Y. Villacampa, F. Verdú and A. Pérez
The purpose of this paper is to carry out a theoretical study of the stability of the mathematical models defined in a class of systems. Furthermore, it will be supposed that the…
Abstract
Purpose
The purpose of this paper is to carry out a theoretical study of the stability of the mathematical models defined in a class of systems. Furthermore, it will be supposed that the models have been obtained from experimental data and by means of the application of a methodology. The studies carried out in this paper are, on one hand, the theoretical framework for an analysis of the sensitivity and stability of a type of systems; on the other hand, they supplement the studies carried out by the authors, in which, using a computational program, the sensitivity of the mathematical models is analyzed with respect to a type of perturbation.
Design/methodology/approach
Initially, a class of systems is considered that are denominated quantifiable systems, in which model systems are defined that are determined by a set and a family of relationships. An initial study of the sensitivity of the mathematical models to perturbations in the experimental data lead to a concept of sensitive and stable models that forms the basis of the theory of stability developed in this paper. Furthermore, this permits a definition of the stability function for the set of the perturbations and, consequently, a determination of stable models according to the defined theoretical structure.
Findings
An analysis of the sensitivity and stability of mathematical models in quantifiable systems from a systems theory perspective will be fundamental for the determination of mathematical model stability in environmental systems.
Originality/value
The studies carried out in this paper supposes an advance in the study and modeling of a type of systems that the authors have denominated as quantifiable systems, applicable to the study of environmental systems and supplementing the numeric studies carried out by the authors.
Details
Keywords
Ailixier Aikebaier, Makoto Takizawa, Isamu Tsuneizumi, Makoto Ikeda and Tomoya Enokido
A group of n (> 1) peers are required to cooperate with each other in distributed applications on P2P overlay networks. A P2P group is distributed without a centralized controller…
Abstract
Purpose
A group of n (> 1) peers are required to cooperate with each other in distributed applications on P2P overlay networks. A P2P group is distributed without a centralized controller and is scalable and heterogeneous. The purpose of this paper is to discuss how to realize a scalable group in P2P overlay networks.
Design/methodology/approach
In a group, messages have to be causally delivered to every peer. In order to realize a scalable group, messages are ordered by taking advantage of linear time (LT) and physical time (PT) since message length is O(1). Here, each peer has to hold information on the accuracy of physical clock of each peer and minimum delay time among every pair of peers. Since the size of the information is O(n2), it is difficult for each peer to hold the information and so the authors discuss a multi‐layered model to reduce the size of group information.
Findings
Through the evaluation studies, it is shown how the size of the group information can be reduced in a multi‐layered group compared with a traditional flat group.
Originality/value
In this paper, the authors discuss a multi‐layered group model for a scalable group, to reduce the size of group information; and also order messages by using both the linear time and physical time.