Scenario: Pipeline

The Pipeline scenario is chosen to investigate the effects of delay propagation. The main issue is whether the calculated delay value from the processing of the first message is sufficient to correctly adjust the variables when the second message is processed. Figure 8 shows the two cases based on the relationship of the adjusted delay value ($x2'$) sent by P2 to P3, and the overhead and waiting time on P3. (Like our earlier models, we assume here for simplicity that this is the first message P3 receives. Clearly, in this case, $x3 = o3$.)

Figure 8: Three-Process, Pipeline - Models and Analysis

The interesting outcome of the models is that the analysis and update of P3's variables during the processing of the second message is effectively independent of the first message. Of course, the $x2'$ delay value sent from P2 is derivative of the effects of the first message and $x1$, but the expressions are invariant compared to those when P2 sends a message to P3 without first receiving a message from P1 (i.e., the Two-Process, General scenario). This conclusion extends to cases where there is an arbitrary number of processes in the pipeline.