Network Function Virtualization (NFV) enables mobile operators to virtualize their network entities as Virtualized Network Functions (VNFs), offering fine-grained on-demand network capabilities. VNFs can be dynamically scale-in out to meet the performance desire and other dynamic behaviors. However, designing the auto-scaling algorithm for desired characteristics with low operation cost and low latency, while considering the existing capacity of legacy network equipment, is not a trivial task. In this paper, we propose a VNF Dynamic Auto Scaling Algorithm (DASA) considering the tradeoff between performance and operation cost. We develop an analytical model to quantify the tradeoff and validate the analysis through extensive simulations. The NFV enabled Evolved Packet Core (EPC) is modeled as queueing model while legacy network equipment are considered as reserved a block of servers; and VNF instances are powered on and off according to the number of job requests present. The results show that the DASA can significantly reduce operation cost given the latency upper-bound. Moreover, the models provide a quick way to evaluate the cost-performance tradeoff and system design without wide deployment, which can save cost and time. Index Terms Auto Scaling Algorithm, Modeling and Analysis, Network Function Virtualization, 5G, Cloud Networks, Virtualized EPC
The basic idea of EMA, ARMA, and ARIMA is moving average, where the most recent input data within a moving window are used to predict the next input data. Specifically, in @cite_21 , the authors proposed an EMA-based scheme to predict the CPU load. The scheme was implemented in Domain Name System (DNS) server and evaluation results showed that the capacities of servers are well utilized. The authors of @cite_22 introduced a novel prediction-based dynamic resource allocation algorithm to scale video transcoding service in the cloud. They used a two-step prediction to predict the load, resulting in a reduced number of required VMs.
@cite_21 @cite_22
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We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. In this paper, an estimation of distribution algorithm (EDA)-based memetic algorithm (MA) is proposed for solving the distributed assembly permutation flow-shop scheduling problem (DAPFSP) with the objective to minimize the maximum completion time. A novel bi-vector-based method is proposed to represent a solution for the DAPFSP. In the searching phase of the EDA-based MA (EDAMA), the EDA-based exploration and the local-search-based exploitation are incorporated within the MA framework. For the EDA-based exploration phase, a probability model is built to describe the probability distribution of superior solutions. Besides, a novel selective-enhancing sampling mechanism is proposed for generating new solutions by sampling the probability model. For the local-search-based exploitation phase, the critical path of the DAPFSP is analyzed to avoid invalid searching operators. Based on the analysis, a critical-path-based local search strategy is proposed to further improve the potential solutions obtained in the EDA-based searching phase. Moreover, the effect of parameter setting is investigated based on the Taguchi method of design-of-experiment. Suitable parameter values are suggested for instances with different scales. Finally, numerical simulations based on 1710 benchmark instances are carried out. The experimental results and comparisons with existing algorithms show the effectiveness of the EDAMA in solving the DAPFSP. In addition, the best-known solutions of 181 instances are updated by the EDAMA. Autoregressive moving average (ARMA) method is applied to modeling the time series of position changes of GPS sites, obtained by the Geographical Survey Institute (GSI) of Japan during the period from April 1996 to March 1998. The present application is focused on denoising of the GPS time series data where only white noise is considered, and detection of data discontinuities and outliers in order to obtain time-averaged velocity and strain fields in central Japan. The data discontinuities are detected by a typical Kalman filter algorithm. The outliers are eliminated by using robust estimation techniques during the ARMA process. The averaged strain field, calculated by the least-squares collocation method from the improved two-year time series data, distinguishes clearly between the tectonically active and inactive regions. Higher maximum shear strain rates were detected in the southern area of the Kanto district. In the areas with very high seismicities, however, the difference between the maximum shear strain rates, that were estimated from the raw time series data and the ARMA-analyzed data, amounted to about 0.2 microstrain yr. This indicates that the existence of noise and discontinuities can lead to an over-prediction of the strain field. We propose a numerical method for finding packings of multiple-input and multiple-output (MIMO) semi-unitary precoding matrices in Grassmannian manifolds with different metrics. The proposed expansion-compression algorithm (ECA) is practical, simple and produces efficient packings without the need for a sophisticated initialization. With chordal distance metric, the algorithm tends to converge into a degenerated point constellation, where two points contain identical as well as orthogonal columns and distance between them cannot increase further along geodesic. Therefore, we alternate between max-min and min-max clustering parts of ECA algorithm, where the latter prevents degenerated constellations. With Fubini-Study distance metric, the algorithm converges to best known packings without extra min-max processing.