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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-09022015-125522


Tipo di tesi
Tesi di laurea magistrale
Autore
NESTI, TOMMASO
URN
etd-09022015-125522
Titolo
Numerical methods for computing the steady-state distribution of a G-network.
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof.ssa Meini, Beatrice
relatore Prof. Giordano, Stefano
Parole chiave
  • G-network
  • Iterative Methods
  • Newton-Raphson Iteration.
  • Nonnegative Matrices
  • Numerical Analysis
  • Queueing Network
Data inizio appello
18/09/2015
Consultabilità
Completa
Riassunto
G-networks are a class of queueing networks introduced by E. Gelembe in 1989, which are characterized by the presence of positive and negative customers. Negative customers have the capability to destroy a positive customer present in a queue, thus reducing the workload. Under ergodicity condition the steady-state distribution of the network is given as the product of the marginal distributions of each queue, but unlike classical queueing network the equation yelding the steady-state distribution are non-linear. In this thesis we develeop two new numerical methods for the computation of the steady-state distribution. Rewriting the problem as a fixed point matrix equation, we study a fixed point iteration and a Newton-Raphson iteration. We prove that both the methods converge, with linear and quadratic rate respectively, choosing the starting value in a neighbourhood of the fixed point. We then compare these methods with an existing algorithm develped by Fourneau, concluding that the Newton-Raphson iteration is preferable for moderate-sized G-networks.
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