstract

We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required perfect symmetry for exact aggregation, we present approximate fluid lumpability, which makes nearby processes perfectly symmetric after a perturbation of their parameters. We prove that small perturbations yield nearby differential trajectories. Numerically, we show that many heterogeneous processes can be aggregated with negligible errors.