  Let $A_1,\ldots,A_d$ be a $d$-tuple of commuting dissipative operators on a
separable Hilbert space $\mathcal{H}$. Using the theory of operator vessels and
their associated systems, we give a construction of a dilation of the
multi-parameter semigroup of contractions on $\mathcal{H}$ given by $e^{i
\sum_{j=1}^d t_j A_j}$.
