  Motivated by sequential budgeted allocation problems, we investigate online
matching problems where connections between vertices are not i.i.d., but they
have fixed degree distributions -- the so-called configuration model. We
estimate the competitive ratio of the simplest algorithm, GREEDY, by
approximating some relevant stochastic discrete processes by their continuous
counterparts, that are solutions of an explicit system of partial differential
equations. This technique gives precise bounds on the estimation errors, with
arbitrarily high probability as the problem size increases. In particular, it
allows the formal comparison between different configuration models. We also
prove that, quite surprisingly, GREEDY can have better performance guarantees
than RANKING, another celebrated algorithm for online matching that usually
outperforms the former.
