During the last decade, Kriging-based sequential algorithms like EGO and its variants have become reference optimization methods in computer experiments. Such algorithms rely on the iterative maximization of a sampling criterion, the expected improvement (EI), which takes advantage of Kriging conditional distributions to make an explicit trade-off between promizing and uncertain search space points. We have recently worked on a multipoints EI criterion meant to simultaneously choose several points, which is useful for instance in synchronous parallel computation. Here we propose extensions of these works to asynchronous parallel optimization and focus on a variant of EI, EEI, for the case where some new evaluation(s) have to be done while the reponses of previously simulations are not all known yet. In particular, different issues regarding EEI's maximization are addressed, and a proxy strategy is proposed.