Optimal Placement Algorithms for Virtual Machines

Cloud computing provides a computing platform for the users to meet their demands in an efficient, cost-effective way. Virtualization technologies are used in the clouds to aid the efficient usage of hardware. Virtual machines (VMs) are utilized to satisfy the user needs and are placed on physical machines (PMs) of the cloud for effective usage of hardware resources and electricity in the cloud. Optimizing the number of PMs used helps in cutting down the power consumption by a substantial amount. In this paper, we present an optimal technique to map virtual machines to physical machines (nodes) such that the number of required nodes is minimized. We provide two approaches based on linear programming and quadratic programming techniques that significantly improve over the existing theoretical bounds and efficiently solve the problem of virtual machine (VM) placement in data centers

Service Chain (SC) Mapping with Multiple SC Instances in a Wide Area Network

Network Function Virtualization (NFV) aims to simplify deployment of network services by running Virtual Network Functions (VNFs) on commercial off-the-shelf servers. Service deployment involves placement of VNFs and in-sequence routing of traffic flows through VNFs comprising a Service Chain (SC). The joint VNF placement and traffic routing is usually referred as SC mapping. In a Wide Area Network (WAN), a situation may arise where several traffic flows, generated by many distributed node pairs, require the same SC, one single instance (or occurrence) of that SC might not be enough. SC mapping with multiple SC instances for the same SC turns out to be a very complex problem, since the sequential traversal of VNFs has to be maintained while accounting for traffic flows in various directions. Our study is the first to deal with SC mapping with multiple SC instances to minimize network resource consumption. Exact mathematical modeling of this problem results in a quadratic formulation. We propose a two-phase column-generation-based model and solution in order to get results over large network topologies within reasonable computational times. Using such an approach, we observe that an appropriate choice of only a small set of SC instances can lead to solution very close to the minimum bandwidth consumption

A Scalable Approach for Service Chain (SC) Mapping with Multiple SC Instances in a Wide-Area Network

Network Function Virtualization (NFV) aims to simplify deployment of network services by running Virtual Network Functions (VNFs) on commercial off-the-shelf servers. Service deployment involves placement of VNFs and in-sequence routing of traffic flows through VNFs comprising a Service Chain (SC). The joint VNF placement and traffic routing is called SC mapping. In a Wide-Area Network (WAN), a situation may arise where several traffic flows, generated by many distributed node pairs, require the same SC; then, a single instance (or occurrence) of that SC might not be enough. SC mapping with multiple SC instances for the same SC turns out to be a very complex problem, since the sequential traversal of VNFs has to be maintained while accounting for traffic flows in various directions. Our study is the first to deal with the problem of SC mapping with multiple SC instances to minimize network resource consumption. We first propose an Integer Linear Program (ILP) to solve this problem. Since ILP does not scale to large networks, we develop a column-generation-based ILP (CG-ILP) model. However, we find that exact mathematical modeling of the problem results in quadratic constraints in our CG-ILP. The quadratic constraints are made linear but even the scalability of CG-ILP is limited. Hence, we also propose a two-phase column-generation-based approach to get results over large network topologies within reasonable computational times. Using such an approach, we observe that an appropriate choice of only a small set of SC instances can lead to a solution very close to the minimum bandwidth consumption. Further, this approach also helps us to analyze the effects of number of VNF replicas and number of NFV nodes on bandwidth consumption when deploying these minimum number of SC instances.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0671

Bayesian Gait Optimization for Bipedal Locomotion

One of the key challenges in robotic bipedal locomotion is finding gait parameters that optimize a desired performance criterion, such as speed, robustness or energy efficiency. Typically, gait optimization requires extensive robot experiments and specific expert knowledge. We propose to apply data-driven machine learning to automate and speed up the process of gait optimization. In particular, we use Bayesian optimization to efficiently find gait parameters that optimize the desired performance metric. As a proof of concept we demonstrate that Bayesian optimization is near-optimal in a classical stochastic optimal control framework. Moreover, we validate our approach to Bayesian gait optimization on a low-cost and fragile real bipedal walker and show that good walking gaits can be efficiently found by Bayesian optimization. © 2014 Springer International Publishing

Information Structure Design in Team Decision Problems

We consider a problem of information structure design in team decision problems and team games. We propose simple, scalable greedy algorithms for adding a set of extra information links to optimize team performance and resilience to non-cooperative and adversarial agents. We show via a simple counterexample that the set function mapping additional information links to team performance is in general not supermodular. Although this implies that the greedy algorithm is not accompanied by worst-case performance guarantees, we illustrate through numerical experiments that it can produce effective and often optimal or near optimal information structure modifications

Design optimization of the JPL Phase B testbed

Increasingly complex spacecraft will benefit from integrated design and optimization of structural, optical, and control subsystems. Integrated design optimization will allow designers to make tradeoffs in objectives and constraints across these subsystems. The location, number, and types of passive and active devices distributed along the structure can have a dramatic impact on overall system performance. In addition, the manner in which structural mass is distributed can also serve as an effective mechanism for attenuating disturbance transmission between source and sensitive system components. This paper presents recent experience using optimization tools that have been developed for addressing some of these issues on a challenging testbed design problem. This particular testbed is one of a series of testbeds at the Jet Propulsion Laboratory under the sponsorship of the NASA Control Structure Interaction (CSI) Program to demonstrate nanometer level optical pathlength control on a flexible truss structure that emulates a spaceborne interferometer

LQG Control and Sensing Co-Design

We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing co-design problem, where one jointly designs sensing and control policies. We focus on the realistic case where the sensing design is selected among a finite set of available sensors, where each sensor is associated with a different cost (e.g., power consumption). We consider two dual problem instances: sensing-constrained LQG control, where one maximizes control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes sensor cost subject to performance constraints. We prove no polynomial time algorithm guarantees across all problem instances a constant approximation factor from the optimal. Nonetheless, we present the first polynomial time algorithms with per-instance suboptimality guarantees. To this end, we leverage a separation principle, that partially decouples the design of sensing and control. Then, we frame LQG co-design as the optimization of approximately supermodular set functions; we develop novel algorithms to solve the problems; and we prove original results on the performance of the algorithms, and establish connections between their suboptimality and control-theoretic quantities. We conclude the paper by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation.Comment: Accepted to IEEE TAC. Includes contributions to submodular function optimization literature, and extends conference paper arXiv:1709.0882