512 research outputs found
An Aggregation Technique for Large-Scale PEPA Models with Non-Uniform Populations
Performance analysis based on modelling consists of two major steps: model
construction and model analysis. Formal modelling techniques significantly aid
model construction but can exacerbate model analysis. In particular, here we
consider the analysis of large-scale systems which consist of one or more
entities replicated many times to form large populations. The replication of
entities in such models can cause their state spaces to grow exponentially to
the extent that their exact stochastic analysis becomes computationally
expensive or even infeasible.
In this paper, we propose a new approximate aggregation algorithm for a class
of large-scale PEPA models. For a given model, the method quickly checks if it
satisfies a syntactic condition, indicating that the model may be solved
approximately with high accuracy. If so, an aggregated CTMC is generated
directly from the model description. This CTMC can be used for efficient
derivation of an approximate marginal probability distribution over some of the
model's populations. In the context of a large-scale client-server system, we
demonstrate the usefulness of our method
A survey of the PEPA tools
This paper surveys the history and the current state of tool support for modelling with the PEPA stochastic process algebra and the PEPA nets modelling language. We discuss future directions for tool support for the PEPA family of languages.
Fluid Model Checking
In this paper we investigate a potential use of fluid approximation
techniques in the context of stochastic model checking of CSL formulae. We
focus on properties describing the behaviour of a single agent in a (large)
population of agents, exploiting a limit result known also as fast simulation.
In particular, we will approximate the behaviour of a single agent with a
time-inhomogeneous CTMC which depends on the environment and on the other
agents only through the solution of the fluid differential equation. We will
prove the asymptotic correctness of our approach in terms of satisfiability of
CSL formulae and of reachability probabilities. We will also present a
procedure to model check time-inhomogeneous CTMC against CSL formulae
Amalgamation of Transition Sequences in the PEPA Formalism
This report presents a proposed formal approach towards reduction of sequences in PEPA components. By performing the described amalgamation procedure we may remove, from the Markov chain underlying an initial PEPA model, those states for which detailed local balance equations cannot be formulated. This transformation may lead to a simpler model with product form solution. Some classes of reduced models preserve those performance measures which we are interested in and, moreover, the steady state solution vector is much easier to find from the computational point of view
Hybrid performance modelling of opportunistic networks
We demonstrate the modelling of opportunistic networks using the process
algebra stochastic HYPE. Network traffic is modelled as continuous flows,
contact between nodes in the network is modelled stochastically, and
instantaneous decisions are modelled as discrete events. Our model describes a
network of stationary video sensors with a mobile ferry which collects data
from the sensors and delivers it to the base station. We consider different
mobility models and different buffer sizes for the ferries. This case study
illustrates the flexibility and expressive power of stochastic HYPE. We also
discuss the software that enables us to describe stochastic HYPE models and
simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055
HYPE with stochastic events
The process algebra HYPE was recently proposed as a fine-grained modelling
approach for capturing the behaviour of hybrid systems. In the original
proposal, each flow or influence affecting a variable is modelled separately
and the overall behaviour of the system then emerges as the composition of
these flows. The discrete behaviour of the system is captured by instantaneous
actions which might be urgent, taking effect as soon as some activation
condition is satisfied, or non-urgent meaning that they can tolerate some
(unknown) delay before happening. In this paper we refine the notion of
non-urgent actions, to make such actions governed by a probability
distribution. As a consequence of this we now give HYPE a semantics in terms of
Transition-Driven Stochastic Hybrid Automata, which are a subset of a general
class of stochastic processes termed Piecewise Deterministic Markov Processes.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Don't Just Go with the Flow: Cautionary Tales of Fluid Flow Approximation
Fluid flow approximation allows efficient analysis of large scale PEPA models. Given a model, this method outputs how the mean, variance, and any other moment of the model's stochastic behaviour evolves as a function of time. We investigate whether the method's results, i.e. moments of the behaviour, are sufficient to capture system's actual dynamics.
We ran a series of experiments on a client-server model. For some parametrizations of the model, the model's behaviour can accurately be characterized by the fluid flow approximations of its moments. However, the experiments show that for some other parametrizations, these moments are not sufficient to capture the model's behaviour, highlighting a pitfall of relying only on the results of fluid flow analysis. The results suggest that the sufficiency of the fluid flow method for the analysis of a model depends on the model's concrete parametrization. They also make it clear that the existing criteria for deciding on the sufficiency of the fluid flow method are not robust
Investigating modularity in the analysis of process algebra models of biochemical systems
Compositionality is a key feature of process algebras which is often cited as
one of their advantages as a modelling technique. It is certainly true that in
biochemical systems, as in many other systems, model construction is made
easier in a formalism which allows the problem to be tackled compositionally.
In this paper we consider the extent to which the compositional structure which
is inherent in process algebra models of biochemical systems can be exploited
during model solution. In essence this means using the compositional structure
to guide decomposed solution and analysis.
Unfortunately the dynamic behaviour of biochemical systems exhibits strong
interdependencies between the components of the model making decomposed
solution a difficult task. Nevertheless we believe that if such decomposition
based on process algebras could be established it would demonstrate substantial
benefits for systems biology modelling. In this paper we present our
preliminary investigations based on a case study of the pheromone pathway in
yeast, modelling in the stochastic process algebra Bio-PEPA
Improved Continuous Approximation of PEPA Models through Epidemiological Examples
We present two individual based models of disease systems using PEPA (Performance Evaluation Process Algebra). The models explore contrasting mechanisms of disease transmission: direct transmission (e.g. measles) and indirect transmission (e.g. malaria, via mosquitos). We extract ordinary differential equations (ODEs) as a continuous approximation to the PEPA models using the Hillston method and compare these with the traditionally used ODE disease models and with the results of stochastic simulation. Improvements to the Hillston method of ODE extraction for this context are proposed, and the new results compare favourably with stochastic simulation results and to ODEs derived for equivalent models in WSCCS (Weighted Synchronous Calculus of Communicating Systems)
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