  We present a systematic study of the kaon to pion multiplicity ratios (K+/pi+
and K-/pi-) in heavy-ion collisions from AGS to RHIC energy using the
Relativistic Quantum Molecular Dynamics (RQMD) model. The model satisfactorily
describes the available experimental data on K+/pi+ and K-/pi-. Within the
model, we find that the strong increase of the ratios with the number of
participants is mainly due to hadronic rescattering of produced mesons with
ingoing baryons and their resonances. The enhancement of K/pi in heavy-ion
collisions with respect to elementary p+p interactions is larger at AGS energy
than SPS energy, and decreases smoothly with bombarding energy. The total
multiplicity ratios at RHIC energy are predicted by RQMD to be K+/pi+ = 0.19
and K-/pi- = 0.15.
