scholarly journals Modeling a New AQM Model for Internet Chaotic Behavior Using Petri Nets

2021 ◽  
Vol 11 (13) ◽  
pp. 5877
Author(s):  
José M. Amigó ◽  
Guillem Duran ◽  
Ángel Giménez ◽  
José Valero ◽  
Oscar Martinez Bonastre
Keyword(s):  
Petri Nets ◽  
Queue Length ◽  
Chaotic Behavior ◽  
Stability Control ◽  
Formal Modeling ◽  
Random Early Detection ◽  
Network Algorithms ◽  
The Matrix ◽  
Invariant Analysis ◽  
Reachability Tree

Formal modeling is considered one of the fundamental phases in the design of network algorithms, including Active Queue Management (AQM) schemes. This article focuses on modeling with Petri nets (PNs) a new scheme of AQM. This innovative AQM is based on a discrete dynamical model of random early detection (RED) for controlling bifurcations and chaos in Internet congestion control. It incorporates new parameters (α,β) that make possible better stability control over oscillations of an average queue length (AQL) at the router. The PN is validated through the matrix equation approach, reachability tree, and invariant analysis. The correctness is validated through the key properties of reachability, boundedness, reversibility, deadlock, and liveness.

Symmetry, bifurcations, and chaos in a distributed respiratory control system

1994 ◽  
Vol 77 (5) ◽  
pp. 2481-2495 ◽  
Author(s):  
M. Sammon
Keyword(s):  
Chaotic Behavior ◽  
Respiratory Control ◽  
Oscillatory Behavior ◽  
Phase Switching ◽  
Control Distribution ◽  
Complex Eigenvalues ◽  
Afferent Information ◽  
Switching Functions ◽  
The Matrix ◽  
Afferent Control

A multivariate model is outlined for a distributed respiratory central pattern generator (RCPG) and its afferent control. Oscillatory behavior of the system depends on structure and symmetry of a matrix of phase-switching functions (F omega, phi) that control distribution of central excitation (CE) and inhibition (CI) within the circuit. The matrix diagonal (F omega) controls activation of CI variables as excitatory inputs are altered (e.g., central and afferent contributions to inspiratory off switch); off-diagonal terms (F phi) distribute excitations within the CI system and produce complex eigenvalues at the switching points between inspiration and expiration. For null F phi, phase switchings of saddle equilibria located at end expiration and end inspiration are overdamped all-or-nothing events; graded control of CI is seen for phi > 0. When coupling is significant (phi >> 0), CI dynamics become underdamped, admitting a domain of inputs where chaotic behavior is predictably observed. For the homogeneous RCPG (symmetric F omega, phi), CE oscillations are one-dimensional limit cycles (D = 1) or weakly chaotic (D approximately equal to 1). When perturbations from symmetry are significant, the distributed RCPG becomes partitioned where strongly chaotic oscillations (D > or = 2) and central apnea (D = 0) are seen more frequently. The equations provide means for mapping Silnikov bifurcations that alter the geometry and dimension of the breathing pattern and formalisms for discussing RCPG processing of afferent information.

Application of Fuzzy Petri Nets in Hydraulic Pump Fault Diagnosis

2014 ◽  
Vol 1008-1009 ◽  
pp. 1176-1179
Author(s):  
Hai Dong ◽  
Heng Bao Xin
Keyword(s):  
Fault Diagnosis ◽  
Petri Nets ◽  
Hydraulic Pump ◽  
Modeling And Analysis ◽  
Matrix Operations ◽  
Knowledge Reasoning ◽  
Fuzzy Production Rules ◽  
The Matrix ◽  
Fuzzy Petri Nets ◽  
Definition Of

In this paper, an approach of fuzzy Petri nets (FPN) is proposed to simulate the fault spreading and diagnosis of hydraulic pump. First, the fuzzy production rules and the definition of FPN were briefly introduced. Then, its knowledge reasoning process and the matrix operations based on an algorithm were conducted, which makes full use of its parallel reasoning ability and makes it simpler and easier to implement. Finally, a case of hydraulic pump fault diagnosis with FPN was presented in detail, for illustrating the interest of the proposed modeling and analysis algorithm.

ALGORITHM FOR CONSTRUCTING A REACHABILITY TREE FOR STOCHASTIC PETRI NETS

2021 ◽  
pp. 34-40
Author(s):  
Д.С. Звягин
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Final Stage ◽  
Distribution Systems ◽  
Stochastic Petri Nets ◽  
Matrix Equations ◽  
Correct Process ◽  
Reachability Sets ◽  
Process Failures ◽  
Reachability Tree

Описываются основные определения дерева достижимости сетей Петри. Также рассматриваются различные примеры стохастических сетей Петри, в которых после выставления начальных маркировок в первых позициях определяются значения во всех остальных позициях. Показаны примеры определения маркировок при помощи высчитывания вектора диагональной свертки. Для каждого примера стохастической сети Петри проводится анализ данной сети. Данный анализ необходим для различных распределительных систем и процессов, особенно на заключительном этапе. Основными методами анализа являются дерево достижимости и матричные уравнения. Рассматривается один из таких методов анализа сетей Петри. С использованием дерева достижимости можно проанализировать, выявить и исправить сбои в процессах, которые могут произойти при наличии тупиковых состояний и при неправильной последовательности срабатывания переходов. Исходя из рассмотренных примеров предлагается обобщенный алгоритм построения дерева достижимости для стохастических сетей Петри. Предложенный алгоритм построения дерева достижимости стохастических сетей Петри можно применять для всех сетей как с конечным, так и с бесконечным множеством достижимости. Данный алгоритм будет являться полезным инструментом при анализе стохастических сетей Петри The article describes the basic definitions of the reachability tree of Petri nets. It also considers various examples of stochastic Petri nets, in which, after setting the initial markings in the first positions, the values in all other positions are determined. The work shows examples of determining markings by calculating the vector of the diagonal convolution. Each example of a stochastic Petri net is analyzed. This analysis is necessary for various distribution systems and processes, especially in the final stage. The main analysis methods are reachability tree and matrix equations. I consider one of such methods for analyzing Petri nets. Using the reachability tree, you can analyze, identify, and correct process failures that can occur when there are deadlocks and when transitions are fired incorrectly. Based on the examples considered, I propose a generalized algorithm for constructing a reachability tree for stochastic Petri nets. The proposed algorithm for constructing the reachability tree of stochastic Petri nets can be applied to all nets with both finite and infinite reachability sets. This algorithm will be a useful tool for analyzing stochastic Petri nets

MODELING THE DYNAMIC INTERACTION PROCESSES USING OF FUZZY TIMED PETRI NETS OF TYPE VF

2019 ◽  
pp. 19-26
Author(s):  
V. A. Mustafayev ◽  
M. N. Salmanova
Keyword(s):  
Petri Nets ◽  
Matrix Theory ◽  
Production Model ◽  
Timed Petri Nets ◽  
Complex Objects ◽  
Structure Representation ◽  
Effective Form ◽  
The Matrix ◽  
Composition Laws ◽  
Analysis Models

The dynamic interacting processes modeling is examined in the article, which shows the complex objects operation in the condition of uncertainty. A formalism intended for the development and analysis models of complex parallel and distributed systems is proposed. It is based on the mathematical apparatus of the fuzzy timed Petri nets (FTPN) of type Vf, representing generalized FTPN of type Vf , combining deterministic and non-deterministic character. The algorithm for the functioning FTPN of type Vf is developed. The proposed algorithm provides a solution to the problem of the triggering solvability of transitions occurring in conflict states, the imposition of a fuzzy structure on the network marking with fuzzy composition laws that determine the values the degrees of belonging the input and output transition positions. The model of parallel functioning processing devices is presented in the FTPN form of type Vf. An approach is proposed for modeling dynamic interacting processes based on the matrix theory of Petri nets, that provides an effective form of structure representation, model state dynamics, the space of achievable states, and triggering transitions sequence in the form of vectors and matrices set. On the example of the production model of mechanical processing, it is shown that the accepted triggering transitions rules fully show the functioning FTPN process of type Vf. As a result of the simulation, the reachability tree is obtained as a sequence of matrices.

scholarly journals Computational Procedures for a Class of GI/D/kSystems in Discrete Time

2009 ◽  
Vol 2009 ◽  
pp. 1-18
Author(s):  
Md. Mostafizur Rahman ◽  
Attahiru Sule Alfa
Keyword(s):  
Discrete Time ◽  
Queue Length ◽  
Computation Time ◽  
Single Server ◽  
The Matrix ◽  
Interarrival Times ◽  
Computational Procedures ◽  
Set Up ◽  
First In First Out ◽  
Service Duration

A class of discrete time GI/D/ksystems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD) type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrixRsimple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures.

An HCPN Pattern for Railway Safety Critical Scenarios Formal Modeling

2015 ◽  
Author(s):  
Zakaryae Boudi ◽  
El Miloudi El Koursi ◽  
Simon Collart-Dutilleul
Keyword(s):  
Petri Nets ◽  
Information Aggregation ◽  
Colored Petri Nets ◽  
Formal Modeling ◽  
Accurate Information ◽  
Safety Critical ◽  
Railway Safety ◽  
High Level ◽  
Term Objective

Analyzing railway critical scenarios usually involves a large team of diverse railway abilities and skills. This paper presents a formal modeling pattern for Hierarchical Colored Petri Nets (HCPN) in modeling railway safety critical scenarios. Indeed, under the French project called “PERFECT”, our long-term objective is to formalize and automate a significant part of railway scenarios modeling. The purpose of this contribution is to bring a first proposition of a standardized modeling way able to deal with the models complexity resulting from the various modeling capabilities for railway scenarios. In fact, HCPN modeling freedom is preventing from accurate information aggregation and a beneficial use of those models in an overall safety analysis. The proposed pattern is based on modular High Level Petri Nets and consists in describing all the railway scenario episodes while incorporating most relevant safety components of the system, such as safety regulation procedures, interlocking and even human involvement, enabling a larger gathering of information and allowing the study of diverse issues in a same global model. This work intends to bring a concrete and reusable HCPN pattern for modeling in order to facilitate studies of accidental scenarios considering automatic mechanisms and human tasks. A concrete application of the pattern was made for the real accidental scenario of “Saint Romain en Gier”.

scholarly journals ε-TPN: definition of a Time Petri Net formalism simulating the behaviour of the timed grafcets

2019 ◽  
Vol Volume 31 - 2019 - CARI 2018 ◽  
Author(s):  
Médésu Sogbohossou ◽  
Medesu Sogbohossou ◽  
Antoine Vianou ◽  
Nabil Gmati ◽  
Eric Badouel ◽  
...  
Keyword(s):  
Petri Nets ◽  
Control Systems ◽  
Timed Automata ◽  
Operational Semantics ◽  
Formal Modeling ◽  
Time Petri Nets ◽  
Time Petri Net ◽  
Finite State ◽  
Definition Of ◽  
Finite State Space

To allow a formal verification of timed GRAFCET models, many authors proposed to translate them into formal and well-reputed languages such as timed automata or Time Petri nets (TPN). Thus, the work presented in [Sogbohossou, Vianou, Formal modeling of grafcets with Time Petri nets, IEEE Transactions on Control Systems Technology, 23(5)(2015)] concerns the TPN formalism: the resulting TPN of the translation, called here ε-TPN, integrates some infinitesimal delays (ε) to simulate the synchronous semantics of the grafcet. The first goal of this paper is to specify a formal operational semantics for an ε-TPN to amend the previous one: especially, priority is introduced here between two defined categories of the ε-TPN transitions, in order to respect strictly the synchronous hypothesis. The second goal is to provide how to build the finite state space abstraction resulting from the new definitions. Afin de permettre la vérification formelle des grafcets temporisés, plusieurs auteurs ont proposé de les traduire dans des langages formels de réputation tels que les automates temporisés et les réseaux de Petri temporels (TPN). Ainsi, les travaux présentés dans [Sogbohossou, Vianou, Formal modeling of grafcets with Time Petri nets, IEEE Transactions on Control Systems Technology, 23(5)(2015)] concernent le formalisme des TPN: le réseau résultant de la traduction, dénommé ici ε-TPN, intègre des délais infinitésimaux (ε) pour simuler la sémantique synchrone du grafcet. Le premier objectif de cet article est de définir la sémantique opérationnelle d'un ε-TPN afin d'améliorer l'ancienne définition: spécifiquement, une priorité est introduite ici entre deux catégories de transitions définies pour ces réseaux, dans l'optique de respecter rigoureusement l'hypothèse synchrone. Le second but est de fournir une méthode de calcul de l'espace d'état fini qui découle des nouvelles définitions.

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