# A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method

arXiv: https://arxiv.org/abs/1708.08343 · HTML: https://mlsanity.com/paper/1708.08343/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [Linear convergence of a policy gradient method for some finite horizon continuous time control problems](https://mlsanity.com/paper/2203.11758/) (2022)
- [Deep Backward and Galerkin Methods for the Finite State Master Equation](https://mlsanity.com/paper/2403.04975/) (2024)
- [Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data](https://mlsanity.com/paper/2606.26498/) (2026)

## Abstract (arXiv)

We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a controlled reflected diffusion with a cost function that depends on the reflection terms in addition to the standard variables: state, control, and the mean field term. This MFG arises from the asymptotic analysis of an N-player game for single server queues with strategic servers. By showing that our scheme is an almost contraction, we establish the convergence of this numerical scheme over a small time interval.