Analysis of Transmissions Scheduling with Packet Fragmentation

We investigate a scheduling problem in which packets, or datagrams, may be fragmented. While there are a few applications to scheduling with datagram fragmentation, our model of the problem is derived from a scheduling problem present in data over CATV networks. In the scheduling problem datagrams of variable lengths must be assigned (packed) into fixed length time slots. One of the capabilities of the system is the ability to break a datagram into several fragments. When a datagram is fragmented, extra bits are added to the original datagram to enable the reassembly of all the fragments. We convert the scheduling problem into the problem of bin packing with item fragmentation, which we define in the following way: we are asked to pack a list of items into a minimum number of unit capacity bins. Each item may be fragmented in which case overhead units are added to the size of every fragment. The cost associated with fragmentation renders the problem NP-hard, therefore an approximation algorithm is needed. We define a version of the well-known Next-Fit algorithm, capable of fragmenting items, and investigate its performance. We present both worst case and average case results and compare them to the case where fragmentation is not allowed

Bin Packing with Fragmentable Items: Presentation and Approximations

15 pagesWe consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity then we present a 6/5 approximation algorithm for a special case in which all bins have the same capacities

Availability-driven NFV orchestration

Virtual Network Functions as a Service (VNFaaS) is a promising business whose technical directions consist of providing network functions as a Service instead of delivering standalone network appliances, leveraging a virtualized environment named NFV Infrastructure (NFVI) to provide higher scalability and reduce maintenance costs. Operating the NFVI under stringent availability guarantees is fundamental to ensure the proper functioning of the VNFaaS against software attacks and failures, as well as common physical device failures. Indeed the availability of a VNFaaS relies on the failure rate of its single components, namely the physical servers, the hypervisor, the VNF software, and the communication network. In this paper, we propose a versatile orchestration model able to integrate an elastic VNF protection strategy with the goal to maximize the availability of an NFVI system serving multiple VNF demands. The elasticity derives from (i) the ability to use VNF protection only if needed, or (ii) to pass from dedicated protection scheme to shared VNF protection scheme when needed for a subset of the VNFs, (iii) to integrate traffic split and load-balancing as well as mastership role election in the orchestration decision, (iv) to adjust the placement of VNF masters and slaves based on the availability of the different system and network components involved. We propose a VNF orchestration algorithm based on Variable Neighboring Search, able to integrate both protection schemes in a scalable way and capable to scale, while outperforming standard online policies

Securing virtual network function placement with high availability guarantees

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 against attacks and software failures. 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 from both endogenous and exogenous threats 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

Production Scheduling

Generally speaking, scheduling is the procedure of mapping a set of tasks or jobs (studied objects) to a set of target resources efficiently. More specifically, as a part of a larger planning and scheduling process, production scheduling is essential for the proper functioning of a manufacturing enterprise. This book presents ten chapters divided into five sections. Section 1 discusses rescheduling strategies, policies, and methods for production scheduling. Section 2 presents two chapters about flow shop scheduling. Section 3 describes heuristic and metaheuristic methods for treating the scheduling problem in an efficient manner. In addition, two test cases are presented in Section 4. The first uses simulation, while the second shows a real implementation of a production scheduling system. Finally, Section 5 presents some modeling strategies for building production scheduling systems. This book will be of interest to those working in the decision-making branches of production, in various operational research areas, as well as computational methods design. People from a diverse background ranging from academia and research to those working in industry, can take advantage of this volume

Mathematical Problems in Molecular Evolution and Next Generation Sequencing

The focus of this work is the development of new mathematical methods for problems in phylogenetic tree inferences. In the first part we solve several problems related to so-called partitioned alignments. In the second part we demonstrate how to calculate all identical subtrees of a given labeled tree. We make use of this to implement an efficient method for avoiding redundant likelihood operations during phylogenetic tree inferences