A Dynamic Random Graph Model for Diameter-Constrained Topologies in Networked Systems

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 61; no. 12; pp. 982 - 986
• Main Authors: Grieco, Luigi Alfredo, Ben Alaya, Mahdi, Monteil, Thierry, Drira, Khalil
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Circuits and systems; Computer Science; Couples; Delays; Dynamical systems; Dynamics; Graph theory; Graphs; Links; Mathematical model; Mathematical models; Network topology; Networks; Steady-state; Topology; Transient analysis; networks; topology; Graph theory; Networks; Topology; Overlay
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2014.2362676

Random graphs have been widely investigated in the literature because of their relevance to many scientific domains. In this brief, the attention is focused on diameter-constrained random graphs, which are useful in analyzing unstructured overlays for delay-bounded network applications and systems. To this end, a general process of arrivals is considered, which describes the sequence of vertex couples (i.e., node couples) among which a path composed of no more than D edges (i.e., links) has to be established. Accordingly, a topology formation mechanism M is formulated, expressing the rules that drive the addition of new edges, obeying to the constraint on the maximum diameter D. Third, using graph-theoretic arguments, an original discrete-time model is proposed, which describes the evolution of the average network degree (i.e., the average number of edges per node) subject to M and D. Fourth, the model is successfully validated using computer simulations in a wide range of scenarios (with up to 2 16 nodes). Finally, concrete examples are provided to illustrate useful applications of the proposed approach, also in the presence of link failures.