Quantitative approach to dynamic networks

We present a quantitative approach to dynamic networks. Dynamic networks, extensively studied in the last decade, are asynchronous networks with arbitrary topology, in which links and processors repeatedly fail and recover. Loosely speaking, we quantify the reliability of a link at a given moment as the time since the link last recovered. This quantitative definition allows us to investigate protocols that either assume a certain amount of reliability, or provide service only to sufficiently reliabile parts of the network. There are several tasks which cannot be solved efficiently when defined in the known (qualitative) approaches, but may be solved efficiently using the new quantitative definitions We demonstrate this on the broadcast task. Broadcast is basically an order preserving transmission of a sequence of messages from a source processor to all other processors. Every processor which satisfies some fairness condition should accept the messages. This requires unbounded resources, if the fairness is defined using the known (qualitative) approaches. Hence, we give a new fairness definition, based on our new, quantitative approach. We then present an efficient protocol which achieves broadcast (with this fairness definition). This is the first broadcast protocol which is tolerant of processor crashes. The protocol has linear communication and time complexities. We also present quantitative definitions, and efficient solutions, for the end-to-end communication and topology update tasks. The solutions have the same properties as our broadcast protocol, with an additional overhead. per processor crash. In contrast, previous end-to-end protocols are not resilient to processor crashes; and previous topology update protocols (resilient to processor crashes) have exponential communication complexity.