  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.
