Total order broadcast and multicast (also called atomic broadcast/multicast) present an important problem in distributed systems, especially with respect to fault-tolerance. In short, the primitive ensures that messages sent to a set of processes are, in turn, delivered by all those processes in the same total order.
/lp/association-for-computing-machinery/total-order-broadcast-and-multicast-algorithms-taxonomy-and-survey-HDbOOueeIb