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To meet the new engine regulations, increasingly sophisticated engine alternative combustion modes have been developed in order to achieve simultaneously the emission regulations and the required engine drivability. However, these new approaches require more complex, reliable and precise control systems and technologies. The 0-D model based control systems have proved to be successful in many applications, but as the complexity of the engines increases, their limitations start to affect the engine control performance. One of the 0-D modeling limitations is their inability to model mass transport time. 1-D modeling allows some of the 0-D models limitations to be overcome, which is the motivation of this work. In this paper, two quasi-steady outflow boundary models are developed: one is based on the isentropic contraction and the other on a momentum conservation approach. Both are compared with computational fluid dynamics (CFD) 3-D simulations.