Einladung zum

Oberseminar Methoden und Theorie der Software-Entwicklung

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Datum und Zeit: Dienstag, 19. April 2011 - 14:15 Uhr

Raum: 057, Oettingenstraße 67

Max Tschaikowski: Continuous-State Explosion of Fluid Performance Models

 

Abstract:

 

Deterministic approximations of discrete-state stochastic processes based on ordinary differential equations (ODEs) - usually referred to as fluid models - have proved successful in the performance evaluation of large-scale systems since the problem size is independent from the number of components in the model. We analyse a class of models described in the stochastic process algebra PEPA which do not enjoy a fluid interpretation that scales well with increasing population sizes. This class covers modelling situations where the system under scrutiny is described in terms of many copies of subsystems, which are themselves composed of large numbers of interacting agents. When the number of subsystems or the number of agents within a subsystem is large, the size of the system of ODEs may render the analysis intractable. We denominate this phenomenon continuous-state explosion, as it parallels the well known problem of state-space explosion typical of the discrete-state Markovian semantics. We present a result of equivalence that relates the original, and potentially massive, ODE system to an simplified one whose size is independent from all the multiplicities in the model. Additionally, we show that this aggregated ODE also characterises the behaviour of another model which is structurally different from the original one - i.e., the fluid approximation is unable to distinguish between models which are not related with respect to any known equivalence relation in PEPA.