Short- and long-range rapidity correlations in the model with a lattice in transverse plane

In the framework of the quark-gluon string model we consider the various fluctuation and correlation observables used in the analysis of the multi-particle production in hadronic interactions at high energy. We express these observables through the fundamental string characteristics and analyze their resulting properties: the dependence on the width of observation window(s), the range of the correlation in rapidity, the intensive or strongly intensive behavior. To take into account the influence of a string fusion processes on the string characteristics and on the behavior of the observables. we use the version of string model with a lattice (grid) in the impact parameter plane. In particular we show that the observable between multiplicities in two acceptance windows separated in rapidity, which is a strongly intensive in the case with independent identical strings, loses this property, when we take into account the string fusion and the formation of strings of a few different types takes place in a collision.