Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability

Communication networks with endogenous link strength

This paper analyzes the formation of networks when players choose how much to invest in each relationship. We suppose that players have a fixed endowment that they can allocate across links, and in the baseline model, suppose that link strength is an additively separable and convex function of individual investments, and that agents use the path which maximizes the product of link strengths. We show that both the stable and efficient network architectures are stars. However, the investments of the hub may differ in stable and efficient networks. Under alternative assumptions on the investment technology and the reliability measure, other network architectures can emerge as efficient and stable

Communication Networks with Endogenous Link Strength

This paper analyzes the formation of communication networks when players choose endogenously their investment on communication links. We consider two alternative de?nitions of network reliability ; product reliability, where the decay of information depends on the product of the strength of communication links, and min reliability where the speed of connection is a¤ected by the weakest communication link. When investments are separable, the architecture of the efficient network depends crucially on the shape of the transformation function linking investments to the quality of communication links. With increasing marginal returns to investment, the efficient network is a star ; with decreasing marginal returns, the con?ict between maximization of direct and indirect bene?ts prevents a complete characterization of efficient networks. However, with min reliability, the efficient network must be a tree. Furthermore, in the particular case of linear transformation functions, in an e¢ cient network, all links must have equal strength. When investments are perfect complements, the results change drastically : under product reliability, the efficient network must contain a cycle, and is in fact a circle for small societies. With min reliability, the e¢ cient network is either a circle or a line. As in classical models of network formation, e fficient networks may not be supported by private invesment decisions. We provide examples to show that the star may not be stable when the transformation functions is strictly convex. We also note that with perfect substitutes and perfect complements (when the e¢ cient network displays a very symmetric structure), the e¢ cient network can indeed be supported by private investments when the society is large.communication networks ; network reliability

Communication networks with endogeneous link strength

This paper analyzes the formation of networks when players choose how much to invest in each relationship. We suppose that players have a fixed endowment that they can allocate across links, and in the baseline model, suppose that link strength is an additively separable and convex function of individual investments, and that agents use the path which maximizes the product of link strengths. We show that both the stable and efficient network architectures are stars. However, the investments of the hub may differ in stable and efficient networks. Under alternative assumptions on the investment technology and the reliability measure, other network architectures can emerge as efficient and stable.communication networks, network reliability, endogenous link strength