A number of characteristics of groups of the highest energy particles in extensive air showers (so-called gamma h-families) measured in the cosmic ray Pamir experiment and the data from the Tian-Shan extensive air shower experiment were compared with those simulated using three different h¹⁴N interaction models distinguished mainly by the dependence of the total inelasticity on energy: namely increasing, constant and decreasing. The chemical composition of the primary cosmic rays varied from so-called normal to extremely enriched by heavy nuclei. The detection of gamma h-families in emulsion chambers was also simulated. On the basis of the comparison, we conclude that the total inelasticity in h¹⁴N interactions up to laboratory energy of 10⁴ TeV is greater than 0.55, and that an energy-independent value of 0.55 is in contradiction with the data we consider at any cross-section which is consistent with the cosmic ray experimental data and for any composition of primary cosmic rays from so-called normal to super-heavy. The quark gluon string model with k_tot increasing up to 0.84 at 10⁴ TeV and the inelastic charge-exchange probability of 0.3-0.5 fits well the data used.