  A simple cellular model for the description of the long-range multiplicity
and $p_t$ correlations in high-energy nuclear collisions originating from the
string fusion model is proposed. Three versions of the model: without fusion,
with local and with global string fusion are formulated.
  A Gauss approximation which enables explicit analytical calculations of the
correlation functions in some asymptotic cases in the framework of the model is
developed. The assumptions of the model and the validity of a Gauss
approximation are checked up in the simplest (no fusion) case when the explicit
solution of the model can be found.
  The role of a size of cells is analysed. The modification of the results in
the case of non-Poissonian distributions is also discussed.
