The sequential sampling strategies based on Gaussian processes are widely used for optimization of time consuming simulators. In practice, such computationally demanding problems are solved by increasing number of processing units. This has therefore induced extensions of sampling criteria which consider the framework of parallel calculation. This report further studies expected improvement criteria for parallel and asynchronous computations. A unified parallel asynchronous expected improvement criterion is formulated. Bounds and strategies for comparing criteria values at various design points are discussed. Finally, the impact of the number of available computing units on the performance is empirically investigated.