D.W. Embley, A. Olivé, and S. Ram (Eds.): ER 2006, LNCS 4215, pp. 155 – 167, 2006. © Springer-Verlag Berlin Heidelberg 2006 Modeling Visibility in Hierarchical Systems * Debmalya Biswas 1 and K. Vidyasankar 2 1 IRISA-INRIA, Campus Universitaire de Beaulieu Rennes, France 35042 dbiswas@irisa.fr 2 Dept. of Computer Science, Memorial University of Newfoundland St. John’s, NL, Canada A1B 3X5 vidya@cs.mun.ca Abstract. We consider hierarchical systems where nodes represent entities and edges represent binary relationships among them. An example is a hierarchical composition of Web services where the nodes denote services and edges repre- sent the parent-child relationship of a service invoking another service. A fundamental issue to address in such systems is, for two nodes X and Y in the hierarchy whether X can see Y, that is, whether X has visibility over Y. In a general setting, X seeing Y may depend on (i) X wishing to see Y, (ii) Y wish- ing to be seen by X, and (iii) other nodes not objecting to X seeing Y. The visibility could be with respect to certain attributes like operational details, exe- cution logs, security related issues, etc. In this paper, we develop a generic con- ceptual model to express visibility. We study two complementary notions: sphere of visibility of a node X that includes all the nodes in the hierarchy that X sees; and sphere of noticeability of X that includes all the nodes that see X. We also identify the dual properties, coherence and correlation, that relate the visibility and noticeability notions. We propose elegant methods of constructing the spheres with these properties. Keywords: Visibility, Noticeability, Hierarchical Systems, Hierarchical Web Services Compositions, Coherence, Correlation. 1 Introduction Hierarchical systems are prevalent everywhere. While hierarchical systems provide an elegant mechanism to analyze the system functionality at different levels of abstrac- tion, most of them allow interaction only between adjacent (parent-child) layers. Such restricted means of communication are often not sufficient for real-life scenarios. For example, in a supply chain management system, [1] states the need for visibility across levels as follows: “The information required by downstream entities are mainly mate- rial and capacity availability information from their suppliers. The information ac- quired by an upstream entity is information about customer demand and orders. The depth of information penetration can be specified in various degrees, e.g., isolated, * Debmalya Biswas’s work is supported by the RNRT (French ministry of research) project SWAN, decision No. 03 S 481. K Vidyasankar’s work is supported in part by the Natural Sciences and Engineering Research Council of Canada Discovery Grant 3182.