Continuity Equation of Human Effort (Dynamic Equilibrium between the Difficulty of Human Labor and the Capabilities of the Work Performers)


By Pavel Barseghyan, PhD

Dallas, USA and Yerevan, Armenia


Flow or flux approach to the quantitative description of various transport phenomena and processes is a key means of quantitative fundamental science. The results of this approach are the continuity equations, which are the cornerstones of such sciences as thermodynamics, electrodynamics, hydrodynamics, quantum mechanics, and many others.

From the point of view of mathematical modeling one of the main advantages of flow or flux approach is that it combines in a harmonic way fundamental quantitative description of various transport phenomena and processes occurring in space and time.

People’s actions and all their activities are also flows through time and space and, therefore, can be described by fundamental methods and approaches already developed in other areas of quantitative science.

In this paper, considering the implementation of the project as a flow of decisions in time and space, are being investigated fundamental functional relationships between such dynamic parameters of projects as its complexity, size, difficulty, time and productivity of the team in the form of the equations of continuity.

In particular, the obtained results indicate that the productivity of the team is the time derivative of the dynamic complexity of work, and the difficulty of the work is a derivative of the same dynamic complexity of work with respect to the current size of the work done.


Continuity equations are relevant fundamental means to many areas of quantitative science, including electrodynamics, fluid dynamics, thermodynamics, wave theory, quantum mechanics, the theory of traffic flow and more.

The main role of the continuity equations is that the adequate qualitative and quantitative representation of flows of different physical nature in time and space. In this connection it is necessary to emphasize that, regardless of the physical nature of the flow under study, whether the flow of heat, the flow of particles, or the flow of probability, the structure and mechanism of their quantitative representation in general remains the same [1].


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About the Author

pavel-barseghyanflag-Armenia-USAPavel Barseghyan, PhD    

Dr. Pavel Barseghyan is a consultant in the field of quantitative project management, project data mining and organizational science. Has over 40 years experience in academia, the electronics industry, the EDA industry and Project Management Research and tools development. During the period of 1999-2010 he was the Vice President of Research for Numetrics Management Systems. Prior to joining Numetrics, Dr. Barseghyan worked as an R&D manager at Infinite Technology Corp. in Texas. He was also a founder and the president of an EDA start-up company, DAN Technologies, Ltd. that focused on high-level chip design planning and RTL structural floor planning technologies. Before joining ITC, Dr. Barseghyan was head of the Electronic Design and CAD department at the State Engineering University of Armenia, focusing on development of the Theory of Massively Interconnected Systems and its applications to electronic design. During the period of 1975-1990, he was also a member of the University Educational Policy Commission for Electronic Design and CAD Direction in the Higher Education Ministry of the former USSR. Earlier in his career he was a senior researcher in Yerevan Research and Development Institute of Mathematical Machines (Armenia). He is an author of nine monographs and textbooks and more than 100 scientific articles in the area of quantitative project management, mathematical theory of human work, electronic design and EDA methodologies, and tools development. More than 10 Ph.D. degrees have been awarded under his supervision. Dr. Barseghyan holds an MS in Electrical Engineering (1967) and Ph.D. (1972) and Doctor of Technical Sciences (1990) in Computer Engineering from Yerevan Polytechnic Institute (Armenia).  Pavel’s publications can be found here: http://www.scribd.com/pbarseghyan and here: http://pavelbarseghyan.wordpress.com/.  Pavel can be contacted at [email protected]