Cloud Computing

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CLOUD COMPUTING

1. IntroductionIn the recent past, cloud computing has come up to be new model that is highly suitable

for the provision of on-request Information Technology resources. The use of cloud computing is rapidly revolutionizing the manner in which Information Technology is managed and delivered to the intended users. The increase in the adoption of cloud computing fosters cooperation among the cloud providers and has over time increased the complexity of the needs of the users. The cloud-computing users need to spread their services and resources beyond certain geographical boundaries. Furthermore, cloud-computing users are interested in distributing their services to a heterogeneous population rather than a homogeneous one.1 It is now possible for cloud users to rent resources such as Virtual Machines on a pay-per-use basis in order to avoid additional operational and capital expenses2. However, the choice of the cloud model to be used by the clients is influenced by the ability of the system to scale the available resources and provide flexible payment options.

A cloud computing environment allows an infrastructure provider (InP) to divide the physical resources that are available in each data center into what is commonly referred to as virtual resources. In most cases, virtual resources constitute a virtual machine (VMs) which are rented to the service providers using an on-demand system. Once the resources have been shared, the service providers use them to organize Information Technology applications with the objective of serving a wider number of customers through the Internet. One setback of using a cloud computing environment in the provision of IT services is that most infrastructure providers do not provide performance guarantees concerning propagation and bandwidth delays.3 Lack of such guarantees has a huge impact on the process of deploying virtual services and applications. Recent research studies have made numerous efforts to address these shortcomings by proposing the use of virtual data centers (VDCs) while offering IT resources.4

1.1. Data Center

Generally, a data center incorporates redundant power supplies or backups, environmental controls (such as fire suppression and air conditioning), data communication connections, as well as a range of security measures through security devices. Large data centers operate at industrial scales, consuming much electricity just as a small town.

Historically, the original data centers were established as isolated server rooms, accommodated within an administration’s facility, holding several discrete servers operating only one application or just two. During the initial days of primary datacenters, a number of establishments were liable for upholding or sustaining their servers, software, hence necessitated a large volume of personnel assets or resources in order to maintain the facility and its servers. Currently, some large organizations still continue managing the internal datacenters, while other organizations and a number of business administrators are now capable of adjusting the levels of their services, covering a greater number of users, and lowering or minimizing the response time by outsourcing their outdated server facilities to a third party datacenter or cloud computing providers.5 Typically, a datacenter is a facility that houses computer systems, alongside the

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supplementary components, including storage systems plus telecommunications systems. Datacenter structure currently extends beyond the mortar and brick walls and further to public clouds, in which data that was once regarded to be too sensitive to leave the building, is now hosted. The servers used here have been consolidated and completely visualized, hence new levels of integration is possibly achieved by the converged infrastructural systems. The datacenter is highly scalable and its operating systems are faster each year. A number of commercial datacenters, such as collocated systems are now overhauled in order to host public cloud providers or network provision facilities.6

In the near future, many enterprise datacenters will be focusing firmly on hosting private clouds, and as a result, there will be a need to retool the datacenters in order to accommodate the essential infrastructure.7 For instance, the intra-datacenter bandwidth is currently no longer supporting the server-to-server communications, while driving immense amounts of virtualized servers. Furthermore, datacenters will witness a much larger number of cores per square foot, while having their own management and power requirements.8 As well, they will be in need of considering diverse approaches for security and governance. The large public clouds will extremely be scattered over the globe, necessitating numerous datacenters, which are entity owned. Several datacenters will have to amalgamate or consolidate for their successful survival, including those used by the government, enterprise, as well as commercial systems.9

One central benefit to the datacenter is due to the fact that the physical storage resources in the hard-drive are combined into a pool of storage, out of which ”logical storage” can be fashioned. Most storage systems have got heterogeneous nature that permits many diverse dealers’ storage hardware to be brought into the system, but with minute or no recognizable effects (with the exception of the superfluous storage space). Such a logical storage space may be reachable to a number of diverse computer systems, which uphold similar pool of storage-space. The most significant benefit of the storage virtualization; apart from the obvious benefits including the necessity for less overall hard-drives and a centralized backup, is due to the assertion that data is viable to replication or transferred to a different location, transparently to the server, using a storage point known as logical storage point. .

Another benefit associated with datacenters, which is a bit unglamorous/hi-tech is revealed to be the merging or linking of all facility resources or informational assets, including electrical, wiring, networking, HVAC, software, personnel, and the hardware. A number of organizations now operate numerous server rooms joined to replicate services across the entire organizations’ managements, which are commonly operated on multitask software and hardware platforms.10 On their endeavors to moderate the reduplication and wastage of expenses, several establishments currently consolidate their server rooms to come up with private datacenters, hence minimizing the chances duplication of software, hardware, alongside all other required facilities to run a business.

1.2. Network Virtualization

Over the past few years, network virtualization has increasingly gained prominence within the fields of networking and telecommunication. Originally, the interests in network

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virtualization was majorly inspired by the Future Internet research initiatives, with a central objective of finding a platform upon which new internet architectures would be experimented or evaluated without constraints or limitations. More important for the network operatives, it was thereby more certain that network virtualization is capable of offering a range of short-term or medium-term business benefits, with significant cost reductions and revenue increases. Therefore, this served as a remarkable tool from the operations’ point-of-view.

Network virtualization technologies have been proved and implemented in several experimental occasions, such as the VIN and PlanetLab, which offer a virtualization overlay across the internet as well as test-beds.11 On a virtualized network control plane, there is always an urge to enhance routing alongside other parallel control functions. Furthermore, a virtual network slices management in the infrastructure necessitates hi-tech mechanisms for the virtual networks’ set-ups and tear-downs during the monitoring and runtime of the virtual network slices’ operation.12 During the virtual network mapping process, the node and link separation implies that the node mapping stage conducted independent of the link mapping stage.13 This owes to the fact that the absence of coordination during these two processes could result into high costs of mapping, hence a decline in a range of accepted virtual networks alongside the revenue generated. However, it had been made clear that virtual network provisioning serves to be the major source allocation problem in NV. Consequently, in cloud computing environments, the applications with pliable resources for diverse clients may possibly be hosted and run on the VM (virtual machines) in geo-distributed data-centers.14

Network virtualization allows for extra freedom since the assorted network technologies and architectures may cohabit the mutual substrate networks.15 With the aid of server virtualization, the entire components of the network may easily be virtualized, leading to an integrated and completely quarantined entity referred to as a VN (virtual network). Such kind of technology closely correlates to the novel viewpoint of computing as a productive service. This occurs owing to the fact that tenants’ applications shall be accommodated in hefty computing firms as virtualization networks, reachable via the internet in form of “pay-per-use” model.

Even though there is a huge interest on the virtualization networks, both from the network operators and the research community, a number of downfalls still inhibit it from being implemented within the real-world environments. Among the most intriguing impediments is the “efficient virtual network embedding on to the physical network. Owing to the fact that this process necessitates a simultaneous optimization of virtual links and nodes placements, it is a bit difficult in nature hence necessitates hefty amounts of computing power.16 The simultaneous link and node mapping optimization can easily be formulated through an inseparable flow problem referred to as NP-hard, hence it is simply manageable for limited amounts of links and nodes.17 Network virtualization is projected to be the key enabler for the future internet. The only difference to the contemporary virtualization techniques in networks such as VPNs (Virtual Private Networks) and the overlay networks is that network virtualization allows for the operation of isolated Virtual Networks (VNs). A VN is capable of holding isolated network elements, links, as well as other IT resources. Within a network virtualization environment, fresh business roles can be triggered, hence realizing different tasks as well as trading virtual resources

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between them. Such resources can be network resources and IT resources, hence new control interfaces and mechanisms are obligatory in order to realize the setup and operation of the heterogeneous VNs.

For the purpose of this research, virtual data centers are defined as a collection of virtual machines, routers, and switches that are interconnected through virtual links. Each virtual link in a virtual data center is characterized by its propagation delay and bandwidth capacity. When VDCs are used, cloud computing users are able to enjoy better capabilities to isolate network resources and improve the performance of the service applications. Though beneficial than using traditional virtual machines, the use of VDCs exposes cloud providers with a new set of challenges referred to as the VDC embedding problem. The problem aims at mapping virtual machines, routers, and switches onto the physical infrastructure.

For efficient allocation of cloud resources and network virtualization that ensures appropriate communication among such resource, the client requests must efficiently be received and distributed across the datacenter depending on their nature. This allows the application providers to ensure that cloud clients rent the bandwidth required for their virtual machines’ inter-datacenter communications. This strategy creates a virtual network of virtual machines that communicate via virtual links, thereby operating in isolation from the other collocated cloud applications. Therefore, cloud clients must be able to specify and pay for their communication resources, which are utilized by their cloud-hosted applications with regards to the used bandwidth in compliance with the required and achievable latency over the links. In cloud mapping and network virtualization servicing, client requests are categorized into service classes. Supposing the demand for one service class is impacted by the prices to a smaller range, then the price of such services will include a larger share of the general service cost. This implies that prices are inversely proportional to the demand sensitivity in every service class. In simple terms, prices at each class is adjustable depending on the willingness of clients to request and pay for bandwidth in a particular service class. This way, as the congestion of clients’ requests increases, the shares of bandwidth cost allocations and prices also increases at a higher rate for the classes where clients show elastic demands, and are willing to pay highly for the low latency classes. Alternatively, in a multicast virtual network, a client may seek to install an application with “one – to – many” communications mode in any given datacenter (cloud). This comprises a single-sourced node plus an array of terminal nodes. These two categories of nodes are linked to all the terminal nodes through the virtual links – with every VL (virtual link) necessitating a precise bandwidth amount.

In most cases, the specifications of clients’ connection requests such as the source, destination, and lifetime are not recognized in prior. The substrate network thereby consists of client nodes and datacenters. Every datacenter has a number of servers which can host a multiple number of virtual machines, minus exceeding the server capacity. A range of virtual machines with different resource configurations are thereby made available.18 Upon the reservation of the virtual machine, a client may request for the connections between the virtual machine (VM) and the client node. In the connection request, the client must typically define the source, destination, the request’s preferred start time, duration (connection lifetime), VM specifications (the

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requested capacity units), as well as the required bandwidth. Such requests thereby presents a problem that has to be solved by the servers. Therefore, clients’ requests are aggregated into virtual network requests (VNRs) on the basis of configurable aggregation factor. Consequently, serving the connection requests is presents a virtual network mapping challenge in which the nodes represent sources and destinations, and edges serve as virtual links between the nodes. Each virtual link denotes a physical network path from the source to the destination. Additionally, every VNR is assigned to a time window, but on the basis of the requested start time. As a result, a single window can easily be distracted as a set of virtual network mapping requests, during the time period it represents. Supposing a VNR lifetime is sufficiently long to span over more than a single window, the VNR is thereby assigned to all of the windows. Such requests are known as “spanning requests.”

In this context, Virtual network mapping (VNM) refers to finding optimal techniques to handle the requests received from clients on a continuous basis. VNM is done by developing virtual networks that have multiple Virtual Machine instances that run on servers in various data centers distributed geographically.

The research paper aims at proposing a management framework that is able to coordinate the distribution of virtual data centers across a geographically distributed infrastructure. The research’s central focus is thereby on modeling the problem of virtual network provisioning within the distributed cloud computing datacenters, using the collected and prioritized connections, and the assessment of their effects.19 Node and link provisioning are thereby performed, and different window-size selection schemes are introduced and evaluated. A technique of dealing with the connection spanning over more than a single window is also introduced, and the proposed algorithm is cross-checked with previous works that are well known within the literature.20 The paper will add to previous research on virtual network mapping as well as introduce new methodologies in the same niche to facilitate easier operating in cloud computing data centers. New contributions to this research paper can be summarized as shown below:

Investigate the mathematical model for cloud computing, datacenter on the basis of the problem modelling of virtual network provisioning within the distributed cloud computing datacenters using diverse window algorithms.21

Implement efficient traffic routing schemes that localize data flows between the virtual machines used within a cloud computing environment.

Decrease the network contention through node and link mapping.

In order to accomplish seamless virtualization, cloud network providers require an effective system that is capable of comprehensively performing the functions of virtual network provisioning, with regards to resource virtualization and allocation, and scheduling their geographic network distribution of data centers. In this research, the task includes the reception of cloud client requests and allocating them the network and computational resources in the best way, which guarantees the service quality conditions for the cloud clients, while maximizing the datacenter resource utility and revenue for the providers. This paper thereby introduces a comprehensive system of solving problems associated to virtual network mapping for a set of connection client requests sent or submitted by the cloud clients. Subsequently, the connections are timely collected at different intervals (these intervals are known as windows), after which the

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node and link provisioning are executed. Thus, different window sizes’ selection schemes are introduced and assessed.

2. Research Problem 1:

2.1. Mathematical model of cloud computing, data center

In the first research model, this research paper will describe an adequate mathematical model of VN provisioning within a distributed cloud computing datacenter.

In this research, the paper tackles the problem of virtual network mapping within a cloud computing datacenter environment. In this context, the VNM implies the finding of the optimal policy/technique to handle or serve the numerous requests that are continuously received from multiple clients. This task is accomplished by constructing VNs , which incorporates multiple VM instances, running on servers within a multiple number of geographically distributed datacenters. Here, the virtual machine instances can possibly be linked via virtual network links or edges, which are mapped onto the substrate (physical) network path. The central network controllers with the cloud computing environments have to deal with the obligation of mapping numerous virtual network mapping requirements or requests a short period. The mathematical model is represented in terms of an undirected graph whose vertices represent datacenters and cloud clients. The network devices included in the graphs include components such as the computing nodes, controllers, and switches. The edges of the graphs represent the network links between the network devices. The mathematical model proposed for use in a cloud computing, data center can be useful in the implementation of efficient traffic routing schemes. These traffic routing schemes are capable of localizing data flows between the virtual machines that constitute a cloud computing data center.22

A better example of the aforementioned situation can be witnessed in the increasingly popular SDN (software defined network) technology in which the SDN controllers are in charge of mapping the clients’ connections requests or flows. Putting this into a perspective denotes that a typical SDN controller is capable of supporting approximately 105 flows per second optimally. This substantial volume of the arriving requests at the SDN controller may possibly cause a considerable performance handicap. Therefore, there will be a significant increase in the computational over-head supposing such requests are to be processed individually as they arrive. Consequently, there is a greater need for connection request aggregation. Perceiving aggregation as the solution to the computational issue thereby brings forth several design questions, and a complete methodology is thereby necessary. The most essential decisions thereby encompasses aggregation techniques, window size, aggregation factor, as well as request prioritizing. This research thereby aims at helping cloud computing users solve the localization problem that develops from traffic generated by geographically distributed cloud computing data centers. The mathematical model is useful in scheduling groups of virtual machines before transmitting the selected nodes and information about the group topology to the controller.23 The controller installs the routing rules to the switches in order to localize the flow of data between the virtual

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machines operating within the cloud computing data center. The topology leads to a decrease of network contention as well as the response time of the software programs that are executed in the virtual machines.24

A VNM process is split into not mapping and link mapping. A number of proposed approaches are inclined at separating the link and node mapping into two distinct stages in order to minimize the complexity, while this work uses coordination between the two (link and node) stages.

Fig. 1: Cloud computing system

Various aspects of cloud computing that set it apart from the traditional computing include feature that are highly instrumental when it comes to the impartment of the technical advantage on the cloud services. The first feature is the Multi-tenancy nature, in which a cloud provider serves to rent storage or computational services to multiple number of clients. These diverse services are mutually managed by cloud infrastructure providers as well as clients. Given the layered architecture typical cloud set up, the service management becomes relatively easier. The infrastructure providers together with clients only need to concentrate on the layer of service location. The second feature is the Shared Resource Pooling, in which the cloud services employ a pool of computational resources which are dynamically allocated to multiple clients on the basis of their specific requirements. This way, the cloud infrastructure providers are capable of efficiently utilizing their resources in a cost-effective way, hence curtailing both management and operational costs. Third is the Wide Geo-distribution of Datacenter and Network Access. Here, the datacenters which offer cloud services are distributed widely across diverse geographical locations. Cloud service providers are thereby able to offer efficient and agile

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services to the clients via such diversified distribution.25 Finally, the feature of Dynamic Resource Provisioning or Allocation suggests that the contemporary cloud computing solutions tolerate an instant dynamic allocation and withdrawal of computing resources to/by clients on the basis of their ever changing requirements.

3. Related Work

3.1. Network Virtual Systems

The proposal of virtualization brings forth an opportunity for the assessment and development of a path for the future Internet. Virtualization deploys different protocols and architectures on the shared physical set-up.26 In its capacity, it could also extenuate the solidifying powers of the present day Internet, hence stimulate more discoveries or innovations.27 The notion behind the use of many co-existing networks are a common technique that the current Internet infrastructure has already been able to support. Examples of already existing virtualization within a network include Multipreprotocol Label Switching (MPLS), T-Mobile UK, and 3UK, as well as the VLAN (Virtual Local Area Network).28 A VPN (Virtual Private Network) can connect with multiple distributed sites through a shared physical infrastructure. However, the connection is restricted since all VNs are required to rely upon a similar protocol stack and technology.29 Currently, network virtualization makes it easier for cloud computing users to achieve independent programmability of virtual networks.30 Also, it has the aptitude to manage or controll multi-provider scenarios as well as hiding the specificities of the network structure.31

The contemporary research efforts focus on the intra-data center networks, hence employ virtualization in order to provide bandwidth sharing amongst tenants within a single data center. For instance, SecondNet is a low time-complexity heuristics-based algorithm which allocates a data center VN by the use of clustered neighboring servers.32 The current demands are accomplished by adjusting (increasing or decreasing) the bandwidth reservation along the existing paths, or via migrating virtual links to new paths. Likewise, Rodrigues et al. proposed the GateKeeper, which guarantees bandwidth among virtual links, while achieving high bandwidth utility of the network.33 GateKeeper serves by setting two bandwidth rates for every virtual link (such as maximum allowed rate and minimum guaranteed rate)34. Conferring to the level of congestion of the network, the sender might control its traffic rate. Benson et al proposed the CloudNaaS, a framework that serves to support the deployment and management of cloud enterprise applications.35 This architectural framework supports both best-effort and bandwidth reservation on the basis of services amongst virtual machines (VM). Nevertheless, the increase in the number of paths with bandwidth reservation may also lead to congestion, starvation of other services, in addition to an inefficient network utility. Another bandwidth allocation technique by Seawall, performs end-to-end proportional sharing of the network resources according to an associated weight with each traffic source by the use of congestion-controlled tunnels.36 As well, Lam proposed Netshare – a statistical multiplexing mechanism, which proportionally allocates bandwidth to the tenants.37 As opposed to Seawall, Netshare shares link bandwidth amongst tenants, rather than sender virtual machines, in order to provide a fair allocation among different

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services. Generally, the abovementioned approaches are hardly suitable for inter-data centers communications. Also, they do not provide the cloud clients (CCs) with the means to effectively and accurately define their network resource demands. Additionally, they do not focus on mechanisms which relate the pricing of the VN services with the profits gained from such actively distributed cloud applications. Finally, a number of these approaches tend to assume that the cloud service providers (CSP) have full knowledge of the traffic patterns of the hosted cloud services in prior.

3.2.1. Virtual Network ManagementThe major focus of the network virtualization literature is commonly directed towards the

development of efficient techniques for an optimal utilization of the physical network resources. For instance, Papagianni et al suggested a method for an efficient and effective mapping of VNs onto a shared substrate interconnecting the formerly isolated islands of computational resources.38 This proposed technique aimed at minimizing the total number of hops serving a virtual link. Periodic re-optimization of the bandwidth allocation on congested physical links is carried-out in order to re-distribute the network resources amongst virtual links. In this technique, the virtual link migration and path-splitting percentages are employed in the re-configuration of the VN’s use of the physical resources.39 In different cloud computing publications, a number of authors proposed a self-organizing virtual node re-allocation scheme as a strategy for managing the physical resources, with an objective of minimizing the span or interval of the paths serving the specified virtual link. Considering the Heuristics, distributed virtual managers are able to detect congested virtual links hence decide on which virtual nodes should be migrated to which new substrate nodes? Rather than migrating the virtual links, Fajjari et al proposed a greedy approach for the re-allocation of star components within the individual VNs with the sole aim of freeing physical resources whenever a new virtual network request is declined.40

Following the same objective, in previous works, the authors proposed a technique that identified congested VNs’ portions that could possibly contribute to the fragmentation of the substrate resources; then re-allocates those portions into other underutilized resources.41 The re-allocation of congested VN portions aims at minimizing the DDCN fragmentation problem, hence creating rooms for future VN client requests. In a nutshell, while complementary to the proposed works, the aforementioned approaches focus majorly on the efficient use of the physical networks, rather than focusing on the enhancement of the performance of the hosted VNs. Contrary to the above approaches, He, et al proposed the “DaVinci”, an adaptive VN resource allocation framework in which virtual resources are dynamically adapted on the basis of the CSPs’ knowledge of VNs performance objectives.42 In Ghazar, et al, a new dynamic VN model is proposed, which serves to determine the users’ current demands with reference to their utility functions and volumes.43 Hence, the VN users are able to determine their requested resources on the basis of a time-of-use pricing.

3.2.2. Current Mapping Algorithms

Various mapping algorithms have been proposed by previous researchers to solve the problems associated with network mapping. The primary goals of mapping algorithms include making good use of the substrate network, increasing the amount of positive mapping, and taking

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the least time in handling tasks.44 Some of the challenges that still exist due to the mapping problems include the constraints connected to the node and link. These constraints may include bandwidth resources available on the links, link delays, processing, computer resources on the nodes, and establishing the location of the nodes.45 Online requests are also still a practical problem affecting the mapping of algorithms. The arrival of the online requests is based on a distribution mechanism since the requests do not arrive once as a large collection.46 Furthermore, the time taken to process each request is infinite. As such, the mapped requests do stay in the substrate network at all times and will only be removed from the substrate network once their time expires.

The simultaneous node and link mapping enhancement can easily be expressed as an un-splittable flow problem commonly known as NP-hard.47 For the solution of this problem, a range of approaches have been proposed, mainly regarding the offline description of the challenge in which the VN requirements are copiously known in prior. According to Zhu et al, a back-tracking method created from a sub-graph isomorphism is proposed.48 This method takes into account the mapping challenges involved in the online version, in which the VN requests are primarily unknown, hence introduces a single-stage approach in which links and nodes are mapped simultaneously; while considering the possible constraints at every step during the mapping process.49 Supposing a malicious mapping decision is sensed, a back-track to the preceding effective decision is made, hence evading a costly or expensive re-map. The back-bone nodes are usually star-connected while the access-nodes are joined to the single back-bone nodes. On the basis of these properties, an iterative algorithm is performed, with diverse procedure for the core-and-access mapping. Nonetheless, the algorithm may simply work in certain topologies.50

A disseminated algorithm deliberates that the computer-generated topologies can be disintegrated in the hub-and-spoke clusters. Every cluster can autonomously be mapped, thereby plummeting the convolution of the entire VN mapping. Zhu et al recommended the heuristic based on a consolidated algorithm in order to deal with VN mapping.51 The central objective of their algorithm was to uphold a low and/or balanced load for both links and nodes within a substrate network. Yu et al also proposed a mapping algorithm that considers limited resources within the physical network, hence enabling path-splitting (virtual links comprising of dissimilar paths), alongside link migration (for changing the underlying mapping) on the embedding process.52 Nevertheless, this high freedom level could result into high fragmentation levels, which are unfeasible to control at large-scale networks. A formal approach is thereby undertaken in order to resolve the on-line VN mapping challenges using a mixed-integer programming design. According to Chowdhury et al, there is a two-step approach in embedding the VNs on the substrate.53 At first step, the virtual nodes are assigned to physical nodes, while in the second step the virtual links are assigned to physical paths. In comparison to the former state of the art heuristics, the formulation proposed by Chowdhury et al provides a better coordination between the two phases, since an ‘augmented substrate graph construction’ is employed.54 The approach by Chowdhury et al is completely different from the mathematical formulation proposed by this paper, which centrally applies a node-link formulation.55 In this approach, the universe of embedding solutions is considered within the ILP formulation, and the VN embedding problem is solved only in a single step using a multi-commodity flow constraint, and by considering the notion of direction of the flows.56

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Houidi et al suggested a topology aware heuristic for VN mapping, and also proposed algorithms to help avoid bottle-necks on the physical infrastructure where they consider virtual node re-allocation and link re-assignment for this purpose.57 As well, Lu et al suggested a heuristic that considers the VNs’ heterogeneity, as well as the physical infrastructure.58 This heuristic can be evaluated by the means of simulation, and also on a small scale test-bed, whereby it achieves mapping times in the order of tens of milliseconds.59 Alternatively, Yu proposed an algorithm for resolving the VN mapping challenges, which as well, considers the CPU demands for the hidden hops. Chowdhury et al thereby extended their preliminary results and included a comprehensive window-based Virtual Network embedding in order to assess the effects of look-ahead on the mapping of VNs.60 As well, Alkmim et al suggested a mathematical formulation,61 which was aimed at:

a) mapping the virtual routers and virtual links;b) minimizing the bandwidth consumption; andc) Minimizing the time needed to instantiate a simulated router.

On the contrary, this work alternatively aims at optimizing link-load and CPU load distribution. Even though all these algorithms offer a concrete resolution to the VN mapping setbacks, an optimal solution for the embedding task and its effectiveness is not given.62 As well, some of these fail to come up with a solution for the assignment problem as a simultaneous optimization of the virtual node and link placement, leading to non-optimal solutions.63

As a remedy to the above problems, the VNE-NLF employs a node-link formulation in order to solve the VN embedding problem in every single step, using the multi-commodity flow restraint. This approach thereby offers the optimal solution to the objective function used since the world of solutions is considered within the ILP formulations.

3.3. NETWORK DESCRIPTION AND PROBLEM FORMULATIONAt this section, the paper introduces the virtual network embedding problem. The VN

embedding notations employed throughout the paper are presented, and the virtual network embedding system is described. The mapping goals are finally introduced in order to support the mathematical formulation.

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Fig. 2: VN Result Life Cycle – Activity Diagram.

A) Network DescriptionHere, a superscript is used to distinguish the physical network from the virtual network, in which p and v correspond to the physical and virtual network respectively.

i) Physical network: Physical network could be defined as a weighted pointless graph Gp = {Np, Lp, Cp,Bp,Dp, Disp} composed by a range of “physical nodes,” Np, plus an array of “physical links,” Lp. Every physical node i is described by its processing capacity, Cpi, commonly referred to as the CPU, and by its physical location, which can be defined by the x and y coordinates. The distance between virtual nodes, Disp, is

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obtainable using the expression bellow (1). In compliance with the physical links, we thereby consider that each link ij has a specific bandwidth, Bpij, and link delay, Dpij , and it is also assumed that every link is an undirected link. The bottom-right of the Fig. 2 above thereby illustrates a physical network topology example comprising of 6 physical nodes and 8 physical links.64 The corresponding capacities of the links and nodes are presented atop the elements.

Dispij = √(xj−xi)2+( yj− yi ) 2 ……………………………………….. (1)

ii) VN Request: VN requests can be defined as weighted undirected graphs Gv = {Nv, Lv, Cv,Bv,Dv, Disv} comprising of a range of virtual nodes, Nv, plus a range of virtual links, Lv. Each virtual node m is characterized by the amount of required CPU, Cvm, and the virtual links mn are logical relations between virtual nodes and characterized by the amount of dedicated band-width, Bvmn, and by the maximum link-delay permitted, Dvmn. Here, it is also assumed that every virtual link is an undirected link. The maximum distance between the virtual nodes, Disv, can be utilized to limit the amount of intermediate hops between virtual nodes. For instance, the left part of Fig. 2 above represents an example of two virtual network requests, VN request 1 on the bottom-left, and VN request k, on the top-left. Every VN request holds a certain lifetime that is, in principle, independent from one another, and each lifetime can have different time-scale, since it is sturdily dependent upon the purpose of the virtual networking request itself.65 Supposing we consider a VN request for a live-rock concert, the time scale will be in terms of hours, though if we consider a VN for a cookery workshop of one week, the time scale will be in terms of days.66

iii) VN Assignment Notations: Foremost, we begin from the convention employed for the index notation: Np denotes the group of nodes fitting the physical network; Lp

represents the range of links in the physical network; and finally, Lpi represent a sub-set of links ij, which are directly linked to the node i. A similar form of notation is usable when representing the VNs using the symbols/letters m and n within the virtual network.67

B) Unfilled Physical Network Resources

The surplus capacity of each physical node at a given time t is shown by the difference between the overall processing capacity and the consumed capacity by all the virtual nodes allocated to that physical node, and it is presented in equation (2) bellow: where u represents the set of all virtual nodes assigned to that precise physical node and at time t.

∀ i∈N :C ip ( t )=Ci

p (0 )−∑u

Cuv (t)….……………………..... (2)

When in parallel, the available bandwidth for every physical link at a given time t is shown by the difference between the overall bandwidth and the bandwidth consumed in all the virtual link segments, allocated on that particular physical link, and is represented as given in expression (3) bellow: where w represents the array of all virtual link segments assigned to that particular physical link, at time t. Any virtual link may comprise of one or more physical links (physical

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path). Therefore, it is considered that every virtual link owns a single physical path, and the link aggregation is not considered (virtual link composed of different physical paths).68 A single physical link can accommodate one or more virtual link segments of different virtual links.

∀ ij∋LP ( k ): Bijp (t )=B ij

p ( 0 )−∑w

Bwv (t )…………………..…. (3)

C) VN Request Embedding Process

The process of VN request embedding can be split into two components: the first component being the component that ensures the virtual nodes’ mapping, and the second handles the virtual links’ mapping.

i) Virtual Node Mapping: Every “virtual node” ought to be mapped into a particular node, and this relationship is given by the mapping function - M {m∈NV ( K ) }=i ; where virtual node m is mapped into a physical node i. Every physical node should have at least the same number of available CPU, as necessitated by the virtual node. See equation (4) bellow:

∀ i , ∀M {m∈N V (K ) }=i :Cmv (k )≤ Ci

p (t)……...……… (4)

ii) Virtual Link Mapping: Any virtual link is capable of being mapped on a single or more physical paths (links). This relationship is shown by the mapping function-

M [ Lmnv ] , in which the virtual link mn is categorically mapped onto a single physical

link/path. Each physical link belong to the physical path that needs to have at least equal amount of bandwidth as required by the virtual link. This is represented as:

∀ ij⊊M ¿……………….. (5)

D) VN Request Life Cycle

The process of embedding begins with the entrance or presentation of a new or subsequent VN request, which is portrayed in Fig. 2 above. A virtual network mapping method, such as the heuristic, is used in embedding the VN; and it assumes as inputs the current state of the physical network (such as the existing CPU capacity and available bandwidth). Supposing the result of the mapping process serves as a viable solution, then the mapping will be considered feasible; however, if it is not, it will be presumed unfeasible and the process of VN embedding stops at that stage.

E) Mapping Metrics

For an easy assessment of the performance of an embedding method, and to compare it with other methods, a range of performance metrics were defined.

i) VN Request Acceptance Ratio: The VN request acceptance ratio (AVN) is given by the expression (6) given bellow. It defines the overall performance of the embedding

15

method. Hence, the number of Virtual Network requests accepted, k’, over the number of all VN requests, k. Given as:

AVN= k 'k

......................................................................... (6)ii) Embedding Factor: Embedding factor, EVN, is given by the expression (7), and it

represents the ratio between the value of virtual resources requested for the VN and the value of physical resources effectively provisioned to accommodate that VN (this represents the efficiency of embedding). The parameters, α, β, γ and η, are used to indicate the diverse types of resources.

ƸVN=α∑

m

Cmv +β∑

mn

Bmnv

γ∑i

C ip+η∑

ij

Bijp …………..............……………….. (7)

3.4. VNE MATHEMATICAL FORMULATION

At this section, we define the mathematical formulation developed for the purpose of solving the online VN embedding problem with defined constraints. The ILP (integer linear programming) approach is employed here to resolve the on-line VN embedding challenges.69 A node-link design is thereby proposed, and two assignment variables are used during the process of embedding.70

A) Assignment VariablesA binary variable x is used in the virtual node mapping and is defined as in equation (8); where x i

m→ Np ×Np matrix. The binary variable y is used with respect to the virtual links, and it is

represented as given in expression (9); where y ijmn→ (Lv )2 × (Lp )2 matrix.

i) Virtual Node Assignment:

x im={1 , virtual nodem isallocated at physicalnode i

0 , else…………. (8)

ii) Virtual Link Assignment:

y ijmn={1 , virtual link mnuses physical link i j

0 , else………………….. (9)

B) Constraints

In order to be assured of the correct mapping of the virtual links plus virtual nodes, and as well obey the conservation law on the capacities of the physical links and physical nodes, an array of constraints are defined.

i. Virtual nodes assignment to the physical nodes: Expression (10) ensures that each and every virtual node is assigned, and it is allocated to only one physical node.

∀m :∑i

x im=1………………………………………………….... (10)

16

ii. Single Virtual Node per Physical Node: Expression (11) bellow guarantees that every physical node is capable of accommodating the maximum virtual node per VN request. However, each physical node can also accommodate other virtual nodes from different VNs. Such constraint is employed in order to certify that every virtual node is assigned a different physical node per VN embedding. It can be suitable in application circumstances where there is a requirement for it to have physical node diversity for redundancy purposes.

∀ i :∑m

x im ≤1………………………………………………. (11)

iii. CPU conservation: Expression (12) ensures that the available CPU capacity of every physical node is not surpassed.

∀ i :∑m

x im . Cm

v ≤ Cip……………………………………...... (12)

iv. Virtual Node distance: Expression (13) ensures that the maximum distance between the virtual nodes, Dv

mn, is never violated. The longest distance between the virtual nodes is a factor of the VN embedding problem. This parameter is provided in distance units and can also be used in expressing the maximum radius between the virtual nodes. Distance between the physical nodes, Disp

ij is obtained using formula (1), where K represents a larger constant used only in situations where the virtual node n is not mapped at physical node i, (xi

n = 0.∀m ,n∈ LM

V , m<n ,∀ i :.

∑j

Dis ijp . x j

m ≤ Dismnv . x i

n+(1−x in) . K…………….. (13).

v. Assignment of virtual links to physical links; multi-commodity flow conservation with node-link formulation: In order to optimize the mapping of virtual links and virtual nodes simultaneously, the multi-commodity flow constraint is employed, with a node-link formulation. Moreover, the notion of direct flows on the virtual links is applied, which is represented as given in Equation (14); where Lv

m represents all the virtual links which are directly linked to the virtual node m, and Li

p represents all the physical links that are connected directly with the physical node i.

∀mn∈ Lmv ,m<n , ∀ i :.

∑ij∈Li

p

( y jimn− y ji

mn)=x im−x i

n

…………………………. (14)

vi. Bandwidth conservation: For the assurance of that the availability of the bandwidth at each physical link is not surpassed, Expression (15) is brought in.

17

∀ ji∈Lip , i< j :.

∑mn∈Lm

v m<n

Bmnv ( y ji

mn+ y jimn )≤ B ji

p

………………….......... (15)

vii. Link delay limit: The virtual link delay, Dvmn, serves as a parameter of the VN

embedding problem, and equals the total sum of the delay of the physical links which comprise the virtual link. In order to ensure that the constraint on link delay is unviolated, we use the expression (16) bellow.

∀mn∈ Lmv ,m<n , ∀ i :.

∑ij∈Li

p i< j

Dijp ( y ji

mn+ y jimn )≤ Dmn

v

………………...………… (16)

3.5. VN ASSIGNMENT – OBJECTIVE FUNCTION The major challenge in the formulation of an ILP model for VN assignment exists in in

the definition of the objective function. In order to support the efficiency of the conforming VN process, the allocation of resources needs to be optimized. Additionally, the most appropriate specification of the VN mapping constraints also presents another challenge in this approach. This section thereby describes the central aims that need to be attained when formulating an objective function for VNE.71

Objective GoalsThe primary goal for the embedding algorithm the minimization of resource

consumption, in order to make resources available for the forthcoming VN embedding requests. Minimization of the resource consumption is only possible for the bandwidth consumption, but depends on the number of involved links during the embedding process. The power of processing has to be installed accurately in the volume required by the VN requests on various physical nodes. Consequently, resource minimization means that the VNs ought to exhibit minimal hop counts on their link paths. In turn, this implies that almost each and every physical node has to be available in order to host a virtual node. Provided the required resources by the VNs are small in relations to the physical capacities of the links and nodes, this availability is guaranteed at a high probability by a load balancing strategy; thereby resulting in to various spare capacities for every physical node or link. Thus, the dominating features in the formulation of an objective function for the ILP problem encompass the bandwidth consumption minimization and load balancing.

Motivation The motivation behind this research study emanates from three major observations. First,

the cost of the inter-datacenter networks is responsible for 15% of the cumulative cost that is much more costly than the cost of the intra-datacenter networks. Secondly, the transit bandwidth covers a much wider area, making it more expensive as compared to developing and maintaining an internal network of the data center. Lastly, there are many worries that the inter-data center network could easily turn into a bottleneck, reducing the probability of acceptance of VDC

18

requests.72 As such, it is important to enhance a reduced reliance on inter-data center traffic to reduce the operational costs as well.73

The proposed VNE-NLF helps in solving the VN embedding problem. The model applies optimization theory in order to simultaneously embed the virtual links and the virtual nodes. Three diverse cost functions are proposed: (i) the LB+_SP, which aims to minimalize the overall load on the network per VN embedding; (ii) the SDP, which aims at minimizing the number of physical links consumed, and at the same time, it selects physical nodes with extreme availability of resources; and finally, (iii) the WSDP which involves the demanded capacity by VN in the objective function.

Simulation experiments proves how far the state of the art heuristics are, from the ILP based optimization method. The variance between the heuristics performance and the VNE-NLF approach is given by at least, 30% for the VN request acceptance ratio. Node utilization is as well higher as compared to the existing heuristics.74 This is the expected outcome since more virtual nodes are to be accommodated on the network. Conversely, the link utilization is similar to the ones of the heuristics, and in a number of cases, it is lower, hence reflecting the better efficiency of the embedding when using the VNE-NLF approach. The embedding parameter of the VNE-NLF is extremely high (close to 1). Results also prove that the maximum distance allowed between the virtual nodes appears to impact the performance of each embedding method differently. In the case of R-ViNE and D-ViNE with three variants, it negatively affects the performance of the VN embedding. For the case of G-SP and G-MCF, it does not seem to cause any direct impact on the embedding; and with regards to the VNE-NLF approach, it does impact positively the VN embedding.

19

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21

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22

NOTES

1 Houidi, I., Louati, W., Zeghlache, D.: A distributed virtual network mapping algorithm. In: Communications, 2008. ICC '08. IEEE International Conference on, pp. 5634 {5640 (2013). DOI 10.1109/ICC.2008.1056

2 “Amazon web services, amazon elastic compute cloud (amazon ec2),” http://aws.amazon.com/fr/ec2/, [Online; accessed September, -2015].

3 “Amazon web services, amazon elastic compute cloud (amazon ec2),” http://aws.amazon.com/fr/ec2/, [Online; accessed September, -2015].

4 Z. Wang, J. Wu, Y. Wang, N. Qi, and J. Lan, “Survivable virtual network mapping using optimal backup topology in virtualized sdn,” Communications, China, vol. 11, no. 2, pp. 26–37, Feb. 2014.

5 F. Petrini, D. Scarpazza and O. Villa, Challenges in Mapping Graph Exploration Algorithms on Advanced Multi-core Processors.

6 M. Rahman and R. Boutaba, “Svne: Survivable virtual network embedding algorithms for network virtualization,” Network and Service Management, IEEE Transactions on, vol. 10, no. 2, pp. 105–118, Jun. 2013.

7 T. Benson, A. Akella, A. Shaikh, and S. Sahu, “Cloudnaas: a cloud networking platform for enterprise applications,” in Proceedings of the 2nd ACM Symposium on Cloud Computing, ser. SOCC ’11. New York, NY, USA: ACM, 2014, pp. 8:1–8:13.

8 M. Brunner, G. Nunzi, T. Dietz, I. Kazuhiko, Customer-oriented GMPLS service management and resilience differentiation, IEEE Trans. Netw. Serv. Manage. (2014) 92–102.


10 “Google cloud platform home page,” https://cloud.google.com/products/app-engine, [Online; accessed September-2015].

11 “Google cloud platform home page,” https://cloud.google.com/products/app-engine, [Online; accessed September-2015].

12 M. Brunner, G. Nunzi, T. Dietz, I. Kazuhiko, Customer-oriented GMPLS service management and resilience differentiation, IEEE Trans. Netw. Serv. Manage. (2014) 92–102.

13 H. Rodrigues, J. R. Santos, Y. Turner, P. Soares, and D. Guedes, “Gatekeeper: supporting bandwidth guarantees for multi-tenant datacenter networks,” in Proceedings of the 3rd conference on I/Ovirtualization, ser. WIOV’11. Berkeley, CA, USA: USENIX Association, 2013, pp. 6–6.


15 G. Alkmim, D. Batista, and N. da Fonseca, “Mapping virtual networks onto substrate networks,” J. Internet Services and Applications, vol. 4, no. 1, pp. 1–15, 2013. Available: http://dx.doi.org/10.1186/1869-0238-4-3


17 M. Yu, Y. Yi, et al., “Rethinking virtual network embedding: substrate support for path splitting and migration,” SIGCOMM Comput. Commun. Rev., vol. 38, no. 2, pp. 17–29, Mar. 2010. Available: http://doi.acm.org/10.1145/1355734.1355737



20 Y. Zhu, M. Ammar, Algorithms for assigning substrate network resources to virtual network components, IEEE INFOCOM In: INFOCOM 2006. 32nd IEEE International Conferenceon Computer Communications. Proceedings (2012) 1–12.

21 X.-H. Sun, Algorithms and architectures for parallel processing : 14th International Conference, ICA3PP 2014, Dalian, China, August 24-27, 2014. Proceedings. Part I, Cham: Springer, 2014.

22 C. Wang, S. Shanbhag, and T. Wolf, “Virtual network mapping with traffic matrices,” in Communications (ICC), 2012 IEEE International Conference on, Jun. 2012, pp. 2717–2722.

23 C. Papagianni, G. Androulidakis, and S. Papavassiliou, “Virtual topology mapping in sdn-enabled clouds,” in Network Cloud Computing and Applications (NCCA), 2014 IEEE 3rd Symposium on, Feb. 2014, pp. 62–67.


25 T. Ghazar and N. Samaan, “Pricing utility-based virtual networks,” Network and Service Management, IEEE Transactions on, vol. 10, no. 2, pp. 119–132, June 2013.

26 F. I., M. Ayari and G. Pujolle, "VN-SLA: A Virtual Network Specification Schema for Virtual Network Provisioning," IEEE Explore Digital Library, pp. 337-342, 2010.

27 N. Mosharaf, K. Chowdhury and R. Boutaba, "A Survey of Network Virtualization," University of Waterloo, Ontario, Canada, 2008.

28 M. Liyanage, A. Gurtov and M. Ylianttila, Software defined mobile networks (SDMN) : beyond LTE network architecture, Chichester: John Wiley & Sons, 2015.

29 G. Held, Virtual private networking : a construction, operation and utilization guide, Chichester; Hoboken, NJ: Wiley, 2004.

30 H. Alshaer, "An overview of network virtualization and cloud network as a service," International Journal of network management, vol. 25, no. 1, pp. 1-30, 2014.

31“Amazon web services, amazon elastic compute cloud (amazon ec2),” http://aws.amazon.com/fr/ec2/, [Online; accessed September, -2015].









40 I. Fajjari, N. Aitsaadi, G. Pujolle, and H. Zimmermann, “VNR algorithm: A greedy approach for virtual networks reconfigurations,” in Global Telecommunications Conference (GLOBECOM 2011), 2011 IEEE, Dec 2011, pp. 1–6.

41 I. Fajjari, N. Aitsaadi, G. Pujolle, and H. Zimmermann, “VNR algorithm: A greedy approach for virtual networks reconfigurations,” in Global Telecommunications Conference (GLOBECOM 2011), 2011 IEEE, Dec 2011, pp. 1–6.

42 J. He, R. Zhang-Shen, Y. Li, C.-Y. Lee, J. Rexford, and M. Chiang, “Davinci: Dynamically adaptive virtual networks for a customized internet,” in Proceedings of the 2008 ACM CoNEXT Conference, ser. CoNEXT ’08. New York, NY, USA: ACM, 2011, pp. 15:1–15:12.


44 K. A. Gallivan, Parallel algorithms for matrix computations, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2000.

45 F. Petrini, D. Scarpazza and O. Villa, Challenges in Mapping Graph Exploration Algorithms on Advanced Multi-core Processors.

46 X.-H. Sun, Algorithms and architectures for parallel processing : 14th International Conference, ICA3PP 2014, Dalian, China, August 24-27, 2014. Proceedings. Part I, Cham: Springer, 2014.



49 X. Ding, C.-H. Liu, L.-C. Wang and X. Zhao, "Coexisting Coverage and Throughput of Multi-RAT Wireless Networks with Unlicensed Band Access," 2014.




53 Chowdhury, M. Rahman, and R. Boutaba, “Vineyard: Virtual network embedding algorithms with coordinated node and link mapping,” Networking, IEEE/ACM Transactions on, vol. 20, no. 1, pp. 206–219, Feb. 2012.



56 J. He, R. Zhang-Shen, Y. Li, C.-Y. Lee, J. Rexford, and M. Chiang, “Davinci: Dynamically adaptive virtual networks for a customized internet,” in Proceedings of the 2008 ACM CoNEXT Conference, ser. CoNEXT ’08. New York, NY, USA: ACM, 2011, pp. 15:1–15:12.


58 J. Lu, J. Turner, Efficient Mapping of Virtual Networks onto a Shared Substrate, Tech. Rep., Washington University in St. Louis, 2013.








66 M. Yu, Y. Yi, J. Rexford, M. Chiang, Rethinking virtual network embedding: substrate support for path splitting and migration, SIGCOMM Comput. Commun. Rev. 38 (2012) 17–29.

67 Chowdhury, N.M.K., Boutaba, R.: Network virtualization: State of the art and research challenges. IEEE Communications Magazine 47(7), 20{26 (2012). URL http://www.mosharaf.com/wp-content/uploads/nv-overview-commag09.pdf








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