“Critical” Terminology - Apropos of a Conjecture

In 1959 J. E. Kelley and. M. Walker had published their well-known and famous method to optimize project schedules with relative precedence restraints and with time-cost tradeoff characteristics at the individual activities (CPMcost). They had also elaborated basic terminology for interpreting results of calculations such as: Critical Activity, Critical Path, Total Float, Free Float, etc. that have been used in Network Techniques since then, though - meanwhile - newer and newer variants of “Network Techniques” have been developed (such as PERT, MPM, PDM, etc.) to assist solving scheduling problems. Due to differing correspondences of graph elements and of time parameters in the various time models, behavior of “critical activities” may differ - according to the specific model within the Network Techniques' family. Returning back to Kelley's original Directed Weighted Graph approach the paper presents a proposal for redefining and generalizing the term “Critical Path” while reviewing possible consequences of changing duration of “critical activities” it also offers a proposal for (re-) establishing a common terminology (set of references) of critical activities better indicating behavior of dominant elements of the network time models.