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

Piotr Więcek, Eitan Altman, Arnob Ghosh

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study a mean-field approximation of the M/M/∞ 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.

Original languageEnglish (US)
Pages (from-to)538-566
Number of pages29
JournalDynamic Games and Applications
Issue number4
StatePublished - Dec 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


  • Admission control
  • Fluid limit
  • Mean-field game
  • Queueing
  • Stochastic game
  • Threshold equilibrium


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