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Content archived on 2024-04-19

Quantitative Modelling In Parallel Systems


A key initial objective is the design of timed stochastic formalisms which are amenable to a mathematical treatment leading to efficiently implementable algorithms. This first objective is mainly of a theoretical nature; it involves fundamental research in theoretical computer science, stochastic processes, discrete event simulation, and various aspects of control.

The long term aim is the design of software prototypes admitting a description of the algorithms and the architecture as an input and providing the basic performance characteristics of the system as an output. The implications of these methods to scheduling and load balancing will only be investigated at the end of the project.
The research describes, predicts and optimizes the dynamic, time dependent behaviour of parallel and distributed systems using quantitative modelling. The foundation of a methodology is developed for the performance evaluation of these systems based on general formalisms stemming from theoretical computer science.

Progress has been made in the following areas:
analysis of a class of 2-dimensional random walks on the lattice and of tandem queues for modelling a sequence of multiplexers;
methodological contributions on stochastic scheduling using Markov decision process (MDP);
analytical results on G-networks which represent adequately semaphores, or online work assignment in distributed environments;
load balancing algorithms based on adaptive control techniques;
development of a probabilistic, timed calculus of communicating systems (CCS) which provides a formalism for discrete event simulation with a rigorous semantics of the type already defined for standard CCS;
collaboration on G-networks and on cache coherency;
new stability properties of general Petri networks;
work on a performance modelling environment based on several of the formalisms;
new results on parallel simulation;
collaboration on product forms in Petri nets;
elaboration of the modularly composed multiprocessor example for the comparison of formalisms;
definition of an Extended Markovian Process Algebra (EMPA) involving exponential and immediate transitions;
elaboration of structural operational semantics (SOS);
development of a spectral expansion method for the solution of MDPs whose state space is a 2-dimensional semiinfinite strip;
work on the reliability of multiprocessor systems;
generalization to P/T Petri net structures of the linear programming technique;
preliminary results for symmetric coloured nets;
application of Courtois-Semal method to SWNs;
new approximation algorithms and simulation methods for TPNs.

Work Package 1 is concerned with research and evaluation studies of the various formalisms.

Queueing models offer a semiformal representation of discrete event systems with stochastic timing together with (some) functional information. They are one of the most prominent classes of models because of their vast analytical tractability.

Structural analysis is a well known qualitative analysis technique for Petri nets. Research on this formalism primarily focuses on the stochastic case using colored nets and the (max,+) approach.

A salient intention of Process Algebras is the support of (functional) constructivity: there is a design methodology which systematically allows one to build complex systems from smaller ones. Research on this aspect bears on the timed case.

Work Package 2 focuses on various types of applied mathematics and discrete event simulation techniques that allow one to capture the quantitative behaviour of these systems, once they have been described in one of the formalisms of WP 1.

Work Package 3 concerns the design of modelling software based on the formalisms and the solution methods of WP 1 and WP 2 and allowing one to predict the performance and to optimise the execution of given parallel algorithms executing on various architectures.


Most of the partners already have extensive industrial collaboration in the field of performance evaluation. Thus, the project will also serve industrial groups that use performance to keep up with the recent initiatives in this direction in the US. We will transfer to industry methods of performance analysis in general, and novel techniques developed within QMIPS in particular. The solution methods developed will lead to readily usable algorithms and to software prototypes. In particular, WP2 will result in an improved version of GREATSPN and on the realisation of a new prototype for the simulation and the analysis of certain stochastic Petri-nets called MAGMAS, and the completion of WP 3. will result in an enriched version of the software tool ARCHISSIME, based on the formalism of task graphs.


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Institut National de Recherches en Informatique et en Automatique (INRIA)
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Domaine de Voluceau Rocquencourt
78153 Le Chesnay

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Participants (6)