  In this work we propose a model to describe the statistical fluctuations of
the self-driven objects (species A) walking against an opposite crowd (species
B) in order to simulate the regime characterized by stop-and-go waves in the
context of pedestrian dynamics. By using the concept of single-biased random
walks (SBRW), this setup is modeled both via partial differential equations and
by Monte-Carlo simulations. The problem is non-interacting until the opposite
particles visit the same cell of the considered particle. In this situation,
delays on the residence time of the particles per cell depends on the
concentration of particles of opposite species. We analyzed the fluctuations on
the position of particles and our results show a non-regular diffusion
characterized by long-tailed and asymmetric distributions which is better
fitted by some chromatograph distributions found in the literature. We also
show that effects of the reverse crowd particles is able to enlarge the
dispersion of target particles in relation to the non-biased case ($\alpha =0$)
after observing a small decrease of this dispersion
