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Abstract The chemical abundances of Milky Way’s (MW's) satellites reflect their star formation histories (SFHs), yet, due to the difficulty of determining the ages of old stars, the SFHs of most satellites are poorly measured. Ongoing and upcoming surveys will obtain around 10 times more medium-resolution spectra for stars in satellites than are currently available. To correctly extract SFHs from large samples of chemical abundances, the relationship between chemical abundances and SFHs needs to be clarified. Here, we perform a high-resolution cosmological zoom-in simulation of a MW-like galaxy with detailed models of star formation, supernova (SN) feedback, and metal diffusion. We quantify SFHs, metallicity distribution functions, and theα-element (Mg, Ca, and Si) abundances in satellites of the host galaxy. We find that star formation in most simulated satellites is quenched before infalling to their host. Star formation episodes in simulated satellites are separated by a few hundred Myr owing to SN feedback; each star formation event produces groups of stars with similar [α/Fe] and [Fe/H]. We then perform a mock observation of the upcoming Subaru Prime Focus Spectrograph (PFS) observations. We find that Subaru PFS will be able to detect distinct groups of stars in [α/Fe] versus [Fe/H] space, produced by episodic star formation. This result means that episodic SFHs can be estimated from the chemical abundances of ≳1000 stars determined with medium-resolution spectroscopy.