ABSTRACT This paper introduces a variant of the dynamic Facility Location Problem with modular capacities. Inspired by the challenges faced by cellular telecommunication networks, the problem seeks to optimize the placement and equipment of facilities to meet the fluctuating demand of clients while minimizing installation and operational costs. Selected facilities must provide coverage to the whole considered area. In addition, clients must be served by the active facility that provides the best quality of service. We propose two integer linear programming formulations and analyze their theoretical properties in terms of lower bound. Furthermore, we propose a reinforcement for one formulation and valid inequalities. To evaluate the performance of the proposed formulations, we performed computational experiments with a commercial solver on instances with up to 20 candidate sites and 60 clients. The formulations proved to be very sensitive to the size of the instances. The analysis, both theoretical and numerical, provides meaningful insights on the formulations performance, and it constitutes a key starting point for developing further approaches, either exact methods or heuristics.

Edge intelligence combined with federated learning is considered as a way to distributed learning and inference tasks in a scalable way, by analyzing data close to where it is generated, unlike traditional cloud computing where data is offloaded to remote servers. In this paper, we address the placement of Artificial Intelligence Functions (AIF) making use of federated learning and hardware acceleration. We model the behavior of federated learning and related inference point to guide the placement decision, taking into consideration the specific constraint and the empirical behavior of a virtualized infrastructure anomaly detection use-case. Besides hardware acceleration, we consider the specific training time trend when distributing training over a network, by using empirical piece-wise linear distributions. We model the placement problem as a MILP and we propose a variant of the problem. Simulation results show the impact that hardware acceleration can have in the decision of the number of AIF to enable, while dividing by a relevant factor the distributed training time. We also show how our approach exacerbates the importance of monitoring an end-to-end learning system delay budget composed of link propagation delay and distributed training time in the location of AIFs.

The Network Function Virtualization (NFV) service chaining problem, which involves locating Virtual Network Functions (VNFs) in an NFV-enabled network and routing network demands through their required VNFs, is key to the success of NFV. Solving the chaining problem can efficiently reduce required network resources, and thus reducing capital expenditures (CAPEX) and operational expenditures (OPEX). Previous works mainly focus on finding heuristic solutions, rather than investigating the intrinsic features of the problem. In this paper, we investigate the features of the problem from both theoretical and numerical points of view, by shrinking the NFV service chaining problem into a particular version and conducting tests to study what makes the NFV service chaining problem fundamentally difficult to solve. Results reveal that the demand routing part of the problem has a significant impact on solving the mathematical formulated problem, i.e., finding a feasible routing can be time-consuming. We further propose constructive methods that improve upon the mathematical formulation, which make the time of finding the optimal solution be reduced in most cases.

Abstract Thanks to the increased availability of computing capabilities in data centers, the recently proposed virtual network function paradigm can be used to keep up with the increasing demand for network services as internet and its applications grow. The problem arises then of managing the virtual network functions, that is, to decide where to instantiate the functions and how to route the demands to reach them. While it arises in an application field, the Virtual Network Function placement and routing problem combines location and routing aspects in an interesting, challenging problem. In this paper, we propose several ILP‐based heuristics and compare them on a dataset that includes instances with different sizes, network topologies, and service capacity. The heuristics prove effective in tackling even large size instances, with up to 50 nodes and more than 80 arcs.

Abstract The mass diffusion of internet applications, both from computers and mobiles, has yielded to an increasing demand for network services with which the expensive and not flexible hardware appliances cannot keep up. On the other hand, computational capability has become available on the network nodes connected with computing servers and the cloud. This has suggested the network functions virtualization paradigm: services are provided on a software basis thus giving a flexible and cost effective response to the request for services. The network functions virtualization proposes challenging optimization problems such as the virtual network functions (VNFs) chaining problem, where service instances must be located on some network nodes and each demand must be routed through the services it requires. Most of the literature is currently focused on heuristic solutions, rather than on studying the problem properties or comparing approaches. With the aim of investigating the problem properties and comparing existing formulations, both from the theoretical and the numerical points of view, we consider a single service VNFs chaining problem, with different link and service capacities and the objective of minimizing the number of installed VNF instances.

This article focuses on the problem of minimizing the energy consumption in a resilient telecommunications network. For each demand, an edge‐disjoint pair of paths (primary and backup) must be provided and the shared protection scheme is used. The energy consumption is due only to edges used in the no‐fault scenario, but both primary and backup paths contribute to capacity consumption. We propose a projected formulation for the problem and show its effectiveness by comparing it with the complete formulation. We propose valid inequalities for both formulations. We evaluate the performances of the proposed formulations and valid inequalities through computational tests. Furthermore, we investigate the relationship between the shared and the dedicated protection version of the problem. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 6–22 2017

Recent data confirm that the power consumption of the information and communications technologies (ICT) and of the Internet itself can no longer be ignored, considering the increasing pervasiveness and the importance of the sector on productivity and economic growth. Although the traffic load of communication networks varies greatly over time and rarely reaches capacity limits, its energy consumption is almost constant. Based on this observation, energy management strategies are being considered with the goal of minimizing the energy consumption, so that consumption becomes proportional to the traffic load either at the individual-device level or for the whole network. The focus of this paper is to minimize the energy consumption of the network through a management strategy that selectively switches off devices according to the traffic level. We consider a set of traffic scenarios and jointly optimize their energy consumption assuming a per-flow routing. We propose a traffic engineering mathematical programming formulation based on integer linear programming that includes constraints on the changes of the device states and routing paths to limit the impact on quality of service and the signaling overhead. We show a set of numerical results obtained using the energy consumption of real routers and study the impact of the different parameters and constraints on the optimal energy management strategy. We also present heuristic results to compare the optimal operational planning with online energy management operation .

Worldwide interest in the delivery of computing and storage capacity as a service continues to grow at a rapid pace. The complexities of such cloud computing centers require advanced resource management solutions that are capable of dynamically adapting the cloud platform while providing continuous service and performance guarantees. The goal of this paper is to devise resource allocation policies for virtualized cloud environments that satisfy performance and availability guarantees and minimize energy costs in very large cloud service centers. We present a scalable distributed hierarchical framework based on a mixed-integer nonlinear optimization of resource management acting at multiple timescales. Extensive experiments across a wide variety of configurations demonstrate the efficiency and effectiveness of our approach.

We propose a multi-period model to minimize the energy consumption of IP networks while guaranteeing the satisfaction of all the traffic demands. Energy savings are achieved by putting into sleep mode cards and chassis. The multi-period optimization is constrained by inter-period limitations necessary to guarantee the stability of the networks. Both exact and heuristic solutions are proposed. Results show that up to 50% of the energy savings can be achieved for realistic test scenarios in networks operated with flow-based routing protocols (i.e. MPLS).

Abstract In many telecommunication networks, a given set of client nodes must be served by different sets of facilities—providing different services and having different capabilities—which must be located and dimensioned in the design phase. Network topology must be designed as well, by assigning clients to facilities and facilities to higher level entities, when necessary. We tackle a particular location problem, where two sets of facilities have to be located, and in which different devices can be installed at each site, providing different capacities at different costs. We optimize location and dimensioning of these facilities simultaneously. We introduce a compact formulation of that problem, we use discretization and Dantzig–Wolfe reformulation techniques to improve models, and we design an exact optimization algorithm. We test our approach on a set of instances derived from existing literature on facility location. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012

Modern cloud infrastructures live in an open world, characterized by continuous changes in the environment and in the requirements they have to meet. Continuous changes occur autonomously and unpredictably, and they are out of control of the cloud provider. Therefore, advanced solutions have to be developed able to dynamically adapt the cloud infrastructure, while providing continuous service and performance guarantees. A number of autonomic computing solutions have been developed such that resources are dynamically allocated among running applications on the basis of short-term demand estimates. However, only performance and energy trade-off have been considered so far with a lower emphasis on the infrastructure dependability/availability which has been demonstrated to be the weakest link in the chain for early cloud providers. The aim of this paper is to fill this literature gap devising resource allocation policies for cloud virtualized environments able to identify performance and energy trade-offs, providing a priori availability guarantees for cloud end-users.

We present a new computational approach to the problem of placing n identical nonoverlapping disks in the unit square in such a way that their radii are maximized. The problem has been studied in a large number of papers, from both a theoretical and a computational point of view. In this paper, we conjecture that the problem possesses a so-called funneling landscape, a feature that is commonly found in molecular conformation problems. Based on this conjecture, we develop a stochastic search algorithm that displays excellent numerical performance. Thanks to this algorithm, we could improve over previously known putative optima in the range n ≤ 130 in as many as 32 instances, the smallest of which is n = 53.