Time management services are one of the key features of the High Level Architecture (HLA) IEEE simulation standard. Several algorithms allow the implantation of HLA time management services ranging from the Chandy-Misra-Bryant (CMB) null message conservative algorithm up to optimistic Jefferson time warp one. For years now, we are interested in enhancing the high and/or real-time performance of our open source RTI (CERTI). In this paper, we precisely describe our updated conservative time management algorithm which, under some assumptions, limits the time creep problem inherent to the classical CMB algorithm. We will provide detailed analysis and experimental results for different implementations of HLA time management services using our new release version called CERTI 4.0.