  We solve the relativistic Riemann problem in viscous gluon matter employing a
microscopic parton cascade. We demonstrate the transition from ideal to viscous
shock waves by varying the shear viscosity to entropy density ratio $\eta/s$
from zero to infinity. We show that an $\eta/s$ ratio larger than 0.2 prevents
the development of well-defined shock waves on timescales typical for
ultrarelativistic heavy-ion collisions. Comparisons with viscous hydrodynamic
calculations confirm our findings.
