Maddalena, Daniela
(2016)

*Stationary states in random walks on networks.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Matematica [LM-DM270], Documento ad accesso riservato.

Documenti full-text disponibili:

## Abstract

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Abstract

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

Maddalena, Daniela

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Indirizzo

Curriculum A: Generale e applicativo

Ordinamento Cds

DM270

Parole chiave

random walks transportation network dynamical systems stationary distribution Markovv processes

Data di discussione della Tesi

18 Marzo 2016

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

Maddalena, Daniela

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Indirizzo

Curriculum A: Generale e applicativo

Ordinamento Cds

DM270

Parole chiave

random walks transportation network dynamical systems stationary distribution Markovv processes

Data di discussione della Tesi

18 Marzo 2016

URI

## Statistica sui download

Gestione del documento: