Researchers dealing with game theoretic issues are well aware that the definition of a model capturing some physical behaviours such as the routing, the pricing, the flow and congestion control, the admission control just to mention some examples in the telecommunication field, is a difficult task, but it is only half of the overall effort. As a matter of fact, a key aspect is the analysis of the equilibrium (or equilibria) towards which the game will (hopefully) converge. The existence, the uniqueness, the efficiency and the structure of the equilibrium are some of the typical properties which are investigated. In this article, we propose a game theoretic model for quality of service (QoS) routing in networks implementing a Differentiated Service model for the QoS support. In particular, we focus on a parallel link network model and we consider a non-cooperative joint problem of QoS routing and dynamic capacity allocation. For this model, we demonstrate that the Nash equilibrium exists, so overcoming a typical problem in the existence proofs appeared in many papers in the area of routing game since 1990s, and we explicitly obtain a suitable set of relations characterising its structure. Moreover, we prove that Nash equilibrium uniqueness cannot be guaranteed in general.

Existence and uniqueness of the Nash equilibrium in the non-cooperative QoS routing / Paolo, Conforto; DELLI PRISCOLI, Francesco; Facchinei, Francisco. - In: INTERNATIONAL JOURNAL OF CONTROL. - ISSN 0020-7179. - 83:4(2010), pp. 776-788. [10.1080/00207170903437111]

Existence and uniqueness of the Nash equilibrium in the non-cooperative QoS routing

DELLI PRISCOLI, Francesco;FACCHINEI, Francisco
2010

Abstract

Researchers dealing with game theoretic issues are well aware that the definition of a model capturing some physical behaviours such as the routing, the pricing, the flow and congestion control, the admission control just to mention some examples in the telecommunication field, is a difficult task, but it is only half of the overall effort. As a matter of fact, a key aspect is the analysis of the equilibrium (or equilibria) towards which the game will (hopefully) converge. The existence, the uniqueness, the efficiency and the structure of the equilibrium are some of the typical properties which are investigated. In this article, we propose a game theoretic model for quality of service (QoS) routing in networks implementing a Differentiated Service model for the QoS support. In particular, we focus on a parallel link network model and we consider a non-cooperative joint problem of QoS routing and dynamic capacity allocation. For this model, we demonstrate that the Nash equilibrium exists, so overcoming a typical problem in the existence proofs appeared in many papers in the area of routing game since 1990s, and we explicitly obtain a suitable set of relations characterising its structure. Moreover, we prove that Nash equilibrium uniqueness cannot be guaranteed in general.
2010
capacity assignment; existence; game theory; nash equilibrium; non-cooperative game; quality of service routing; uniqueness
01 Pubblicazione su rivista::01a Articolo in rivista
Existence and uniqueness of the Nash equilibrium in the non-cooperative QoS routing / Paolo, Conforto; DELLI PRISCOLI, Francesco; Facchinei, Francisco. - In: INTERNATIONAL JOURNAL OF CONTROL. - ISSN 0020-7179. - 83:4(2010), pp. 776-788. [10.1080/00207170903437111]
File allegati a questo prodotto
File Dimensione Formato  
VE_2010_11573-224328.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 432.72 kB
Formato Adobe PDF
432.72 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/224328
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 3
social impact