A space-efficient self-stabilizing algorithm for measuring the size of ring networks

There are several execution models discussed in self-stabilizing systems. The simplest one is synchronous model, in which all privileged processors execute their actions at each step. Another one is called synchronized distributed model, in which an arbitrary nonempty subset of privileged processors execute their actions at each step. To carry out a step in the synchronous model or synchronized distributed model, logically, a global clock pulse is necessary to trigger the processors to execute actions. When the clock pulse comes, a privileged processor decides whether it executes its action or not. Moreover, an action is completed before the next clock pules comes. Getting rid of this clock pulse comes the distributed model, in which a privilege processor executes its action whenever it wants. In this paper, it is assumed that the system works under synchronized distributed model.