# Mean-field Game Approach to Admission Control of an M/M/$\infty$ Queue with Decreasing Congestion 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/$\infty$ queuing system. This queue is often used to model the number of cellular phone users in a cell. We assume that congestion here has a positive impact on the performance so that the more there are users, the less it is costly to offer a service per cell phone, for example, if a base station broadcasts a film then the cost per customer decreases. We obtain closed-form formulas for the equilibria. 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.
Document type :
Conference papers
Complete list of metadata

Cited literature [14 references]

https://hal.inria.fr/hal-01066458
Contributor : Eitan Altman <>
Submitted on : Saturday, September 20, 2014 - 2:51:58 PM
Last modification on : Monday, May 28, 2018 - 2:12:11 PM
Long-term archiving on: : Sunday, December 21, 2014 - 10:15:49 AM

### File

piotr-netgcoop.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01066458, version 1

### Citation

Piotr Wiecek, Eitan Altman, Arnob Ghosh. Mean-field Game Approach to Admission Control of an M/M/$\infty$ Queue with Decreasing Congestion Cost. 7th International Conference on NETwork Games COntrol and OPtimization (NETGCOOP 2014), Oct 2014, Trento, Italy. ⟨hal-01066458⟩

Record views