Modèles probabilistes pour choisir un itinéraire dans un réseau de trafic
Modelling the dynamical behaviour of computer systems
Monte Carlo simulation and analytic approximation of epidemic processes on large networks
Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic...
Node assignment problem in Bayesian networks
This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.
Nonlinear Markov processes in big networks
Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly,...
On -wise arc forwarding index and wavelength allocations in faulty all-optical hypercubes
Motivated by the wavelength division multiplexing in all-optical networks, we consider the problem of finding an optimal (with respect to the least possible number of wavelengths) set of internally node disjoint dipaths connecting all pairs of distinct nodes in the binary -dimensional hypercube, where . This system of dipaths constitutes a routing protocol that remains functional in the presence of up to faults (of nodes and/or links). The problem of constructing such protocols for general...
On Markovian traffic with applications to TES processes.
On ƒ-wise Arc Forwarding Index and Wavelength Allocations in Faulty All-optical Hypercubes
Motivated by the wavelength division multiplexing in all-optical networks, we consider the problem of finding an optimal (with respect to the least possible number of wavelengths) set of ƒ+1 internally node disjoint dipaths connecting all pairs of distinct nodes in the binary r-dimensional hypercube, where 0 ≤ ƒ < r. This system of dipaths constitutes a routing protocol that remains functional in the presence of up to ƒ faults (of nodes and/or links). The problem of constructing such...
Performance analysis of multi-hop wireless packet networks.
Probability distribution function for the capacity of a multiterminal network
Process parameter prediction via markov models of sub-activities
This work aims to fill a lacunae in the project-oriented production systems literature providing a formal analytic description of the rework effects formulae and the determination of the extended design time due to a certain degree of overlapping in a pair of activities. It is made through the utilization of concepts of workflow construction with hidden (semi) Markov models theory and establishing a way to disaggregate activities into sub-activities, in order to determine the activity parameters...
Product form solution for g-networks with dependent service
We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. The following node types are considered: (0) an exponential node with servers, infinite buffer and FIFO discipline; (1) an infinite-server node; (2) a single-server node with infinite buffer and LIFO PR discipline; (3) a single-server...
Product form solution for g-networks with dependent service
We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. The following node types are considered: Negative customers arriving at each node also form a Poisson flow. A negative customer entering a node with k customers in service, with probability 1/k chooses one of served positive customer...
Production management in a Petri net environment
Prognosis and optimization of homogeneous Markov message handling networks
Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchic networks is found a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of the system design and management are discussed, as well as a program product 5P (Program for Prognosis of Performance Parameters and Problems) based on the presented theoretical conclusions. The theoretic achievements as well as the practical...
Random networks with sublinear preferential attachment: degree evolutions.
Real time scheduling and routing for flexible manufacturing systems with unreliable machines
Réseaux stochastiques
Sensitivity error bounds for non-exponential stochastic networks
Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree.