A positive acknowledgment protocol for causal broadcasting

Causal broadcasting has been introduced to reduce the asynchrony of communication channels inside groups of processes. It states that if two broadcast messages are causally related by the happened-before relation, these messages are delivered in their sending order to each process of the group. Even though protocols implementing causal broadcasting do not add control messages, they suffer from the typical pitfall of the timestamping technique: To ensure causal ordering, application messages have to piggyback a vector time of counters whose range of variation is unbounded. In this paper, we investigate such a range and define the concept of causal window of a process in which all counters of a vector time of a just arrived message at that process fall. We prove that, by using a causal broadcasting (one-to-all) protocol that follows a positive acknowledgment method, the width of the causal window of each process is limited. This allows a modulo k implementation of vector times when considering k greater than the width of the causal window of each process. The protocol is applicable to data link or transport layers using acknowledge messages to ensure reliable transfer of data. The paper also proposes two variants of the protocol based on causal windows. Both of them increase the concurrency of the protocol at the expense of wider causal windows.