1,373 research outputs found
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
Analysis of Petri Net Models through Stochastic Differential Equations
It is well known, mainly because of the work of Kurtz, that density dependent
Markov chains can be approximated by sets of ordinary differential equations
(ODEs) when their indexing parameter grows very large. This approximation
cannot capture the stochastic nature of the process and, consequently, it can
provide an erroneous view of the behavior of the Markov chain if the indexing
parameter is not sufficiently high. Important phenomena that cannot be revealed
include non-negligible variance and bi-modal population distributions. A
less-known approximation proposed by Kurtz applies stochastic differential
equations (SDEs) and provides information about the stochastic nature of the
process. In this paper we apply and extend this diffusion approximation to
study stochastic Petri nets. We identify a class of nets whose underlying
stochastic process is a density dependent Markov chain whose indexing parameter
is a multiplicative constant which identifies the population level expressed by
the initial marking and we provide means to automatically construct the
associated set of SDEs. Since the diffusion approximation of Kurtz considers
the process only up to the time when it first exits an open interval, we extend
the approximation by a machinery that mimics the behavior of the Markov chain
at the boundary and allows thus to apply the approach to a wider set of
problems. The resulting process is of the jump-diffusion type. We illustrate by
examples that the jump-diffusion approximation which extends to bounded domains
can be much more informative than that based on ODEs as it can provide accurate
quantity distributions even when they are multi-modal and even for relatively
small population levels. Moreover, we show that the method is faster than
simulating the original Markov chain
Modelling dynamic reliability via Fluid Petri Nets
Combinatorial models for reliability analysis (like fault-trees or block diagram) are static models that cannot include any type of component dependence. In the CTMC (Continuous Time Markov Chain) framework, the transition rates can depend on the state of the system thus allowing the analyst to include some dependencies among components. However, in more general terms, the system reliability may depend on parameters or quantities that vary continuously in time (like temperature, pressure, distance, etc.). Systems whose behavior in time can be described by discrete as well as continuous variables, are called hybrid systems. In the
dependability literature, the case in which the reliability characteristics vary continuously versus a process parameter, is sometimes referred to as dynamic reliability [1]. The modelling and analysis of hybrid dynamic
systems is an open research area. The present paper discusses the evaluation of a benchmark on dynamic reliability proposed in [1] via a modelling framework called Fluid Stochastic Petri Net (FSPN)
Fluid Stochastic Petri Nets: From Fluid Atoms in ILP Processor Pipelines to Fluid Atoms in P2P Streaming Networks
© 2012 Mitrevski and Kotevski, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Fluid Stochastic Petri Nets: From Fluid Atoms in ILP Processor Pipelines to Fluid Atoms in P2P Streaming Networ
About Dynamical Systems Appearing in the Microscopic Traffic Modeling
Motivated by microscopic traffic modeling, we analyze dynamical systems which
have a piecewise linear concave dynamics not necessarily monotonic. We
introduce a deterministic Petri net extension where edges may have negative
weights. The dynamics of these Petri nets are well-defined and may be described
by a generalized matrix with a submatrix in the standard algebra with possibly
negative entries, and another submatrix in the minplus algebra. When the
dynamics is additively homogeneous, a generalized additive eigenvalue may be
introduced, and the ergodic theory may be used to define a growth rate under
additional technical assumptions. In the traffic example of two roads with one
junction, we compute explicitly the eigenvalue and we show, by numerical
simulations, that these two quantities (the additive eigenvalue and the growth
rate) are not equal, but are close to each other. With this result, we are able
to extend the well-studied notion of fundamental traffic diagram (the average
flow as a function of the car density on a road) to the case of two roads with
one junction and give a very simple analytic approximation of this diagram
where four phases appear with clear traffic interpretations. Simulations show
that the fundamental diagram shape obtained is also valid for systems with many
junctions. To simulate these systems, we have to compute their dynamics, which
are not quite simple. For building them in a modular way, we introduce
generalized parallel, series and feedback compositions of piecewise linear
concave dynamics.Comment: PDF 38 page
Region-Based Analysis of Hybrid Petri Nets with a Single General One-Shot Transition
Recently, hybrid Petri nets with a single general one-shot transition (HPnGs) have been introduced together with an algorithm to analyze their underlying state space using a conditioning/deconditioning approach. In this paper we propose a considerably more efficient algorithm for analysing HPnGs. The proposed algorithm maps the underlying state-space onto a plane for all possible firing times of the general transition s and for all possible systems times t. The key idea of the proposed method is that instead of dealing with infinitely many points in the t-s-plane, we can partition the state space into several regions, such that all points inside one region are associated with the same system state. To compute the probability to be in a specific system state at time Ï„, it suffices to find all regions intersecting the line t = Ï„ and decondition the firing time over the intersections. This partitioning results in a considerable speed-up and provides more accurate results. A scalable case study illustrates the efficiency gain with respect to the previous algorithm
Methodologies synthesis
This deliverable deals with the modelling and analysis of interdependencies between critical infrastructures, focussing attention on two interdependent infrastructures studied in the context of CRUTIAL: the electric power infrastructure and the information infrastructures
supporting management, control and maintenance functionality. The main objectives are: 1) investigate the main challenges to be addressed for the analysis and modelling of interdependencies, 2) review the modelling methodologies and tools that can be used to address these challenges and support the evaluation of the impact of interdependencies on the dependability and resilience of the service delivered to the users, and 3) present the preliminary directions investigated so far by the CRUTIAL consortium for describing and modelling interdependencies
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