In this paper, we propose an end to end joint radio and virtual network function (VNF) resource allocation for next-generation networks providing different types of services with different requirements in term of latency and data rate. We consider both the access and core parts of the network and formulate a novel optimization problem whose aim is to perform the radio resource allocation jointly with VNF embedding, scheduling, and resource allocation such that the network cost, defined as the consumed energy and the number of utilized network servers, is minimized. The proposed optimization problem is non-convex, NP-hard, and mathematically intractable, and hence, we use an alternative search method (ASM) to decouple the main problem into some sub-problems of lower complexity. We propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm. We compare the performance of the proposed algorithm with a greedy-based solution in terms of the acceptance ratio and the number of active servers. Our simulation results show that the proposed algorithm outperforms the conventional ones.
In @cite_3 , an online scheduling and embedding algorithm by considering the capacity of available buffers and the processing time of each VNF is proposed for NFV. The authors propose a set of greedy algorithms and tabu search algorithm for mapping and scheduling. Moreover, cost, revenue, and acceptance ratio of these algorithms are compared together. VNF placement in a network with several mobile virtual network operators (MVNOs) are investigated in @cite_16 in which the slice scheduling mechanism is introduced in order to isolate the traffic flow of MVNOs. In this paper, the goal is optimizing VNF placement based on the available radio resources. black Joint VNF placement and admission control (AC) are studied in @cite_24 . In this paper, the aim is to maximize networks provider revenue in terms of bandwidth and capacity. black The authors in @cite_0 , propose an RA algorithm which integrates placement and scheduling of VNF together. In @cite_15 , a VNF scheduling problem is investigated and joint VNF scheduling and traffic steering is formulated as a mixed integer linear program. In the optimization problem, both the processing latency of VNFs and service chain transmission latency at virtual links are considered.
@cite_3 @cite_24 @cite_0 @cite_15 @cite_16
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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. 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. Network Function Virtualization (NFV) has revolutionized service provisioning in cloud datacenter networks. It enables the complete decoupling of Network Functions (NFs) from the physical hardware middle boxes that network operators deploy for implementing service-specific and strictly ordered NF chains. Precisely, NFV allows for dispatching NFs as instances of plain software called virtual network functions (VNFs) running on virtual machines hosted by one or more industry standard physical machines. Nevertheless, NF softwarization introduces processing vulnerability ( e.g. , failures caused by hardware or software, and so on). Since any failure of VNFs could break down an entire service chain, thus interrupting the service, the functionality of an NFV-enabled network will require a higher reliability compared with traditional networks. This paper encloses an in-depth investigation of a reliability-aware joint VNF chain placement and flow routing optimization. In order to guarantee the required reliability, an incremental approach is proposed to determine the number of required VNF backups. Through illustration, it is shown herein that the formulated single path routing model can be easily extended to support resource sharing between adjacent backup VNF instances. This paper advocates the absolute existence of a share-resource-based VNF assignment strategy that is capable of trading off all of the reliability, bandwidth, and computing resources consumption of a given service chain. A heuristic is proposed to work around the complexity of the presently formulated integer linear programming (ILP). Thorough numerical analysis and simulations are conducted in order to verify and assert the validity, correctness, and effectiveness of this proposed heuristic reflecting its ability to achieve very close results to those obtained through the resolution of the complex ILP within a negligible amount of time. Above and beyond, the proposed resource-sharing-based VNF placement scheme outperforms existing resource-sharing agnostic schemes by 15.6 and 14.7 in terms of bandwidth and CPU utilization respectively. 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. Network function virtualization (NFV) has been introduced by network service providers to overcome various challenges that hinder them from satisfying the growing demand for networking services with higher return-on-investment. The association of NFV with the leading technologies of information technology virtualization and software defined networking is paving the way for flexible and dynamic orchestration of the VNFs, but still, various challenges need to be addressed. The VNFs instantiation and placement problems on data center’s (DC) servers are key enablers to achieve the desired flexible and dynamic NFV applications. In this paper, we have addressed the VNF placement problem by providing a novel mixed integer linear programming (MILP) optimization model and a novel heuristic solution, Betweenness centrality Algorithm for Component Orchestration of NFV platform (BACON), for small- and large-scale DC networks. The proposed solution addresses the VNF placement while taking into consideration the carrier-grade nature of the NFV applications and at the same time, minimizing the intra- and end-to-end delays of the service function chain (SFC). Also, the proposed approach enhances the reliability and the quality of service (QoS) of the SFC by maximizing the count of the functional group members. To evaluate the performance of the proposed solution, this paper conducts a comparative analysis with an NFV-agnostic algorithm and a greedy-k-NFV approach, which is proposed in the literature work. Also, this paper defines the complexity and the order of magnitude of the MILP model and BACON. BACON outperforms the greedy algorithms especially the greedy-k-NFV solution and has a lower complexity, which is calculated as @math . The simulation results show that finding an optimized VNF placement can achieve minimal SFCs delays and enhance the QoS accordingly. 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. Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical infrastructure). In the offline setting, the two natural objectives are profit maximization, i.e., embedding a maximal number of request graphs subject to the resource constraints, and cost minimization, i.e., embedding all requests at minimal overall cost. The VNEP can be seen as a generalization of classic routing and call admission problems, in which requests are arbitrary graphs whose communication endpoints are not fixed. Due to its applications, the problem has been studied intensively in the networking community. However, the underlying algorithmic problem is hardly understood. This paper presents the first fixed-parameter tractable approximation algorithms for the VNEP. Our algorithms are based on randomized rounding. Due to the flexible mapping options and the arbitrary request graph topologies, we show that a novel linear program formulation is required. Only using this novel formulation the computation of convex combinations of valid mappings is enabled, as the formulation needs to account for the structure of the request graphs. Accordingly, to capture the structure of request graphs, we introduce the graph-theoretic notion of extraction orders and extraction width and show that our algorithms have exponential runtime in the request graphs' maximal width. Hence, for request graphs of fixed extraction width, we obtain the first polynomial-time approximations. Studying the new notion of extraction orders we show that (i) computing extraction orders of minimal width is NP-hard and (ii) that computing decomposable LP solutions is in general NP-hard, even when restricting request graphs to planar ones. Network virtualization allows multiple heterogeneous virtual networks (VNs) to coexist on a shared infrastructure. Efficient mapping of virtual nodes and virtual links of a VN request onto substrate network resources, also known as the VN embedding problem, is the first step toward enabling such multiplicity. Since this problem is known to be NP-hard, previous research focused on designing heuristic-based algorithms that had clear separation between the node mapping and the link mapping phases. In this paper, we present ViNEYard-a collection of VN embedding algorithms that leverage better coordination between the two phases. We formulate the VN embedding problem as a mixed integer program through substrate network augmentation. We then relax the integer constraints to obtain a linear program and devise two online VN embedding algorithms D-ViNE and R-ViNE using deterministic and randomized rounding techniques, respectively. We also present a generalized window-based VN embedding algorithm (WiNE) to evaluate the effect of lookahead on VN embedding. Our simulation experiments on a large mix of VN requests show that the proposed algorithms increase the acceptance ratio and the revenue while decreasing the cost incurred by the substrate network in the long run. This paper investigates the optimal rate allocation problem with end-to-end delay constraints in multi-hop wireless networks. We introduce Virtual Link Capacity Margin (VLCM), which is the gap between the schedulable link capacity and the maximum allowable flow rate over a link, for link delay control. We formulate the problem as a utility maximization framework with two sets of constraints: 1) capacity and schedulability constraints and 2) end-to-end delay constraints. By dual decomposition of the original optimization problem, we present a control algorithm that jointly tunes the flow rates and VLCMs, through a double-price scheme derived with regard to the constraints: the link congestion price reflecting the traffic load of a link, and the flow delay price reflecting the margin between the average packet delay and the delay requirement of a flow. We prove that the algorithm converges to a global optimum where the aggregate network utility defined over the flow rate set is maximized, while the delay constraints are satisfied. A key feature of our algorithm is it does not rely on a specific traffic model. The algorithm is implemented distributedly via joint wireless link scheduling and congestion control. Simulation results show that our algorithm outperforms heuristic rate allocation algorithms while satisfying the end-to-end delay constraints. The SDN and NFV paradigms enable novel network services which can be realized and embedded in a flexible and rapid manner. For example, SDN can be used to flexibly steer traffic from a source to a destination through a sequence of virtualized middleboxes, in order to realize so-called service chains. The service chain embedding problem consists of three tasks: admission control, finding suitable locations to allocate the virtualized middleboxes and computing corresponding routing paths. This paper considers the offline batch embedding of multiple service chains. Concretely, we consider the objectives of maximizing the profit by embedding an optimal subset of requests or minimizing the costs when all requests need to be embedded. Interestingly, while the service chain embedding problem has recently received much attention, so far, only non- polynomial time algorithms (based on integer programming) as well as heuristics (which do not provide any formal guarantees) are known. This paper presents the first polynomial time service chain approximation algorithms both for the case with admission and without admission control. Our algorithm is based on a novel extension of the classic linear programming and randomized rounding technique, which may be of independent interest. In particular, we show that our approach can also be extended to more complex service graphs, containing cycles or sub-chains, hence also providing new insights into the classic virtual network embedding problem. Recently network virtualization has been proposed as a promising way to overcome the current ossification of the Internet by allowing multiple heterogeneous virtual networks (VNs) to coexist on a shared infrastructure. A major challenge in this respect is the VN embedding problem that deals with efficient mapping of virtual nodes and virtual links onto the substrate network resources. Since this problem is known to be NP-hard, previous research focused on designing heuristic-based algorithms which had clear separation between the node mapping and the link mapping phases. This paper proposes VN embedding algorithms with better coordination between the two phases. We formulate the VN em- bedding problem as a mixed integer program through substrate network augmentation. We then relax the integer constraints to obtain a linear program, and devise two VN embedding algo- rithms D-ViNE and R-ViNE using deterministic and randomized rounding techniques, respectively. Simulation experiments show that the proposed algorithms increase the acceptance ratio and the revenue while decreasing the cost incurred by the substrate network in the long run. Network function virtualization (NFV) decouples software implementations of network functions from their hosts (or hardware). NFV exposes a new set of entities, the virtualized network functions (VNFs). The VNFs can be chained with other VNFs and physical network functions to realize network services. This flexibility introduced by NFV allows service providers to respond in an agile manner to variable service demands and changing business goals. In this context, the efficient establishment of service chains and their placement becomes essential to reduce capital and operational expenses and gain in service agility. This paper addresses the placement aspect of these service chains by finding the best locations and hosts for the VNFs and to steer traffic across these functions while respecting user requirements and maximizing provider revenue. We propose a novel eigendecomposition-based approach for the placement of virtual and physical network function chains in networks and cloud environments. A heuristic based on a custom greedy algorithm is also presented to compare performance and assess the capability of the eigendecomposition approach. The performance of both algorithms is compared to a multi-stage-based method from the state of the art that also addresses the chaining of network services. Performance evaluation results show that our matrix-based method, eigendecomposition of adjacency matrices, has reduced complexity and convergence times that essentially depend only on the physical graph sizes. Our proposal also outperforms the related work in provider’s revenue and acceptance rate. The objective of this paper is to study the performance of a multicell vector perturbation (MVP) precoding technique under practical situations in a network multiple-input multiple-output (MIMO) scheme employing joint transmission. The conventional perturbation strategy that minimizes the total power is considered, and the power at each base station (BS) is properly scaled to enforce per-BS power constraints. In our scenario, we consider multiple-antenna users and use block diagonalization (BD) as the linear front-end precoder for VP. The sum rate for the MVP in the case of uniformly distributed input and an asymptotic upper bound on the sum rate at high signal-to-noise ratios (SNRs) are derived. In addition, using the asymptotic upper bound on the individual user rates, we propose a proportionally fair (PF) user scheduling algorithm of lower complexity and better performance compared with the benchmark fair semiorthogonal user selection (SUS) algorithm. As opposed to the PF-SUS, the proposed PF scheduling algorithm requires no predefined correlation threshold. Furthermore, we study the impact of backhaul delay on the performance of both VP and BD by deriving bounds on the sum rate. The numerical results show that MVP in the case of perfect channel state information (CSI) outperforms multicell BD. In the presence of a backhaul delay, the performance of MVP significantly degrades, but the upper bound on the sum rate for MVP is still higher than for multicell BD. Providing real-time cloud services to Vehicular Clients (VCs) must cope with delay and delay-jitter issues. Fog computing is an emerging paradigm that aims at distributing small-size self-powered data centers (e.g., Fog nodes) between remote Clouds and VCs, in order to deliver data-dissemination real-time services to the connected VCs. Motivated by these considerations, in this paper, we propose and test an energy-efficient adaptive resource scheduler for Networked Fog Centers (NetFCs). They operate at the edge of the vehicular network and are connected to the served VCs through Infrastructure-to-Vehicular (I2V) TCP IP-based single-hop mobile links. The goal is to exploit the locally measured states of the TCP IP connections, in order to maximize the overall communication-plus-computing energy efficiency, while meeting the application-induced hard QoS requirements on the minimum transmission rates, maximum delays and delay-jitters. The resulting energy-efficient scheduler jointly performs: (i) admission control of the input traffic to be processed by the NetFCs; (ii) minimum-energy dispatching of the admitted traffic; (iii) adaptive reconfiguration and consolidation of the Virtual Machines (VMs) hosted by the NetFCs; and, (iv) adaptive control of the traffic injected into the TCP IP mobile connections. The salient features of the proposed scheduler are that: (i) it is adaptive and admits distributed and scalable implementation; and, (ii) it is capable to provide hard QoS guarantees, in terms of minimum maximum instantaneous rates of the traffic delivered to the vehicular clients, instantaneous rate-jitters and total processing delays. Actual performance of the proposed scheduler in the presence of: (i) client mobility; (ii) wireless fading; and, (iii) reconfiguration and consolidation costs of the underlying NetFCs, is numerically tested and compared against the corresponding ones of some state-of-the-art schedulers, under both synthetically generated and measured real-world workload traces. This paper presents the first study on scheduling for cooperative data dissemination in a hybrid infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) communication environment. We formulate the novel problem of cooperative data scheduling (CDS). Each vehicle informs the road-side unit (RSU) the list of its current neighboring vehicles and the identifiers of the retrieved and newly requested data. The RSU then selects sender and receiver vehicles and corresponding data for V2V communication, while it simultaneously broadcasts a data item to vehicles that are instructed to tune into the I2V channel. The goal is to maximize the number of vehicles that retrieve their requested data. We prove that CDS is NP-hard by constructing a polynomial-time reduction from the Maximum Weighted Independent Set (MWIS) problem. Scheduling decisions are made by transforming CDS to MWIS and using a greedy method to approximately solve MWIS. We build a simulation model based on realistic traffic and communication characteristics and demonstrate the superiority and scalability of the proposed solution. The proposed model and solution, which are based on the centralized scheduler at the RSU, represent the first known vehicular ad hoc network (VANET) implementation of software defined network (SDN) concept. This paper proposes a new class of online policies for scheduling in input-buffered crossbar switches. Given an initial configuration of packets at the input buffers, these policies drain all packets in the system in the minimal amount of time provided that there are no further arrivals. These policies are also throughput optimal for a large class of arrival processes which satisfy strong-law of large numbers. We show that it is possible for policies in our class to be throughput optimal even if they are not constrained to be maximal in every time slot. Most algorithms for switch scheduling take an edge based approach; in contrast, we focus on scheduling (a large enough set of) the most congested ports. This alternate approach allows for lower-complexity algorithms, and also requires a non-standard technique to prove throughput-optimality. One algorithm in our class, Maximum Vertex-weighted Matching (MVM) has worst-case complexity similar to Max-size Matching, and in simulations shows slightly better delay performance than Max-(edge)weighted-Matching (MWM). The design, management, and operation of network infrastructure have evolved during the last few years, leveraging on innovative technologies and architectures. With such a huge trend, due to the flexibility and significant economic potential of these technologies, software-defined networking (SDN) and network functions virtualization (NFV) are emerging as the most indispensable key catalysers. SDN NFV enhancing the infrastructure agility, thus network operators and service providers are able to program their own network functions (e.g., gateways, routers, load balancers) on vendor-independent hardware substrate. One of the most important considerations in NFV deployment is how to allocate the virtual resources that are needed to provide flexible virtual network services in an NFV-based network infrastructure. Thus, the most important prerequisite for NFV deployment is achieved fast, scalable and dynamic composition and allocation of networks functions (NFs) to implement network services (NSs). We have proposed a revised RA algorithm that integrates embedding and scheduling of virtual network functions (VNFs) simultaneously. In this paper, performance evaluation of the revised RA algorithm is performed and the proposed algorithm is applied more effectively in NFV environment where the demand for resources is flexible and concentrated. We consider the canonical shared link caching network formed by a source node, hosting a library of @math information messages (files), connected via a noiseless multicast link to @math user nodes, each equipped with a cache of size @math files. Users request files independently at random according to an a-priori known demand distribution q. A coding scheme for this network consists of two phases: cache placement and delivery. The cache placement is a mapping of the library files onto the user caches that can be optimized as a function of the demand statistics, but is agnostic of the actual demand realization. After the user demands are revealed, during the delivery phase the source sends a codeword (function of the library files, cache placement, and demands) to the users, such that each user retrieves its requested file with arbitrarily high probability. The goal is to minimize the average transmission length of the delivery phase, referred to as rate (expressed in channel symbols per file). In the case of deterministic demands, the optimal min-max rate has been characterized within a constant multiplicative factor, independent of the network parameters. The case of random demands was previously addressed by applying the order-optimal min-max scheme separately within groups of files requested with similar probability. However, no complete characterization of order-optimality was previously provided for random demands under the average rate performance criterion. In this paper, we consider the random demand setting and, for the special yet relevant case of a Zipf demand distribution, we provide a comprehensive characterization of the order-optimal rate for all regimes of the system parameters, as well as an explicit placement and delivery scheme achieving order-optimal rates. We present also numerical results that confirm the superiority of our scheme with respect to previously proposed schemes for the same setting. In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are single-hop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on special-case topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network's topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one time-slot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions. Finally, we show that it is NP-hard to approximate the scheduling problem to within n 1-epsiv factor, for any constant epsiv > 0, in the non-geometric SINR model, in which path-loss is independent of the Euclidean coordinates of the nodes. Network function virtualization (NFV) brings great conveniences and benefits for the enterprises to outsource their network functions to the cloud datacenter. In this paper, we address the virtual network function (VNF) placement problem in cloud datacenter considering users’ service function chain requests (SFCRs). To optimize the resource utilization, we take two less-considered factors into consideration, which are the time-varying workloads, and the basic resource consumptions (BRCs) when instantiating VNFs in physical machines (PMs). Then the VNF placement problem is formulated as an integer linear programming (ILP) model with the aim of minimizing the number of used PMs. Afterwards, a Two-StAge heurisTic solution (T-SAT) is designed to solve the ILP. T-SAT consists of a correlation-based greedy algorithm for SFCR mapping (first stage) and a further adjustment algorithm for virtual network function requests (VNFRs) in each SFCR (second stage). Finally, we evaluate T-SAT with the artificial data we compose with Gaussian function and trace data derived from Google's datacenters. The simulation results demonstrate that the number of used PMs derived by T-SAT is near to the optimal results and much smaller than the benchmarks. Besides, it improves the network resource utilization significantly.