International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Estimating the size of a multi-agent system (MAS) is a fundamental task with applications in routing, resource management, distributed coordination, etc. Achieving accurate network size estimation in MASs is challenging due to the absence of a central authority, lack of global identifiers, dynamic network changes, communication constraints, etc. This paper investigates the applicability of distributed consensus algorithms with asymptotic convergence for estimating MAS size. Specifically, we examine the average consensus algorithm using four different weighting schemes: Maximum Degree (MD), Metropolis-Hastings (MH), Best Constant (BC), and Convex Optimized (OW) weights. Experimental results on a random geometric graph demonstrate that all weighting schemes enable agents’ internal states to asymptotically converge to the value 1/n, where n is the total number of agents. Differences among the schemes are observed in convergence speed and early-stage oscillations, with BC providing the fastest convergence and OW exhibiting more initial fluctuations. Overall, the study confirms that distributed average consensus algorithms with the examined weights can effectively estimate network size in MASs.

This paper discusses a case of implementing Industry 4.0 solutions with existing legacy informational system in cement-producing factory. One of the main reasons the company wants to keep its existing ERP solution is because is too complex and cannot be ported to a contemporary computer architecture. The plant also needs to automate and modernize the process of loading their products, but the company management does not want to invest in modern computer servers and a new ERP system. That’s why they decided to implement a hybrid solution – a modern Industry 4.0 IoT devices with .NET client application using the existing legacy DEC Alpha as a server. Here, the required technologies used for developing that software solution are overviewed and all parts of the software solution are described. Finally, the benefits and effectiveness of such a hybrid software solution are shown.