Grid topology

1. A Theoretical Framework for Mitigating Delay in3D Wireless Data Center NetworksKai ZhouAdvisor: Dr. Xiaohua Tian Recently, a novel 3D wireless mechanism based on 60 GHz band has been proposed to mitigate the job completion time (JCT) in Data Center Networks (DCNs), where signals bounce off DC ceilings to establish wireless connections. The 3D scheme could alleviate hotspots in DCNs with flexible multi-gigabit wireless links, which bypasses the line-of-sight limitation of 60 GHz wireless links. However, the novel wireless transmission mechanism incurs significant change in the traditional interference model for wireless networks, and the theoretical analysis tool for such hybrid networks is still unavailable. This paper presents a theoretical framework for such 3D DCNs, where the entire network is first transformed from 3D to 2D by remodeling the 3D interference effects. The transformed graph is then processed with a multi-dimensional conflict graph methodology, where the wired and wireless sub-graphs induced by the DCN topology are jointly analyzed. The last but not least, the processed graph is modeled as a minimum job completion time (MJCT) problem, where the optimal traffic engineering, channel allocation and scheduling schemes in the original DCN can be obtained. Simulation results are presented to demonstratethe delay performance of our proposed approach. • Modified Multiple Commodity Flow (MCF) problem: calculate the flow distribution on each wired and wireless link. • Convex optimization problem: allocate flows evenly among the links to minimize the job completion time • Subject to: • Flow balance constrains • Radio interface constrains • MIS constrains Modified MCF problem 3 Modeling Interference 5 Contributions • Protocol model: • Links separated far away enough will not cause interference to each other • Receivers out of the signal coverage of other transmitters will not be interfered • Joint Traffic engineering , Channel allocation and Scheduling (TCS) scheme • Traffic engineering: flow assignment on each link • Channel allocation: tuples in conflict graph • Scheduling: time fraction each MIS occupies 1 3D Wireless Data Centers 6 Performance Evaluation Rack Ceiling Protocol model • Conflict graph: • the node in the conflict graph is a tuple consisting of a ink , the radios utilized by the transmission nodes and the channel occupied by this link • Conflict condition: • E1 According to the protocol interference model, the nodes in two different tuples are with in each other’s interference range. • E2 The links in two different tuples are occupying the same channel. • E3 Two different tuples share common radio interfaces at one or two nodes. • two tuples in the MDCG as in conflict with each other if the condition E1E2E3 ∪E3 is true. 3D beamforming Grid topology • Basic structure: • A data center is consist of hundreds of racks that are organized in a grid topology and inter-connected by wire line • .Each rack contains several servers which have data transmission demands to other severs. • Augmenting 60 GHz wireless technology with DC • On top of each rack, there is a switch for data transferring and multi-radios to establish wireless transmission. • Radios are controlled by electrical motors to set the beams in the right directions with high accuracy and speed. • Beams are bounced off the ceiling to reach the right destination within one hop • Advantages: • Wireless links with capacity up to multi-gigabit are set up and scheduled in demand to alleviate hot spot problem • Interference is greatly reduced Simulation topology 2 Joint TCS scheme design Flow completion time with different number of flows Joint TCS scheme design Conflict graph • A central controller connected to each rack • gathering flow demands from each rack • executing algorithm to give the Traffic engineering, Channel allocation and Scheduling (TCS) result. • sending commands to each rack for flow transmission • Maximum Independent Set: • a set of tuples where no edge exists between two tuples indicating that the links involved in the tuples can be active simultaneously and adding one more tuple to this independent set will make it nonindependent • Each MIS is allocated to a time fraction α Wired links • Wireless links with scaled capacity Wireless links Flow completion time with different number of channels and radio interfaces 4 Minimum job completion time 7 Related Publication Coexisted wired links with scaled capacity • Flow transmission time on each link Kai Zhou, XiaohuaTian and Yu Cheng, “A Theoretical Framework for Mitigating Delay in 3D Wireless Data Center Networks”, submitted to IEEE ICC 2013 • Interfered wireless links are formulated to equivalent coexisted wired links with scaled capacity