Near eutectic AlSi alloys (e.g. AlSi10Mg) are of the most popular materials for light structures manufactured by Powder-Bed Fusion-Laser Beam (PBF-LB). The grain structure of PBF-LB AlSi alloys shows fusion boundary nucleation with elongated grains towards melt pool center where epitaxial growth dominates. At the sub-grain scale, the as-built microstructure represents a fine cellular-dendritic structure, where supersaturated α-Al cells of several hundred nanometers are enveloped by a continuous thin Si eutectic network. These findings suggest that a comprehensive physics-based process-structure-properties linkage should incorporate microstructural aspects at both scales: grain structure (including texture), and substructure. The authors have recently developed a Cellular Automata (CA) simulation approach that can properly address the first scale, i.e. grain structure and texture. The second scale is targeted in this work by establishing an inclusive analytical model of rapid solidification. Growth kinetics and microsegregation models are coupled to investigate grain substructure evolution as a function of solidification rate, thermal gradient and alloy composition. The growth kinetic model mainly describes the solidification front where the solid/liquid interface is defined among planar, non-planar (cell/dendrite) and eutectic types based on the interfaces selection criterion. The tip radius and undercooling are also specified at various local temperature fields. Following that, the microsegregation model defines the substructure evolution, including the interdendritic phases and compositions, as well as the type of solidification end. In accord with the experimental observations, the model results indicated the eutectic Si network structure under common PBF-LB conditions while a complete solute trapping was estimated at solidification rates of more than ~5 m/s. The cell size, tip radius, eutectic fraction and eutectic composition were also calculated at various solidification rates and alloy compositions.