Failure detector in timing model

There are basically 3 timing models.

1. Synchronous
2. Asynchronous
3. Partial Synchronous

Synchronous

Where we know the upper bound for communication time, computation time and the time difference for the physical clock. Which means we know the upper bound of response for a process.

Asynchronous

Where we do not have any idea of time bound and we can not make any assumption about time.

Partial Synchronous

When we assume that after some finite time the system becomes synchronous.

Now let us consider different timing models on the failure detectors. For any failure detector completeness property can be satisfied by any timing model as it is a liveness property and can be satisfied in later execution.

So the property to worry about is the accuracy property. For details see here.

Strong Accuracy

Can only be satisfied in synchronous system. Because strong accuracy does not allow to detect a correct node as failed even once. To check if a node is alive we use heartbeat technique. Which introduces a timeout to check the pulse to determine the node failure. In synchronous model we can specify a time out and be happy with it, because we know the time bound of the system. But for asynchronous system we do not have any time bound and can not assume anything about time. So any kind of timeout is meaningless in asynchronous model. 

So strong accuracy(Perfect failure detector) is only achievable by synchronous system.

Eventual Strong Accuracy

Well it is same as strong accuracy only that it is given a some finite time to get strong accurate. So it is implementable in partial synchronous model. As partial synchronous gets synchronous eventually.

Weak Accuracy

weak accuracy says that at least one correct node will not be suspected by other correct nodes. That weakens strong accuracy by reducing the number of correct nodes that are not suspected. But never the less we have to ensure accuracy for one node which does not allows us to reduce our timing model to less then synchronous model. At least there should be one node with every one is well connected. And for those links the timing synchrony holds.

Eventual Weak Accuracy

Then it turns out that the timing model of Eventual weak Accuracy will be same as Eventual Strong Accuracy.