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Multicomponent dark matter with self-interactions, which allows forinter-conversions of species into one another, is a promising paradigm that isknown to successfully and simultaneously resolve major problems of theconventional $\Lambda$CDM cosmology at galactic and sub-galactic scales. Inthis paper, we present $N$-body simulations of the simplest two-component(2cDM) model aimed at studying the distribution of dark matter halos withmasses $M\lesssim10^{12}M_\odot$. In particular, we investigate how the maximumcircular velocity function of the halos is affected by the velocity dependenceof the self-interaction cross-sections, $\sigma(v)\propto v^a$, and comparethem with available observational data. The results demonstrate that the 2cDMparadigm with the range of self-interaction cross-section per particle mass(evaluated at $v=100$ km s$^{-1}$) of $0.01\lesssim \sigma_0/m\lesssim 1 $cm$^2$g$^{-1}$ and the mass degeneracy $\Delta m/m\sim 10^{-7}-10^{-8}$ isrobustly resolving the substructure and too-big-to-fail problems by suppressingthe substructure having small maximum circular velocities, $V_{\rmmax}\lesssim100$ km s$^{-1}$. We also discuss the disagreement between theradial distribution of dwarfs in a host halo observed in the Local Group andsimulated with CDM. This can be considered as one more small-scale problem ofCDM. We demonstrate that such a disagreement is alleviated in 2cDM. Finally,the computed matter power-spectra of the 2cDM structure indicate the model'sconsistency with the existing Ly-$\alpha$ forest constraints.

Dark matter halos in the multicomponent model. I. Substructure