Tight bounds for weakly-bounded protocols

Abstract

In this paper we present tight bounds on the efficiency of protocols that transmit messages through a communications channel that can lose and recorder packets and discuss new ways to measure the behavior of such protocols. The contributions are: 1. We show the existence of weakly-bounded protocols. This class of protocols, introduced by Lynch et al. [LMF88], have the property that they can recover from faults in the channel after the next message is delivered. Lynch et al. showed the impossibility of O(1)-weakly-bounded protocols whereas we have a protocol with bound O(n). This also shows that the notion of boundedness used by Lynch et al. and that used by Wang and Zuck [WZ89] and Mansour and Schieber [MS89] are different. 2. We introduce three characteristics of protocols: ideal transmission cost which describes how many packets the protocol requires when the channel is behaving ideally, recovery cost which describes how quickly the protocol can recover from a channel fault, and lookahead which decribes how much of the input sequence the Sender uses to guide its operation. These characteristics serve to unify and extend previous results in this area. 3. We show that protocols with constant recovery cost and constant lookahead must have ideal transmission cost Ω(n). This matches our upper bound, as weakly-bounded protocols correspond to those with recovery cost 1 and lookahead 0.