Optimal Orchestration of Virtual Network Functions

-The emergence of Network Functions Virtualization (NFV) is bringing a set of novel algorithmic challenges in the operation of communication networks. NFV introduces volatility in the management of network functions, which can be dynamically orchestrated, i.e., placed, resized, etc. Virtual Network Functions (VNFs) can belong to VNF chains, where nodes in a chain can serve multiple demands coming from the network edges. In this paper, we formally define the VNF placement and routing (VNF-PR) problem, proposing a versatile linear programming formulation that is able to accommodate specific features and constraints of NFV infrastructures, and that is substantially different from existing virtual network embedding formulations in the state of the art. We also design a math-heuristic able to scale with multiple objectives and large instances. By extensive simulations, we draw conclusions on the trade-off achievable between classical traffic engineering (TE) and NFV infrastructure efficiency goals, evaluating both Internet access and Virtual Private Network (VPN) demands. We do also quantitatively compare the performance of our VNF-PR heuristic with the classical Virtual Network Embedding (VNE) approach proposed for NFV orchestration, showing the computational differences, and how our approach can provide a more stable and closer-to-optimum solution

Robust Energy Management for Green and Survivable IP Networks

Despite the growing necessity to make Internet greener, it is worth pointing out that energy-aware strategies to minimize network energy consumption must not undermine the normal network operation. In particular, two very important issues that may limit the application of green networking techniques concern, respectively, network survivability, i.e. the network capability to react to device failures, and robustness to traffic variations. We propose novel modelling techniques to minimize the daily energy consumption of IP networks, while explicitly guaranteeing, in addition to typical QoS requirements, both network survivability and robustness to traffic variations. The impact of such limitations on final network consumption is exhaustively investigated. Daily traffic variations are modelled by dividing a single day into multiple time intervals (multi-period problem), and network consumption is reduced by putting to sleep idle line cards and chassis. To preserve network resiliency we consider two different protection schemes, i.e. dedicated and shared protection, according to which a backup path is assigned to each demand and a certain amount of spare capacity has to be available on each link. Robustness to traffic variations is provided by means of a specific modelling framework that allows to tune the conservatism degree of the solutions and to take into account load variations of different magnitude. Furthermore, we impose some inter-period constraints necessary to guarantee network stability and preserve the device lifetime. Both exact and heuristic methods are proposed. Experimentations carried out with realistic networks operated with flow-based routing protocols (i.e. MPLS) show that significant savings, up to 30%, can be achieved also when both survivability and robustness are fully guaranteed

Energy management in communication networks: a journey through modelling and optimization glasses

The widespread proliferation of Internet and wireless applications has produced a significant increase of ICT energy footprint. As a response, in the last five years, significant efforts have been undertaken to include energy-awareness into network management. Several green networking frameworks have been proposed by carefully managing the network routing and the power state of network devices. Even though approaches proposed differ based on network technologies and sleep modes of nodes and interfaces, they all aim at tailoring the active network resources to the varying traffic needs in order to minimize energy consumption. From a modeling point of view, this has several commonalities with classical network design and routing problems, even if with different objectives and in a dynamic context. With most researchers focused on addressing the complex and crucial technological aspects of green networking schemes, there has been so far little attention on understanding the modeling similarities and differences of proposed solutions. This paper fills the gap surveying the literature with optimization modeling glasses, following a tutorial approach that guides through the different components of the models with a unified symbolism. A detailed classification of the previous work based on the modeling issues included is also proposed

A robust optimization approach for the Advanced Scheduling Problem with uncertain surgery duration in Operating Room Planning - an extended analysis

We consider the Advanced Scheduling Problem (ASP) in the operating room block scheduling, taking into account stochastic patient surgery duration. A surgery waiting list, a set of Operating Room (OR) blocks, and a planning horizon are given. The problem herein addressed is to determine the subset of patients to be scheduled in the considered time horizon and their assignment to the available OR blocks. The problem aims at minimizing a measure of the waiting time of the patients. To this purpose, we introduce a penalty function associated to waiting time, urgency and tardiness of patients. We propose a robust optimization model to solve the ASP with uncertain surgery durations. The proposed approach does not need to generate a set of scenarios, and guarantees that solutions remain feasible for some variations of the surgery length parameters. We solve the problem on a set of real-based instances to test the behavior of the proposed model. The solution quality is evaluated with regards to the number of patients operated and their tardiness. Furthermore, assuming lognormal distribution for the surgery times, we use a set of randomly generated scenarios in order to assess the performance of the solutions in terms of OR utilization rate and number of cancelled patients

A rolling horizon framework for the operating rooms planning under uncertain surgery duration

We consider the Advanced Scheduling Problem (ASP) assuming a block scheduling strategy. A set of patients and the related surgery waiting list are given, together with a set of Operating Room (OR) blocks and a planning horizon. The problem asks to determine the subset of patients to be scheduled and their assignment to the available OR blocks. We consider a so-called rolling horizon approach in order to solve the ASP over a planning horizon of several weeks. The approach is iterative and readjusts the schedule each week: at each iteration the mid-term schedule over the next $n$ weeks is generated by solving an optimization problem, minimizing a penalty function based on patients' delay and tardiness; the first week schedule is then implemented. Unpredictable extensions of surgeries and new arrivals may disrupt the schedule. The schedule is then repaired in the next week iteration, again optimizing over $n$ weeks the penalty function while limiting the number of disruptions from the previously computed plan. The total delay and tardiness minimization problem is formulated as an ILP model and solved with a commercial solver. A deterministic formulation and a robust one are proposed and compared over different stochastic realization of surgery times

Optimal Probabilistic Energy-Aware Routing for Duty-Cycled Wireless Sensor Networks

International audienceNetwork lifetime is still the key issue when we deploy wireless sensor networks and IoT solutions in real-world applications. Current WSN research trends include duty-cycling at MAC layer and energy efficient routing at network layer, among others. In this study we propose an Optimal Probabilistic Energy-Aware Routing Protocol (OPEAR) for duty-cycled WSNs which aims at maximizing the network lifetime by keeping low energy consumption and balancing network traffic between nodes. Our experimental campaign reveals that our OPEAR protocol outperforms the popular Energy Aware Routing Protocol (EAR) from the literature, proving to be more effective in extending the network lifetime

GTOC5: Results from the European Space Agency and University of Florence

http://www.esa.int/gsp/ACT/doc/ACTAFUTURA/AF08/papers/AF08.2014.45.pdfInternational audienc

Improved bounds for interatomic distance in Morse

We improve the best known lower bounds on the distance between two points of a Morse cluster in R 3, with ρ ∈ [4.967, 15]. Our method is a generalization of the one applied to the Lennard-Jones potential in [2], and it also leads to improvements of lower bounds for the energy of a Morse cluster. Some of the numerical results have been announced in [1].