Forwarding and Optical Indices in an All-Optical BCube Networks

Optical technologies based on Wavelength Division Multiplexing (WDM) are gaining popularity for Data Center Networks (DCNs) due to their technological strengths such as low communication latency, low power consumption, and high link bandwidth. Observe that the BCube networking topology has been widely applied to modular DCNs due to its high scala-bility and cost effectiveness. Therefore, it is worth investigating optical techniques into BCube DCNs. Routing and Wavelength Assignment (RWA) is a critical problem in optical networks, which can be formulated as an integer programming problem. To gain better insights into RWA solutions, researchers proposed two concepts: the forwarding and optical indices. Consider the all-to-all traffic in an all-optical network, where every host sets up a connection with every other host. The optical index is defined as the minimum number of wavelengths, required to support simultaneous all-to-all communication, under the restriction that each connection is assigned a fixed wavelength. The forwarding index is measured to be the minimum of maximum link loads over all possible all-to-all routings, where we define the maximum link load as the maximum number of paths passing through any link, and define an all-to-all routing as a set of paths specified for all host pairs. In this paper, we study the forwarding and optical indices of an all-optical BCube DCN. First, we compute the forwarding index, which is also a natural lower bound of the optical index. Second, we propose an oblivious RWA scheme, which is further used to derive an upper bound of the optical index. Finally, we derive a tighter upper bound of the optical index by means of the chromatic numbers in Graph Theory.