Virtual Network Functions as a Service (VNFaaS) is currently under attentive study by telecommunications and cloud stakeholders as a promising business and technical direction consisting of providing network functions as a service on a cloud (NFV Infrastructure), instead of delivering standalone network appliances, in order to provide higher scalability and reduce maintenance costs. However, the functioning of such NFVI hosting the VNFs is fundamental for all the services and applications running on top of it, forcing to guarantee a high availability level. Indeed the availability of an VNFaaS relies on the failure rate of its single components, namely the servers, the virtualization software, and the communication network. The proper assignment of the virtual machines implementing network functions to NFVI servers and their protection is essential to guarantee high availability. We model the High Availability Virtual Network Function Placement (HA-VNFP) as the problem of finding the best assignment of virtual machines to servers guaranteeing protection by replication. We propose a probabilistic approach to measure the real availability of a system and design both efficient and effective algorithms that can be used by stakeholders for both online and offline planning.
This paper deals with the multiple vehicle balancing problem (MVBP). Given a fleet of vehicles of limited capacity, a set of vertices with initial and target inventory levels and a distribution network, the MVBP requires to design a set of routes along with pickup and delivery operations such that inventory is redistributed among the vertices without exceeding capacities, and routing costs are minimized. The MVBP is NP‐hard, generalizing several problems in transportation, and arising in bike‐sharing systems. Using theoretical properties of the problem, we propose an integer linear programming formulation and introduce strengthening valid inequalities. Lower bounds are computed by column generation embedding an ad‐hoc pricing algorithm, while upper bounds are obtained by a memetic algorithm that separate routing from pickup and delivery operations. We combine these bounding routines in both exact and matheuristic algorithms, obtaining proven optimal solutions for MVBP instances with up to 25 stations.
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