  We study the online stochastic matching problem. Consider a bipartite graph
with offline vertices on one side, and with i.i.d.online vertices on the other
side. The offline vertices and the distribution of online vertices are known to
the algorithm beforehand. The realization of the online vertices, however, is
revealed one at a time, upon which the algorithm immediately decides how to
match it. For maximizing the cardinality of the matching, we give a
$0.711$-competitive online algorithm, which improves the best previous ratio of
$0.706$. When the offline vertices are weighted, we introduce a
$0.7009$-competitive online algorithm for maximizing the total weight of the
matched offline vertices, which improves the best previous ratio of $0.662$.
  Conceptually, we find that the analysis of online algorithms simplifies if
the online vertices follow a Poisson process, and establish an approximate
equivalence between this Poisson arrival model and online stochstic matching.
Technically, we propose a natural linear program for the Poisson arrival model,
and demonstrate how to exploit its structure by introducing a converse of
Jensen's inequality. Moreover, we design an algorithmic amortization to replace
the analytic one in previous work, and as a result get the first
vertex-weighted online stochastic matching algorithm that improves the results
in the weaker random arrival model.
