  We present an N-body model for the barred Milky Way (MW) galaxy that
reproduces many of its properties, including the overall mass distribution, the
disc kinematics, and the properties of the central bar. Our high-resolution (N
~ 10^8 particles) simulation, performed with the Ramses code, starts from an
axisymmetric non-equilibrium configuration constructed within the AGAMA
framework. This is a self-consistent dynamical model of the MW defined by the
best available parameters for the dark matter halo, the stellar disc and the
bulge.
  For the known (stellar and gas) disc mass (4.5 x 10^10 Msun) and disc mass
fraction at R ~ 2.2 R_d (f_d ~ 0.3 - 0.6), the low mass limit does not yield a
bar in a Hubble time. The high mass limit adopted here produces a box/peanut
bar within about 2 Gyr with the correct mass (~10^10 Msun), size (~5 kpc) and
peak pattern speed (~ 40-45 km/s/kpc).
  In agreement with earlier work, the bar formation timescale scales inversely
with f_d (i.e. log [T/Gyr] ~ 0.60/f_d - 0.83 for 1 < f_d < 0.3). The disc
radial heating is strong, but, in contrast to earlier claims, we find that disc
vertical heating outside of the box/peanut bulge structure is negligible.
  The synthetic barred MW exhibits long-term stability, except for the slow
decline (roughly -2 km/s/kpc/Gyr) of the bar pattern speed, consistent with
recent estimates. If our model is indicative of the Milky Way, we estimate that
the bar first emerged 3-4 Gyr ago.
