A Hierarchy of Totally Ordered Multicasts

The increased interest in protocols that provide a total order on message delivery has led to several diierent deenitions of total order. In this paper we investigate these diierent deenitions and propose a hierarchy that helps to better understand the implications of the diierent possibilities in terms of guarantees and communication cost. We identify two definitions: weak total order and 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 deenitions.