  We propose a non-equilibrium, hadronic kinetic model for describing the
relative abundance of strange particles in ultra-relativistic heavy-ion
collisions. The energy dependence of the multiplicity ratios of charged kaons
and lambdas to pions are studied in detail. The pronounced peak in positively
charged K/pi is conjectured to be due to the decreasing lifetime of a fireball
with an increase in beam energy above 30 AGeV. Such a behaviour may be the
consequence of a stronger stopping at lower beam energies. We study the
dependence of the multiplicity ratios on energy and baryon density of the
fireball and its total lifetime.
