Causal delivery of messages with real-time data in unreliable networks

Causal order states that for any process the order in which it is delivered messages cannot violate the happened-before relation of the corresponding sendings. Such a communication abstraction has been defined for reliable distributed systems in which data of application messages have unlimited time validity. In this paper we extend the notion of causal order to cope with unreliable communication networks in which messages have real-time delivery constraints. In particular, we assume that messages have a limited time validity, , after which their data can no longer be used by the application, and that some of them can be lost by the communication network. This new abstraction, called -causal order, requires to deliver as many messages as possible within their validity time in such a way that these deliveries respect causal order. Two efficient implementations are proposed in the case of one-to-one and broadcast communication. Examples of distributed multimedia real-time applications, in which scheduling messages deliveries respecting -causal order is a crucial point for the quality of the service, are given.