Selecting the best locations for data centers in resilient optical grid/cloud dimensioning

For optical grid/cloud scenarios, the dimensioning problem comprises not only deciding on the network dimensions (i.e., link bandwidths), but also choosing appropriate locations to install server infrastructure (i.e., data centers), as well as determining the amount of required server resources (for storage and/or processing). Given that users of such grid/cloud systems in general do not care about the exact physical locations of the server resources, a degree of freedom arises in choosing for each of their requests the most appropriate server location. We will exploit this anycast routing principle (i.e., source of traffic is given, but destination can be chosen rather freely) also to provide resilience: traffic may be relocated to alternate destinations in case of network/server failures. In this study, we propose to jointly optimize the link dimensioning and the location of the servers in an optical grid/cloud, where the anycast principle is applied for resiliency against either link or server node failures. While the data center location problem has some resemblance with either the classical p-center or k-means location problems, the anycast principle makes it much more difficult due to the requirement of link disjoint paths for ensuring grid resiliency

On equivalency of various geometric structures

In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann-Christoffel curvature tensor, the same type structure given by imposing same restriction on other curvature tensors being studied. The main object of the present paper is to study the equivalency of various geometric structures obtained by same restriction imposing on different curvature tensors. In this purpose we present a tensor by combining Riemann-Christoffel curvature tensor, Ricci tensor, the metric tensor and scalar curvature which describe various curvature tensors as its particular cases.Comment: The paper contains 27 pages, 3 tables and 2 tree diagra