A distributed system protocol is implemented over a communication service with omission failures to provide at-least-once invocation semantics. In the first case the implementor assumes an asynchronous distributed system. In the second case the implementor assumes that the maximum time for the communication and the execution of a remote method is T. In what way does the latter assumption simplify the implementation?

In the second case, an omission failure observed by the client cannot   be due to the server taking too long

Explanation:

In the first case, the implementor assumes that if the client observes an omission failure it cannot tell whether the omission is because  of loss of the request or reply message, or because of the server having crashed or having taken longer than usual. Therefore when the request  is re-transmitted the client may receive late replies to the original  request. The implementation must deal with this.  In the second case, therefore, when the request is re-ransmitted after time T, it is certain that a late reply will not  come from the server. There is no need to deal with late replies. In  this way, the implementation is simplified.

Sorry do not know but if you need with math, i will

It can sometimes be called a process chart.