  We study the late acceleration of the universe by incorporating bulk viscous
matter with the running vacuum. The vacuum energy density varies as the squares
of the Hubble parameter ($\rho_{\Lambda}\propto H^2$), and the coefficient of
bulk viscosity of matter is proportional to the velocity of expansion ($\xi
\propto H$). We obtained an analytical solution to the Friedmann equations and
estimated the model parameters using the combined data set SN1a+CMB+BAO+OHD. We
have evaluated the universe's age as 14 Gyr, which is slightly higher than the
age-predicted by the $\Lambda$CDM model. However, it is an improved result
compared to the age-predicted by a class of bulk viscous matter-dominated
models. Interestingly, we have obtained the coefficient of bulk viscosity of
the matter component as $1.316\times 10^5$ kg $\textnormal m^{-1}$ $\textnormal
s^{-1}$ which is one to two orders of magnitude less than the value predicted
by most of the bulk viscous matter-dominated models and it falls in the range
of highly viscous materials found on the earth. The Hubble parameter is a
decreasing function of the scale factor, and it attains a constant value in the
far future that corresponds to an end deSitter phase of evolution. The
deceleration parameter shows a transition from matter-dominated decelerated
phase to vacuum energy-dominated accelerating phase, and the transition
redshift is obtained as $z_T = 0.73$. The statefinder analysis distinguishes
our model from the $\Lambda$CDM model at present, and the $r-s$ trajectory
reveals the quintessence behaviour of the vacuum energy. The phase space
analysis shows that the universe is evolving towards a mechanically stable
state in the far future. The entropy evolution satisfies the generalised second
law of thermodynamics, and the entropy is maximised in the far future
evolution.
