  We extend the 2 dimensional Causal Dynamical Triangulation (CDT) model from
the usual model of closed string to the one of open-closed string. The
matrix-vector model describing the loop gas model is modified so as to possess
the nature of the CDT, i.e. the time foliation structure. Stochastic
quantization method produces interactions of loop and line variables similar to
those in the non-critical open-closed string field theories. By taking an
appropriate scaling, we realize an extended model of the generalized CDT
(GCDT), which keeps the causality in a broad sense.
