Network Function Virtualization (NFV) is a new paradigm, enabling service innovation through virtualization of traditional network functions located flexibly in the network in form of Virtual Network Functions (VNFs). Since VNFs can only be placed onto servers located in networked data centers, which is the NFV's salient feature, the traffic directed to these data center areas has significant impact on network load balancing. Network load balancing can be even more critical for an ordered sequence of VNFs, also known as Service Function Chains (SFCs), a common cloud and network service approach today. To balance the network load, VNF's can be placed in a smaller cluster of servers in the network thus minimizing the distance to the data center. The optimization of the placement of these clusters is a challenge as also other factors need to be considered, such as the resource utilization. To address this issue, we study the problem of VNF placement with replications, and especially the potential of VNFs replications to help load balance the network. We design and compare three optimization methods, including Linear Programing (LP) model, Genetic Algorithm (GA) and Random Fit Placement Algorithm (RFPA) for the allocation and replication of VNFs. Our results show that the optimum placement and replication can significantly improve load balancing, for which we also propose a GA heuristics applicable to larger networks.
Due to the inherent complexity of optimizations, heuristic or meta-heuristic algorithms have been proposed to finding near optimal solutions. Paper @cite_1 minimizes the OPEX in the VNF placement problem separating into two NP-hard sub-problems, and proposing heuristic algorithms. Similarly, paper @cite_6 proposes heuristics to reducing computational complexity considering the resource demand in data centers. In @cite_2 two solutions are presented to the VNF-orchestration problem, an ILP model computing the optimal solution using CPLEX for small networks and a heuristic computing sub-optimal solutions for large networks. Paper @cite_0 proposes a genetic algorithm for the VNF chain placement to satisfy the SLA and QoS objectives with dynamic traffic demands. Similar to the previous work we use optimizations and heuristics to solve the VNF placement problem. Unlike previous work, we consider the replications, which is novel. Also, our approach is tailored to suiting the operational mobile core networks, where the optimum placement of VNFs in data centers can be found based on maximizing the network load balancing, thus enabling a scalable growth of the mobile data traffic over years, critical to the emerging 5G networks.
@cite_0 @cite_1 @cite_6 @cite_2
2281709771 1997650479 2015462215 2025397485
In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show how the hit probability evolves as the deployment density of the SBSs varies. We show that the heuristic of placing the most popular content in the MBSs is almost optimal after deploying the SBSs with optimal placement policies. Also, for the SBSs no such heuristic can be used; the optimal placement is significantly better than storing the most popular content. Finally, we show that solving the individual problems to find the optimal placement policies for different types of BSs iteratively, namely repeatedly updating the placement policies, does not improve the performance. In an operator's datacenter, optical technologies can be employed to perform network function (NF) chaining for larger aggregated flows in parallel with the conventional packet-based fine-grained traffic steering schemes. When network function virtualization (NFV) is enabled, virtualized NFs (vNF) can be placed when and where needed. In this study, we identify the possibility of minimizing the expensive optical electronic optical (O E O) conversions for NFV chaining in packet optical datacenters, which is introduced by the on-demand placement of vNFs. When the vNFs of the same NF chain are properly grouped into fewer pods, traffic flows can avoid unnecessary traversals in the optical domain. We formulate the problem of optimal vNF placement in binary integer programming (BIP), and propose an alternative efficient heuristic algorithm to solve this problem. Evaluation results show that our algorithm can achieve near-optimal O E O conversions comparable to BIP. We also demonstrate the effectiveness of our algorithm under various scenarios, with comparison to a simple first-fit algorithm. Abstract The problem of locating hub facilities and allocating non-hub nodes to those hubs arises frequently in the design of communication networks, airline passenger flow and parcel delivery networks. In this paper we consider uncapacitated multiple and single allocation p -hub median problems. We develop new mixed 0 1 linear formulations with tight linear programming relaxations. The approach is tested on a well known and heavily used benchmark data set of real-world problems with resulting LP relaxations ranging from 10010 to 391 250 variables and from 2 101 to 31 901 constraints, which proved to be difficult linear programs. Yet, this approach proved to be very effective: in almost all instances the linear programming solution was integer. In cases with fractional solutions, the integrality was achieved by adding a small partial set of integrality constraints. Therefore, we extended the range of optimally solvable instances of these NP-hard hub location problems, which have defied researchers for the last ten years. As an additional result for the single allocation case we were able to establish optimality of all heuristic solutions obtained via tabu search algorithm from a previous study. For the more difficult single allocation p -hub median problem we also used the best known heuristic solution as a guidance in adding integrality constraints. This novel linkage between optimal and heuristic solutions has a potential impact in a number of other problem settings, where efficient heuristic solutions exist and are probably, but not provably optimal. Mixed-machine heterogeneous computing (HC) environments utilize a distributed suite of different high-performance machines, interconnected with high-speed links, to perform different computationally intensive applications that have diverse computational requirements. HC environments are well suited to meet the computational demands of large, diverse groups of tasks. The problem of optimally mapping (defined as matching and scheduling) these tasks onto the machines of a distributed HC environment has been shown, in general, to be NP-complete, requiring the development of heuristic techniques. Selecting the best heuristic to use in a given environment, however, remains a difficult problem, because comparisons are often clouded by different underlying assumptions in the original study of each heuristic. Therefore, a collection of 11 heuristics from the literature has been selected, adapted, implemented, and analyzed under one set of common assumptions. It is assumed that the heuristics derive a mapping statically (i.e., off-line). It is also assumed that a metatask (i.e., a set of independent, noncommunicating tasks) is being mapped and that the goal is to minimize the total execution time of the metatask. The 11 heuristics examined are Opportunistic Load Balancing, Minimum Execution Time, Minimum Completion Time, Min?min, Max?min, Duplex, Genetic Algorithm, Simulated Annealing, Genetic Simulated Annealing, Tabu, and A*. This study provides one even basis for comparison and insights into circumstances where one technique will out-perform another. The evaluation procedure is specified, the heuristics are defined, and then comparison results are discussed. It is shown that for the cases studied here, the relatively simple Min?min heuristic performs well in comparison to the other techniques.