Wilhelm, U. G.Schiper, A.2005-05-202005-05-202005-05-20199510.1109/RELDIS.1995.526218https://infoscience.epfl.ch/handle/20.500.14299/213899WOS:A1995BE11Q00012The increased interest in protocols that provide a total order on message delivery has led to several different definitions of total order. In this paper we investigate these different definitions and propose a hierarchy that helps to better understand the implications of the different possibilities in terms of guarantees and communication cost. We identify two definitions: {\em weak total order} and {\em strong total order}, which are at the extremes of the proposed hierarchy, and incorporate them into a consistent design. Finally, we propose high-level algorithms based on a virtually synchronous communication environment that implement the given definitions.text::conference output::conference proceedings::conference paper