Combining Decomposition and Lumping to Evaluate Semi-hierarchical Systems

Abstract

Abstract-Determining performance and fault tolerance properties of distributed systems is a challenging task. One common approach to quantify such properties is to construct the state space and a transition model of the distributed system that is to be evaluated. The challenge lies in the state space being exponentially large in the size of the system. One popular approach to tackle this challenge is to combine decomposition and lumping. The system is decomposed, transition models of the subsystems are constructed and minimized by lumping bisimilar states under an equivalence relation, and the intermediate marginal transition systems are composed to construct the minimal aggregate transition model. The approach allows to circumvent the necessity to construct a full transition model while preserving the ability to compute precise measures. The decomposition yet hinges on the structure of the communication within the system. When processes do not influence each other, decomposition is trivial as it is arbitrary. On the contrary, when all processes are influenced by all other processes -known as heterarchical structure -systems cannot be decomposed at all. Between systems of independent and heterarchical processes are i) hierarchically structured systems and ii) systems that are globally hierarchical, but contain locally heterarchical subsystems. The hierarchical type has been addressed elsewhere. This paper targets the second typereferred to as semi-hierarchically structured -, thus expanding the frontier from decomposing purely hierarchically structured systems to decomposing semi-hierarchically structured systems. Furthermore, this paper points out the role of different types of execution semantics regarding the decomposition.

40 years of research on eating disorders in domain-specific journals: Bibliometrics, network analysis, and topic modeling

“…The latter assumes that behavior is directed in a hierarchical fashion, where a central authority passes instructions to all agents in the system [ 54 ]. Second, although it still recognizes a hierarchical structure composed by diverse classes of subsystems, it assumes heterarchy [ 43 , 61 ], which means that both hierarchical and nonhierarchical elements can be present in a system; holarchy , which means that systems are composed of components that can be recognized as subsystems [ 62 ]; and glocal control , which means that local and global phenomena in a system are achieved by local actions [ 63 ]. In simple words, sampling a set of domain-specific journals reduces complexity without affecting assumptions such as a categorical hierarchy of journals.…”