Extended lamport time

The extended Lamport time or extended Lamport clock is an extension of the Lamport clock developed by Leslie Lamport .

The following applies to the Lamport period:

 ${\displaystyle LC(a)=LC(b)\not \Rightarrow a=b}$

In order to allow this implication, the time stamp of the Lamport clock is expanded to include additional information that is subject to total order. In the context of the Lamport watch, the name of the process would be possible here. The clock condition of the extended lamport time is defined as follows:

Let A be a process. Then let the extended Lamport time of the process A for an event e , and we have: ${\displaystyle LC_{E}(A,e)}$

 ${\displaystyle LC_{E}(A,a)<LC_{E}(B,b)\Leftrightarrow LC(a)<LC(b)\lor (LC(a)=LC(b)\land A<B)}$

This gives all events a unique time stamp, which is subject to a total order. The weak consistency condition is retained, because it applies (in the Happened-Before notation):

 ${\displaystyle a\Rightarrow b\Longrightarrow LC(a)<LC(b)\Longrightarrow LC_{E}(A,a)<LC_{E}(B,b)}$

With the extended Lamport time, the implication applies

 ${\displaystyle LC(a)=LC(b)\Rightarrow a=b}$