Convergence/response tradeoffs in concurrent systems

A self-stabilizing system is one which if started at any unsafe state, is guaranteed to converge to a safe state within a finite number of state transitions. The convergence span of such a system is defined as the maximum number of critical transitions that can be executed before the system reaches a safe state. The authors discuss the tradeoff between the convergence span of a self-stabilizing system and its response span. In particular, they argue that the convergence span can be reduced by some factor by increasing the response span by the same factor, and vice versa. The discussion is centered on a class of self-stabilizing systems for detecting termination on a uni-directional ring