Related papers: Unbounded product-form Petri nets
In this paper, domination in Signed Petri net(SPN) has been introduced.We identify some of the Petri net structures where a dominating set can exist.Applications of producer consumer problem, searching of food by bees and finding similarity…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains.…
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an…
As engineered systems expand, become more interdependent, and operate in real-time, reliability assessment is indispensable to support investment and decision making. However, network reliability problems are known to be #P-complete, a…
We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence,…
State estimation allows to monitor power networks, exploiting field measurements to derive the most likely grid state. In the literature, measurement errors are usually assumed to follow zero-mean Gaussian distributions; however, it has…
Petri Net is a formalism to describe changes between 2 or more states across discrete time and has been used to model many systems. We present PNet - a pure Python library for Petri Net modeling and simulation in Python programming…
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…
Bipolar synchronization systems (BP-systems) constitute a class of coloured Petri nets, well suited for modeling the control flow of discrete, dynamical systems. Every BP-system has an underlying ordinary Petri net, which is a T-system.…
Technologies and their production systems are used by archaeologists and anthropologists to study complexity of sociotechnical systems. However, there are several issues that hamper agreement about what constitutes complexity and how we can…
The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components $n$. Mean-field approximations provide an effective reduction in complexity of the…
Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…
Barwise and Seligman stated the first principle of information flow: "Information flow results from regularities in the distributed system." They represent a distributed system in terms of a classification consisting of a set of objects or…
We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
We present results for a finite variant of the one-dimensional Toom model with closed boundaries. We show that the steady state distribution is not of product form, but is nonetheless simple. In particular, we give explicit formulas for the…
This paper presents a method for calculating steady state probabilities of $M|E_r|c|K$ queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this…
A crucial question in analyzing a concurrent system is to determine its long-run behaviour, and in particular, whether there are irreversible choices in its evolution, leading into parts of the reachability space from which there is no…