To realize the cooperation of a group of multiple peer processes (peers), messages sent by peers must be causally delivered to every peer. In a scalable group, it is necessary to reduce the communication overhead to causally deliver messages. In this paper, the authors take advantage of the linear time (LT) and physical time (PT) protocols, as the message length is O(n) for the number n of peers. However, some pairs are unnecessarily ordered, that is, even if a pair of messages is ordered in the protocols, the messages may not be causally ordered. The greater the number of messages that are unnecessarily ordered, the larger the overhead is implied since the messages must be kept in a receipt queue if a message is lost or delayed. This paper discusses a hybrid time group communication (HT) protocol that reduces the number of messages unnecessarily ordered. The HT protocol is evaluated in terms of the number of unnecessarily ordered messages compared with the PT and LT protocols. It is demonstrated that the number of unnecessarily ordered messages can be reduced in the HT protocol compared with the LT and PT protocols.
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