Using experimental techniques developed previously by the authors, the combustion wave microstructure in a gas-solid reaction system (specifically, the Ti-N-2 system) was studied. A quantitative analysis of the location, shape and propagation of the combustion wave front was carried out. The relay-race mechanism of combustion wave propagation was observed for a wide range of experimental conditions. In conjunction with the experiments, a micro-heterogeneous cell model was developed that simulates the local propagation of the combustion wave in a random porous medium. For both experiments and calculations, the initial organization of the reaction medium (porosity, particle size, etc.) was found to affect the heterogeneity of the combustion wave. The fluctuations of the combustion wave, in terms of both shape and propagation, increased monotonically with increasing heterogeneity of the reaction medium (i.e., larger porosity or particle size).