MathMC: A mathematica-based tool for CSL model checking of deterministic and stochastic Petri nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discreteevent systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. CSL (Continuous Stochastic Logic) is a (branching) temporal logic developed to express probabilistic properties in continuous time Markov chains (CTMCs). In this paper we present a Mathematica-based tool that implements recent developments for model checking CSL style properties on DSPNs. Furthermore, as a consequence of the type of process underlying DSPNs (a superset of Markovian processes), we are also able to check CSL properties of Generalized Stochastic Petri Nets (GSPNs) and labeled CTMCs

CSL model checking of Deterministic and Stochastic Petri Nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described

Nonlinear Dynamics in Distributed Systems

We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a systematic way using Van Kanpen's expansion method for Markov processes. We present some results for both stationary and time-dependent states. Our approach allows the effect of fluctuations to be explored, particularly in finite systems where such processes assume increasing importance.Comment: Two parts: 8 pages LaTeX file and 5 (uuencoded) figures in Postscript forma

Laws of large numbers for the frog model on the complete graph

The frog model is a stochastic model for the spreading of an epidemic on a graph, in which a dormant particle starts to perform a simple random walk on the graph and to awake other particles, once it becomes active. We study two versions of the frog model on the complete graph with $N + 1$ vertices. In the first version we consider, active particles have geometrically distributed lifetimes. In the second version, the displacement of each awakened particle lasts until it hits a vertex already visited by the process. For each model, we prove that as $N \to \infty$, the trajectory of the process is well approximated by a three-dimensional discrete-time dynamical system. We also study the long-term behavior of the corresponding deterministic systems

Bounding the End-to-End Execution Time in Distributed Real-Time Systems: Arguing the case for Deterministic Networks in Lingua Franca

Designing and implementing distributed systems with real-time requirements quickly reveal the complexity of handling time and logic across multiple systems. As data traverse a network, it is subjected to variable delay due to interfering traffic and variable load on network components. This introduces an element of non-determinism in execution time for distributed algorithms, which translates into increased error logic and pessimistic worst-case estimates. Over the next few years, it is expected that Cyber-Physical Systems will see many new use cases, and the network connecting these will play an ever more important role. Combined with the onset of the fourth industrial revolution, IEEEs Time Sensitive Networking, IETFs Deterministic Networking, and 3GPPs Ultra Reliable Low Latency profile will play a vital role in realizing these systems. Coordination languages such as Lingua Franca can offer a substantial contribution to the design process and implementation of distributed systems such as Cyber-Phyiscal Systems, both through its model of computation which elevates time to a first-class citizen and with its support for distributed models. In this paper, we show that by introducing deterministic network channels with a fixed delay, the worst-case execution time is not increased whereas the variance in total execution time from start to finish is greatly reduced. For a coordination language such as LF, this means that we can analyze a system using much tighter delay bounds for network traffic, which in turn can yield better resource utilization.publishedVersio

Modelling IEEE 802.11 CSMA/CA RTS/CTS with stochastic bigraphs with sharing

Stochastic bigraphical reactive systems (SBRS) is a recent formalism for modelling systems that evolve in time and space. However, the underlying spatial model is based on sets of trees and thus cannot represent spatial locations that are shared among several entities in a simple or intuitive way. We adopt an extension of the formalism, SBRS with sharing, in which the topology is modelled by a directed acyclic graph structure. We give an overview of SBRS with sharing, we extend it with rule priorities, and then use it to develop a model of the 802.11 CSMA/CA RTS/CTS protocol with exponential backoff, for an arbitrary network topology with possibly overlapping signals. The model uses sharing to model overlapping connectedness areas, instantaneous prioritised rules for deterministic computations, and stochastic rules with exponential reaction rates to model constant and uniformly distributed timeouts and constant transmission times. Equivalence classes of model states modulo instantaneous reactions yield states in a CTMC that can be analysed using the model checker PRISM. We illustrate the model on a simple example wireless network with three overlapping signals and we present some example quantitative properties

Analysis of DC microgrids as stochastic hybrid systems

A modeling framework for dc microgrids and distribution systems based on the dual active bridge (DAB) topology is presented. The purpose of this framework is to accurately characterize dynamic behavior of multi-converter systems as a function of exogenous load and source inputs. The base model is derived for deterministic inputs and then extended for the case of stochastic load behavior. At the core of the modeling framework is a large-signal DAB model that accurately describes the dynamics of both ac and dc state variables. This model addresses limitations of existing DAB converter models, which are not suitable for system-level analysis due to inaccuracy and poor upward scalability. The converter model acts as a fundamental building block in a general procedure for constructing models of multi-converter systems. System-level model construction is only possible due to structural properties of the converter model that mitigate prohibitive increases in size and complexity. To characterize the impact of randomness in practical loads, stochastic load descriptions are included in the deterministic dynamic model. The combined behavior of distributed loads is represented by a continuous-time stochastic process. Models that govern this load process are generated using a new modeling procedure, which builds incrementally from individual device-level representations. To merge the stochastic load process and deterministic dynamic models, the microgrid is modeled as a stochastic hybrid system. The stochastic hybrid model predicts the evolution of moments of dynamic state variables as a function of load model parameters. Moments of dynamic states provide useful approximations of typical system operating conditions over time. Applications of the deterministic models include system stability analysis and computationally efficient time-domain simulation. The stochastic hybrid models provide a framework for performance assessment and optimization --Abstract, page iv

Mixed-integer-linear-programming-based energy management system for hybrid PV-wind-battery microgrids: Modeling, design, and experimental verification

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksMicrogrids are energy systems that aggregate distributed energy resources, loads, and power electronics devices in a stable and balanced way. They rely on energy management systems to schedule optimally the distributed energy resources. Conventionally, many scheduling problems have been solved by using complex algorithms that, even so, do not consider the operation of the distributed energy resources. This paper presents the modeling and design of a modular energy management system and its integration to a grid-connected battery-based microgrid. The scheduling model is a power generation-side strategy, defined as a general mixed-integer linear programming by taking into account two stages for proper charging of the storage units. This model is considered as a deterministic problem that aims to minimize operating costs and promote self-consumption based on 24-hour ahead forecast data. The operation of the microgrid is complemented with a supervisory control stage that compensates any mismatch between the offline scheduling process and the real time microgrid operation. The proposal has been tested experimentally in a hybrid microgrid at the Microgrid Research Laboratory, Aalborg University.Peer ReviewedPostprint (author's final draft

Performance Analysis of Distributed and Asynchronous Systems using Probabilistic Timed Actors

Many real-time distributed applications exhibit probabilistic and non-deterministic behaviors. In this paper, we introduce Probabilistic Timed Rebeca (PTRebeca) as an actor-based language for modeling probabilistic distributed real-time systems with asynchronous message passing. We propose the semantics of PTRebeca model in Timed Markov Decision Process (TMDP), the integral semantics of probabilistic timed automaton (PTA) with one digital clock. To analyze PTRebeca models, we develop a tool set to automatically generate a TMDP model from a PTRebeca model in the form of the input language of PRISM model checker. We use PRISM for performance analysis of PTRebeca models against expected reachability and probabilistic reachability properties. We show the applicability of our approach using a few case studies and experimental results