  Type-I X-ray bursts are rapid-brightening transient phenomena on the surfaces
of accreting neutron stars (NSs). Some X-ray bursts, called {\it clocked
bursters}, exhibit regular behavior with similar light curve profiles in their
burst sequences. The periodic nature of clocked bursters has the advantage of
constraining X-ray binary parameters and physics inside the NS. In the present
study, we compute numerical models, based on different equations of state and
NS masses, which are compared with the observation of a recently identified
clocked burster, 1RXS J180408.9$-$342058. We find that the relation between
accretion rate and recurrence time is highly sensitive to the NS mass and
radius. We determine, in particular, that 1RXS J180408.9$-$342058 appears to
possess a mass less than $1.7M_{\odot}$ and favors a stiffer nuclear equation
of state (with an NS radius $\gtrsim12.7{\rm km}$). Consequently, the
observations of this new clocked burster may provide additional constraints for
probing the structure of NSs.
