The study of hadrons production in relativistic heavy ion collisions at STAR provides the researchers with valuable techniques to investigate the properties of quark gluon plasma (QGP) and the subsequent hadronizations. In the present work, we are going to investigate the asymmetry in hadron and anti-hadron productions at the relativistic heavy ion collisions with parameters; Δϕ: the azimuthal angle of the transverse momentum vector (p_t ) ⃗ with respect to the reaction plane, p_t: the transverse momentum, η:seudo rapidity, and Y: the rabidity, and allowing for event by event (i.e. local) studies. HIJING and HYDJET++ models are used to explain the data of the experiments produced at the RHIC for Au-Au relativistic collision by STAR, PHENIX, and BRAHMS experiments. Hadrons and the anti-hadrons productions are based on Monte Carlo techniques in the models. The particles selected for this study are proton and lambda (P^±,〖 Λ〗^± ) for baryons, and pi and kaon (π^±,κ^±) for mesons in order to determine the most probable production-asymmetries regions in phase-space of hadrons and anti-hadrons for heavy ions 〖^197〗 Au_79 -〖^197〗 Au_79 collisions at √(S_NN )=200 GeV with about ≥800 events, which are generated from each model event generator. It is found that, HYDJET++ 2.0.2 event generator is more realistic in comparing the results of simulations with those of the experimental data published by the BRAHMS, PHENIX, and STAR Collaboration.