Mobile edge computing (MEC) is a promising technique for providing low-latency access to services at the network edge. The services are hosted at various types of edge nodes with both computation and communication capabilities. Due to the heterogeneity of edge node characteristics and user locations, the performance of MEC varies depending on where the service is hosted. In this paper, we consider such a heterogeneous MEC system, and focus on the problem of placing multiple services in the system to maximize the total reward. We show that the problem is NP-hard via reduction from the set cover problem, and propose a deterministic approximation algorithm to solve the problem, which has an approximation ratio that is not worse than @math . The proposed algorithm is based on two sub-routines that are suitable for small and arbitrarily sized services, respectively. The algorithm is designed using a novel way of partitioning each edge node into multiple slots, where each slot contains one service. The approximation guarantee is obtained via a specialization of the method of conditional expectations, which uses a randomized procedure as an intermediate step. In addition to theoretical guarantees, simulation results also show that the proposed algorithm outperforms other state-of-the-art approaches.
In addition to the MEC-related work mentioned in , our work is also related to virtual network embedding (VNE) @cite_19 , which studies the scheduling of distributed tasks to multiple machines. However, service components that are shareable among multiple users is usually not considered in VNE, which is an important characteristic in MEC @cite_24 .
@cite_24 @cite_19
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A key challenge in network virtualization is to efficiently map a virtual network (VN) on a substrate network (SN), while accounting for possible substrate failures. This is known as the survivable VN embedding (SVNE) problem. The state-of-the-art literature has studied the SVNE problem from infrastructure providers’ (InPs’) perspective, i.e., provisioning backup resources in the SN. A rather unexplored solution spectrum is to augment the VN with sufficient spare backup capacity to survive substrate failures and embed the resulting VN accordingly. Such augmentation enables InPs to offload failure recovery decisions to the VN operator, thus providing more flexible VN management. In this paper, we study the problem of jointly optimizing spare capacity allocation in a VN and embedding the VN to guarantee full bandwidth in the presence of multiple substrate link failures. We formulate the optimal solution to this problem as a quadratic integer program that we transform into an integer linear program. We also propose a heuristic algorithm to solve larger instances of the problem. Based on analytical study and simulation, our key findings are: 1) provisioning shared backup resources in the VN can yield 33 more resource efficient embedding compared to doing the same at the SN level and 2) our heuristic allocates 21 extra resources compared to the optimal, while executing several orders of magnitude faster. Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): the problem of finding a mapping of a request graph (describing a workload) onto a substrate graph (describing the physical infrastructure). Applications range from mapping testbeds (from where the problem originated), over the embedding of batch-processing workloads (virtual clusters) to the embedding of service function chains. The different applications come with their own specific requirements and constraints, including node mapping constraints, routing policies, and latency constraints. While the VNEP has been studied intensively over the last years, complexity results are only known for specific models and we lack a comprehensive understanding of its hardness.This paper charts the complexity landscape of the VNEP by providing a systematic analysis of the hardness of a wide range of VNEP variants, using a unifying and rigorous proof framework. In particular, we show that the problem of finding a feasible embedding is @math -complete in general, and, hence, the VNEP cannot be approximated under any objective, unless @math holds. Importantly, we derive @math -completeness results also for finding approximate embeddings, which may violate, e.g., capacity constraints by certain factors. Lastly, we prove that our results still pertain when restricting the request graphs to planar or degree-bounded graphs. Driven by the visions of Internet of Things and 5G communications, recent years have seen a paradigm shift in mobile computing, from the centralized mobile cloud computing toward mobile edge computing (MEC). The main feature of MEC is to push mobile computing, network control and storage to the network edges (e.g., base stations and access points) so as to enable computation-intensive and latency-critical applications at the resource-limited mobile devices. MEC promises dramatic reduction in latency and mobile energy consumption, tackling the key challenges for materializing 5G vision. The promised gains of MEC have motivated extensive efforts in both academia and industry on developing the technology. A main thrust of MEC research is to seamlessly merge the two disciplines of wireless communications and mobile computing, resulting in a wide-range of new designs ranging from techniques for computation offloading to network architectures. This paper provides a comprehensive survey of the state-of-the-art MEC research with a focus on joint radio-and-computational resource management. We also discuss a set of issues, challenges, and future research directions for MEC research, including MEC system deployment, cache-enabled MEC, mobility management for MEC, green MEC, as well as privacy-aware MEC. Advancements in these directions will facilitate the transformation of MEC from theory to practice. Finally, we introduce recent standardization efforts on MEC as well as some typical MEC application scenarios. To accelerate the implementation of network functions middle boxes and reduce the deployment cost, recently, the concept of network function virtualization (NFV) has emerged and become a topic of much interest attracting the attention of researchers from both industry and academia. Unlike the traditional implementation of network functions, a software-oriented approach for virtual network functions (VNFs) creates more flexible and dynamic network services to meet a more diversified demand. Software-oriented network functions bring along a series of research challenges, such as VNF management and orchestration, service chaining, VNF scheduling for low latency and efficient virtual network resource allocation with NFV infrastructure, among others. In this paper, we study the VNF scheduling problem and the corresponding resource optimization solutions. Here, the VNF scheduling problem is defined as a series of scheduling decisions for network services on network functions and activating the various VNFs to process the arriving traffic. We consider VNF transmission and processing delays and formulate the joint problem of VNF scheduling and traffic steering as a mixed integer linear program. Our objective is to minimize the makespan latency of the overall VNFs’ schedule. Reducing the scheduling latency enables cloud operators to service (and admit) more customers, and cater to services with stringent delay requirements, thereby increasing operators’ revenues. Owing to the complexity of the problem, we develop a genetic algorithm-based method for solving the problem efficiently. Finally, the effectiveness of our heuristic algorithm is verified through numerical evaluation. We show that dynamically adjusting the bandwidths on virtual links connecting virtual machines, hosting the network functions, reduces the schedule makespan by 15 –20 in the simulated scenarios.