# Mean-Field Game Approach to Admission Control of an M/M/∞ Queue with Shared Service Cost

2 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We study a mean field approximation of the M/M/$\infty$ queueing system. The problem we deal is quite different from standard games of congestion as we consider the case in which higher congestion results in smaller costs per user. This is motivated by a situation in which some TV show is broadcast so that the same cost is needed no matter how many users follow the show. Using a mean-field approximation, we show that this results in multiple equilibria of threshold type which we explicitly compute. We further derive the social optimal policy and compute the price of anarchy. We then study the game with partial information and show that by appropriate limitation of the queue-state information obtained by the players we can obtain the same performance as when all the information is available to the players. We show that the mean-field approximation becomes tight as the workload increases, thus the results obtained for the mean-field model well approximate the discrete one.
Type de document :
Article dans une revue
Dynamic Games and Applications, Springer Verlag, 2015, pp.1-29. 〈10.1007/s13235-015-0168-9〉
Domaine :

Littérature citée [17 références]

https://hal.inria.fr/hal-01260958
Contributeur : Sara Alouf <>
Soumis le : samedi 23 janvier 2016 - 22:51:49
Dernière modification le : lundi 28 mai 2018 - 14:12:11
Document(s) archivé(s) le : lundi 25 avril 2016 - 08:29:26

### Fichier

mminf-10.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Piotr Wiecek, Eitan Altman, Arnob Ghosh. Mean-Field Game Approach to Admission Control of an M/M/∞ Queue with Shared Service Cost. Dynamic Games and Applications, Springer Verlag, 2015, pp.1-29. 〈10.1007/s13235-015-0168-9〉. 〈hal-01260958〉

### Métriques

Consultations de la notice

## 347

Téléchargements de fichiers