eprintid: 2731
rev_number: 5
eprint_status: archive
userid: 69
dir: disk0/00/00/27/31
datestamp: 2015-07-24 12:54:54
lastmod: 2015-07-24 12:54:54
status_changed: 2015-07-24 12:54:54
type: article
metadata_visibility: show
creators_name: Tschaikowski, Max
creators_name: Tribastone, Mirco
creators_id: max.tschaikowski@imtlucca.it
creators_id: mirco.tribastone@imtlucca.it
title: A unified framework for differential aggregations in Markovian process algebra
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Markovian process algebra, Fluid semantics, Lumpability
abstract: Fluid semantics for Markovian process algebra have recently emerged as a computationally attractive approximate way of reasoning about the behaviour of stochastic models of large-scale systems. This interpretation is particularly convenient when sequential components characterised by small local state spaces are present in many independent copies. While the traditional Markovian interpretation causes state-space explosion, fluid semantics is independent from the multiplicities of the sequential components present in the model, just associating a single ordinary differential equation (ODE) with each local state. In this paper we analyse the case of a process algebra model inducing a large ODE system. Previous work, known as exact fluid lumpability, requires two symmetries: ODE aggregation is possible for processes that i) are isomorphic and that ii) are present with the same multiplicities. We first relax the latter requirement by introducing the notion of ordinary fluid lumpability, which yields an ODE system where the sum of the aggregated variables is preserved exactly. Then, we consider approximate variants of both notions of lumpability which make nearby processes symmetric after a perturbation of their parameters. We prove that small perturbations yield nearby differential trajectories. We carry out our study in the context of a process algebra that unifies two synchronisation semantics that are well studied in the literature, useful for the modelling of computer systems and chemical networks, respectively. In both cases, we provide numerical evidence which shows that, in practice, many heterogeneous processes can be aggregated with negligible errors.
date: 2015-03
date_type: published
publication: Journal of Logical and Algebraic Methods in Programming
volume: 84
number: 2
publisher: Elsevier
pagerange: 238-258
id_number: 10.1016/j.jlamp.2014.10.004
refereed: TRUE
issn: 2352-2216
official_url: http://www.sciencedirect.com/science/article/pii/S2352220814000741
citation:   Tschaikowski, Max and Tribastone, Mirco  A unified framework for differential aggregations in Markovian process algebra.  Journal of Logical and Algebraic Methods in Programming, 84 (2).  pp. 238-258.  ISSN 2352-2216      (2015)