  The increase in strangeness production with charged particle multiplicity, as
seen by the ALICE collaboration at CERN in p-p, p-Pb and Pb-Pb collisions, is
investigated in the hadron resonance gas model taking into account interactions
among hadrons using S-matrix corrections based on known phase shift analyses.
Strangeness conservation is taken into account in the framework of the
canonical strangeness ensemble. A very good description is obtained for the
variation of the strangeness content in the final state as a function of the
number of charged hadrons in the mid-rapidity region using the same fixed
temperature value as obtained in the most central Pb-Pb collisions. It is shown
that the number of charged hadrons is linearly proportional to the volume of
the system. For small multiplicities the canonical ensemble with local
strangeness conservation restricted to mid-rapidity leads to a stronger
suppression of (multi-)strange baryons than seen in the data. This is
compensated by introducing a global conservation of strangeness in the whole
phase-space which is parameterized by the canonical correlation volume larger
than the fireball volume at the mid-rapidity. The results on comparing the
hadron resonance gas model with and without S-matrix corrections, are presented
in detail. It is shown that the interactions introduced by the phase shift
analysis via the S-matrix formalism are essential for a better description of
the yields data.
