We construct a new, simple model of the heavy ion collision. This model is local in the impact parameter plane and appropriate for the CERN Super Proton Synchrotron (SPS) energy range. It can be regarded as a new realization of the “fire-streak” approach, originally applied to studies of lower energy reactions. Starting from local energy and momentum conservation, we nicely describe the whole centrality dependence of the pion rapidity distribution in Pb+Pb collisions at √sNN =17.3 GeV. In particular we explain the broadening of the pion rapidity distribution when going from central to peripheral collisions. The results of our calculations are compared to experimental data from the NA49 detector at the SPS. We discuss the resulting implications on the role played by energy and momentum conservation for the dynamics of particle production in the heavy ion collision. We conclude that the latter conservation laws play a dominant role in the centrality dependence of the absolute size and shape of pion rapidity spectra. A specific space-time picture emerges, where the longitudinal evolution of the system strongly depends on the position in the impact parameter (bx, by) plane. In non-central collisions we predict the existence of “streams” of excited matter moving very close to the spectator system in configuration (x, y, z) space. This picture is consistent with our earlier findings on the longitudinal evolution of the system as deduced from electromagnetic effects on charged pion directed flow and charged pion ratios.