PR-VNE: Preventive Reliable Virtual Network ... - IEEE Xplore

Globecom 2013 - Communications QoS, Reliability and Modelling Symposium

PR-VNE: Preventive Reliable Virtual Network Embedding Algorithm in Cloud’s Network Oussama Soualah, Ilhem Fajjari† , Nadjib Aitsaadi and Abdelhamid Mellouk LiSSi, University of Paris-Est Creteil Val de Marne (UPEC): 122 rue Paul Armangot, 94400 Vitry-sur-Seine, France † VIRTUOR: 4 Residence de Galande, 92320 Chatillon, France [email protected], [email protected], [email protected], [email protected] Abstract—In this paper, we propose a new preventive reliable virtual network embedding algorithm denoted by PR-VNE within the Cloud’s backbone network. The proposal does not allocate any backup resources and takes into consideration the ageing of the hardware backbone network. The main objective is to maximise the number of hosted virtual networks while minimising the rate of crashed virtual networks impacted by physical (i.e., routers or links) failures. The problem is a multi-objective non-linear optimisation and classified as NP-hard. To overcome its complexity, PR-VNE is based on the artificial bee colony metaheuristic. Moreover, it makes use of a multi commodity flow algorithm in order to maximise the load balancing of bandwidth usage within the physical network. Based on extensive simulations, the performance obtained is better than the related strategies found in literature in terms of reject and blackout rates of virtual networks.

Keywords: Cloud Computing, IaaS, Virtual Network Embedding, Reliability, Bee Colony metaheuristic. I. I NTRODUCTION Nowadays, Cloud Computing occupies a very important role in the companies [1]. In fact, the main add value consists in subcontracting all the software services (i.e., Software and Platform as a Serivce, SaaS and PaaS) and even the hardware platform (i.e., Infrastructure as a Service, IaaS) to a third party: Cloud computing Providers (CP) [2]. Indeed, the sharing of software and hardware resources within Clouds is allowed thanks to virtualization technology [3]. Many Cloud computing definitions have been found in literature [4]. However, the definition given in [5] is widely adopted: “Cloud computing is a model for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, servers, storage, applications, and services) that can be rapidly provisioned and released with minimal management effort or service provider interaction”. A Cloud infrastructure is formed by a set of a large data centers geographically distributed. The latter are connected via a backbone network in which the virtualization technology is deployed. Hence, a distributed application of a company is hosted in many data centers and communicates thanks to its dedicated Virtual Network (VN ) embedded over the cloud’s backbone network (i.e., substrate network SN ). By allowing multiple heterogeneous network architectures to cohabit on a shared physical infrastructure, network virtualization promises better flexibility, security, manageability and decreased power consumption for the Internet. It is worth noting that the VN is fully administered by the company and the CP only allocates the required resources. It is straightforward to see that the communication between the different sites (i.e., data centers) of the company depends strongly on the reliability of its VN . Hence, the revenue and productivity of the company are also widely impacted. In this paper, we tackle the embedding VN problem within the cloud’s backbone network by taking i) the reliability of the hardware platform and ii) the revenue of CP into consideration. The 978-1-4799-1353-4/13/$31.00 ©2013 IEEE

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objective is to maximise the CP’s turnover by maximising the number of hosted VN s while the proportion of VN breakdown is minimised. In other words, the goal is to minimise the rate of VN blackout while maximising the acceptance rate of VN s in the SN . In fact, previous VN embedding research focused on heuristic algorithms problem assuming that the cloud infrastructure provider network permanently remains operational, which is not realistic. In this research work, we propose a novel Preventive Reliable Virtual Network Embedding algorithm called PR-VNE and based on artificial bee colony metaheuristic [6] [7]. It is worth pointing out that our proposal does not allocate any backup resources for clients. The main idea of PR-VNE consists in dividing the VN topology into many star topologies named Solution Component SCs. Then, each SC is embedded by the artificial bees. To do so, the scout bees search the potential candidates (i.e., food) to host the SC’s virtual node. Afterwards, each source food found by scout bees is associated with an artificial employed bee which exploits its nectar. Indeed, the nectar amount of each food source quantifies the fitness of the candidate solution. Finally, the onlooker bee watching the dance of employed bees will select the source food containing the most nectar to embed the SC. Note that, the employed bees will simulate the mapping of the SC and only the onlooker bee can choose the best one. On the other hand, the employed bees make use the Dijkstra algorithm based on our new metric which takes into consideration i) the residual resources and ii) the reliability of physical resources. Besides, in order to maximise the load balancing within the SN , the employed bees run a combinatorial multicommodity flow algorithm [8] which guarantees !optimal flow performance. Based on extensive simulations, our proposal ourperforms prominent related strategies in terms of reject rate of VN s and the rate of impacted VN s (i.e., clients) by the substrate failures. The rest of this paper is organised as follows. The next section will summarise related work focusing on survivable VN embedding problem. In Section III, we will formulate both the network model and the reliable VN optimisation mapping problem. Then, we will describe our survivable embedding algorithm, PR-VNE and the simulation results respectively obtained in Section IV and Section V. Finally, Section VI will conclude the paper. II. R ELATED WORK Few survivable virtual network algorithms have been proposed in literature. Indeed, we can classify the related methods into two main groups: i) centralised and ii) distributed approaches. It is worth pointing out that in each group that the survivable virtual network embedding algorithm can deal with link and/or node failures. Moreover, in literature the distributed


approaches have not been developed in depth [9] and have not been interested by our comunity. Indeed, this can be explained by the fact that operators have many reluctances to deploy an autonomous multi-agent systems within their backbone networks. Hereafter, we will summarise the prominent centralised strategies in each group. In [10], the authors proposed a new Survivable Virtual Network Embedding algorithm, named SVNE, dealing only with physical link failures. Note that the authors assume when a link failure occurs, a fast re-routing strategy is executed by using preserved quota for backup on each physical link. In other words, in order to protect against single substrate link failure, SVNE dedicates a certain rate of its bandwidth for a backup usage. SVNE heuristic is composed of three stages. First, SVNE proactively computes a set of possible backup detours for each substrate link. Afterwards, SVNE embeds for each new VN request by calling the embedding strategy D-ViNE [11]. Finally, when a link failure occurs, a reactive backup detour optimisation solution is invoked. It reroutes the affected bandwidth along candidate backup detours selected in the first stage. To do so, the authors formulated the problem of the VN embedding problem and re-mapping of virtual links as linear programs. The main objective is to minimise the bandwidth consumption and the penalties due to link failures. Based on simulations, SVNE outperforms the baseline strategies. Unfortunately, the authors have not evaluated the recovery rate of virtual links impacted by failures. Besides, the substrate node failures are not considered in their model. In [12], the authors propounded an algorithm, named RMap, for mapping of VN s with considering failures of substrate links. To maximise the resilience, RMap allocates backup links. To do so, first RMap embeds the VN request by embedding virtual nodes then deals with virtual links. Next SN is formulated as weighted graph by defining for each link its stress. Note that the latter quantifies the number of virtual links transiting through the substrate link. Afterwards, if a link stress is higher than a predefined threshold then RMap will compute its backup detour based on Loop Free Alternate resilience approach [13]. When a link failure occurs, virtual links transiting over this substrate link will migrate to the backup links. Hence, the offered service will not be interrupted. Based on simulations, RMap achieves 70% of virtual link protection. We notice that authors deal only with link protection but substrate node failure is very critical for the operating virtual networks. Moreover, RMap ensures protection only for stressed link. Thus, if a failure occurs within a non stressed link, all VN will be impacted. Furthermore, the rejection rate of VN requests is not evaluated. Finally, we notice that the calibration of stress threshold has not been discussed in the paper. In [14], the authors tackled the resilience VN embedding problem by considering the substrate node failures. A new heuristic approach is proposed denoted Survivable Virtual Infrastructure Mapping (SVIM) algorithm. This latter is based on the K-redundant scheme for surviving facility node failure (K ≥ 1). Note a K-redundant scheme means that K substrate nodes are dedicated to serve as a backup for all critical nodes. Hence, if K = 1, only one substrate node will be used as a backup for all critical virtual nodes. The objective is to minimise the usage rate of physical resource and maximise the reliability of VN s. To do so, the problem is formulated as a Mixed Integer Linear Programming (MILP) optimisation problem. SVIM is based on two stages. First, the VN request is increased with

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redundant virtual nodes and links attached to the selected nodes. Note that this stage takes the virtual critical nodes. Hence, a reliable VN is built into consideration. In the second stage, the increased VN request is mapped in the SN with respect to the usage rate of resource. In order to minimise the total cost of the mapping, SVIM makes use of the backup share approach. Indeed, since only one substrate node can fail at a time, backup paths belonging to different critical virtual nodes can share the same bandwidth. Besides, the cross-share approach is adopted. It consists in sharing the original primary paths with the corresponding backup paths. In order to embed the increased VN request, SVIM operates as following. First, it calls the VN embedding strategy D-ViNE [11] algorithm to find the working mapping for the original VN request. Then, SVIM solve the simplified MILP to obtain only the backup solution using CPLEX. The results show that if K > 1, the reliability increases whereas the node cost ratio is higher than 1. Unfortunately, the authors assumed that physical links remain operational at all times, which is not realistic. Moreover, the authors do not deal with the rejection rate of VN request. In [15], the authors proposed an Opportunistic Redundancy Pooling (ORP) algorithm for reliable VN embedding problem. The main idea behind their proposal is to share redundant resources between many VN s. In other words, backups of some VN s are pooled together as if they belong to the same VN request. In such a way, the number of redundant resources is minimised. The number of backup nodes is calculated analytically such that each VN can guarantee the required reliability guarantees. To do so, the VN request is increased with backup links and nodes. Then, the problem is formulated as a Mixed Integer Programming. Afterwards, the latter is solved using the open-source CBC solver. To evaluate the performance of ORP strategy, the authors compare it to reliable approach but without sharing redundancy resources between VN s. Besides, ORP is compared with the baseline solution in order to gauge the additional amount of resources consumed for reliability. The simulations show that ORP is better than non share approach in terms of rejection rate of VN s and number of required backup resources. In [16], more technical details of ORP are exposed. In fact, the authors extended the Virtual eXecution Description Language (VXDL) to enable the specification of reliable virtual infrastructures. Unfortunately, ORP does not deal with substrate link failures. Moreover, the authors did not explain how the matching should be between a critical node and its associated backup. In [17] two survivable VN embedding algorithms have been proposed named Separate Optimisation with Unconstrained Mapping (SOUM) and Incremental Optimisation with Constrained Mapping (IOCM). The challenging point in [17] is the consideration of geographic region failures that can affect a set of substrate resource (links and/or nodes). In general, a failure of a geographic region infers a simultaneous fail of nodes and links due to events such as natural disasters, etc. To do so, similar to [10], the problem is formulated as a mixed integer linear programming (MILP). The proposal embeds the VN request with respect to the survivability against any single regional failure as follows. First, the VN request is mapped depending on the adopted algorithm SOUM or IOCM. Then, the redundant nodes and links are allocated. Next, if the regional failure occurs then the virtual resources migrate to the backup resources. SOUM calculates the mapping of VN request regardless of any regional failures. Afterwards, for each regional failure it instantiates the


backup resources. The order of regional failures does not affect the mapping result. Unlike IOCM, the mapping depends on the order of dealing regional failures. The proposal has been evaluated and a comparison is performed between the SOUM and IOCM in terms of i) mapping cost, ii) average number of migrations and iii) recovery blocking probability. Unfortunately, the rejection rate of VN s is not evaluated. In this paper we propose a new preventive centralised VN embedding strategy named PR-VNE . Unlike [10], [12], [14], [15], [17], our proposal does not allocate any backup resources. Indeed, it takes into consideration the reliability of physical equipment with the backbone network. Similarly, unlike strategies related above, our proposal takes into account both substrate node and link failures. To the best of our knowledge, this research work is the first one that tackles the preventive approach to maximise the reliability of VN s. III. P ROBLEM

FORMALISATION

In this section, we will formulate the preventive survivable VN embedding problem. As in our previous work [18], we denote the VN by D and the SN by G. Each substrate equipment (i.e., router or link) is typified by its : i) reliability, ii) bandwidth, iii) processing power and iv) memory. Moreover, we assume that the resources mentioned previously in G are limited. Hence, G cannot serve an infinite number of VN requests. Besides, the physical equipment reliability is inversely proportional to its age. In other words, the probability of physical failure increases with time. Consequently, a knowledgeable and smart VN embedding in G is necessary in order to maximise the acceptance rate of VN requests and to minimise the number of hosted VN s impacted by physical failures. Thus, the CP’s revenue is maximised by accepting more clients and paying less penalties due to outage. The SN is formulated as an undirected graph denoted by G = (V (G) , E (G)) where V (G) and E (G) are respectively the sets of physical routers and their connected links. Each physical router, w ∈ V (G), is characterised by its i) residual processing power B (w), ii) residual memory M (w), iii) type: access or core X (w) and iv) reliability Rn (w, t) at time t. Note that if X (w) = 1, then w is an access router. Otherwise, X (w) = 0. Likewise, each physical link, e ∈ E (G), is typified by its i) residual bandwidth C (e), ii) capacity bandwidth Cˆ (e) and iii) reliability Rl (e, t) at time t. As in [19], we model the Mean Time Between Failures (MTBF) as a Weibull distribution. Thanks to the latter, we can estimate the equipment’s reliability at any time and simulate the failures within the SN . The Cumulative Distribution Function (CDF) of the MTBF is expressed as following: ! x "b F (x) = 1 − exp(− ), x ≥ 0 (III.1) a where a and b are the parameters of the Weibull distribution. It is worth pointing out that we assume a heterogeneous age physical network. This means that any equipment in G has its own initial age denoted by A (w) and A (e) for substrate node w and substrate link e respectively. Consequently, we can classify the equipments within the SN in three groups: i) young, ii) adult and iii) old. Note that Rn (w, t) = F (A (w) + t) and Rl (e, t) = F (A (e) + t) where t is the current simulation time. As well, a VN request is formulated as an undirected graph, denoted by D = (V (D) , E (D)) where V (D) and E (D) are respectively the sets of virtual routers and their virtual links.

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Each virtual router, v ∈ V (D), is characterised by its i) required processing power B (v) and memory M (v) and ii) its type X (v). In addition, each virtual link d ∈ E (D) is characterised by its bandwidth capacity C (d). We focus on hosting the virtual graph D in the substrate graph G considering i) the reliability of G and ii) the same VN mapping constraints as in our previous work [18]. We also remind in the following some constraints such as: i) virtual router v must be embedded only in one physical router w, ii) one physical router w can host only one virtual router v belonging to the same VN , iii) the sum of required resources in each substrate router or link cannot exceed its capacity iv) a virtual link is assigned to one unsplittable path, etc. All the constraints and the mathematical formulation are described in [18]. In this paper, our objective is to i) minimise the rejection rate of VN requests as in [18] and ii) to minimise the number of embedded VN s impacted by physical failures. The first objective can be formulated as a minimisation of the resource amount needed to map VN s, hence maximising the residual resources. Moreover, the load balancing of the resource usage rate within the SN should be maximised. To reach the latter, the standard deviation of residual resources is minimised. Formally, # $ # $ maximise# min {C (e)} $, minimise#std {C (e)} $ maximise# min {B (w)} $, minimise#std {B (w)} $ (III.2) maximise min {M (w)} , minimise std {M (w)} e ∈ E (G) , w ∈ V (G) The new second reliability objective consists in embedding the virtual nodes and links within the substrate resources offering the highest reliability during the lifetime of each VN . Hence, for each virtual node v ∈ V (D) within VN , we formulate the node reliability objective as: % & maximise Rn (wv , Twv ) , wv ∈ V (G) (III.3)

where wv denotes the substrate node hosting v and Twv is the age of wv when the virtual network D leaves physical backbone network G. On the other hand, for each virtual link d ∈ E (D), we express the link reliability objective as: '( ( C (ed ) l d maximise ˆ d) × ed ∈P C(e ed ∈P R (e , Ted ) × ) (III.4) ( n d w d ∈P R (w , Tw d ) , P ∈ Paths(d) where Paths(d) denotes the set of substrate paths which can host the virtual link d, {ed } and {wd } denote the set of substrate links and nodes forming the substrate path P ∈ Paths(d). As defined above, Twd and Ted are the ages of the physical node wd and link ed when the virtual network D leaves the backbone network G. We will now outline our preventive survivable VN embedding optimisation problem. Our problem is a non-linear multi-objective combinatorial optimisation problem. It has been proved to be NP-hard [20] [21]. In the next section, we will propose a new scalable preventive reliable VN embedding algorithm based on the artificial bee colony metaheuristic, denoted by PR-VNE. IV. P ROPOSAL : P REVENTIVE R ELIABLE -VNE BASED ON A RTIFICIAL B EE C OLONY As exposed above, the survivable virtual network embedding problem is complex and the optimal solution cannot be generated within polynomial time for a large network. To overcome


maximise minimise maximise minimise maximise maximise ∀v ∈ V (D) , maximise ∀d ∈ E (D) ,

mine∈E(G) {C (e)} stde∈E(G) {C (e)} minw∈V (G) {B (w)} stdw∈V (G) {B (w)} minw∈V (G) {M (w)} stdw∈V (G) {M (w)}

∀w ∈ Nv , B (w) ≥ B (v) M (w) ≥ M (v) X (w) = X (v) = 1

Then, the virtual router v is mapped within wv ∈ Nv offering the highest reliability. Formally, ∀w ∈ Nv ,

{Rn (wv , Twv )} , wv ∈ V (G)

( C (ed ) maximise ed ∈P R (e , Ted ) × ed ∈P C(e ˆ d) × ) ( n d w d ∈P R (w , Tw d ) , P ∈ Paths(d) subject to: All the VN embedding resource and geographical constraints [18] '(

l

d

Problem 1: Preventive reliable VN embedding optimisation problem the high complexity, in this section we will describe our proposal named Preventive Reliable Virtual Network Embedding algorithm denoted by PR-VNE. Indeed, it is based on artificial bee colony metaheuristic [6] [7] and operates as follows. First, PR-VNE embeds the virtual access routers and virtual links connecting them. Then, PR-VNE subdivides the remaining VN topology into many star topologies denoted by Solution Component {SC i }. In fact, each SC i is composed by one virtual node and its hanging links. Afterwards, the {SC i } are embedded sequentially by the artificial bees in the same order of their generation. Note that for each SC i , a colony of scout bees search for potential candidates which can host the SC’s virtual router. Next, employed bees will simulate the embedding with respect to the residual and reliability of hardware resources. At the end, the onlooker bee will select the best embedding in terms of employed bees’ nectar (i.e., mapping cost). The PR-VNE’s pseudo-algorithm is summarised in Algorithm 1. Algorithm 1: PR-VNE 1 Mapping of access routers and virtual links connecting them ˆ = {SC i } 2 Erecting the set of SC ˆ 3 for i ← 1 to |SC| do 4 Send scout bees to locate candidate routers of SC i ’s centre router 5 Employed bees explore and evaluate the nectar of candidate routers 6 Onlooker bee selects the best employed bee’s solution

Hereafter, Mapping of components, artificial bee

(IV.5)

we will describe the main PR-VNE stages: i) virtual access routers ii) Erecting of solution iii) Mapping of solution components based on colony.

A. Mapping of virtual access routers Since the virtual access routers in V (D) can be mapped only within a predefined geographical area Zv∈V (D) , hence PR-VNE embeds first all the access virtual routers as following. For each v ∈ V (D) and X (v) = 1, PR-VNE selects within the geographical zone Zv all the physical access routers w ∈ V (G) satisfying the required resources denoted by Nv . Formally,

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Rn (wv , Twv ) ≥ Rn (w, Tw )

(IV.6)

where Tw is the age of router w when the VN of v leaves the SN . Afterwards, the virtual links d ∈ E (D) connecting the virtual access routers are mapped. To do this, PR-VNE makes use Dijkstra algorithm with a new metric which takes into consideration the substrate residual resources and reliability. Finally, PR-VNE applies the multi-commodity flow algorithm in order to load balance the usage rate of bandwidth within the SN . The details of the embedding link algorithm will be presented in Section IV-C2. B. Erecting of solution components Once the access routers and their connecting virtual links have been mapped, the remaining virtual topology is denoted ˜ We notice that some virtual links have one extremity (i.e., D. virtual router) already mapped. We call the latter virtual links as hanging links. ˜ virtual topology into Now, PR-VNE can subdivide the D many star topologies named solution components {SC i }. Note that each SC i is composed of one single virtual router and all its attached virtual hanging links. Besides, PR-VNE selects the virtual node having the highest number of hanging links ˜ ← D\SC ˜ to construct the SC i . Then D i and the process is ˜ repeated until D = ∅. C. Mapping of solution components based on an artificial bee colony Each solution component SC i is formed by one single virtual node denoted by v i and a set of hanging links denoted by {dij }. The onlooker bee will send scout bees within the SN to locate a set of candidate substrate routers that can host v i . Based on the source foods found by scout bees, the onlooker will now send the employed bees to explore them and evaluate their nectar amount. It is worth noting that embedding cost and its reliability depends strongly on the nectar amount. When all the employed bees come back to the hive, the onlooker (i.e., queen) bee will select the best source food containing the highest value of nectar. Hereafter, we will describe i) how the scout bees choose the candidate solutions (i.e., sources food) and ii) the employed bees quantifies the nectar of the source foods. 1) Scout artificial bees: select the potential candidates that will be explored by the employed bees. To do so, the scout bees choose the substrate routers located within H hops from the nearest substrate router to the barycentre point of the substrate nodes hosting the virtual nodes of hanging links {dij }. It is worth pointing out that the residual resources of the latter substrate routers must be greater than v i ’s request in terms of i) processing power and ii) memory. We name the selected substrate nodes i as S v . 2) Employed artificial bees: For each substrate node w ∈ i S v , one employed bee will simulate the mapping of SC i (i.e., v i and {dij }) in order to evaluate the mapping cost. Hence, the quantity of nectar is estimated. To do so, an employed bee looks for the best path that maximises the defined metric in


equation III.4 by running the shorts path (i.e., Dijkstra algorithm). We recall that the latter metric takes into consideration i) the residual resources and reliability of substate links and ii) reliability of transiting substrate routers. Once the first solution of embedding SC i ’s virtual links is generated, PR-VNE will apply the multi-commodity flow algorithm [8] in order to load balance the usage rate of virtual links. The virtual links of the SC i represent the K commodities of the multi-commodity flow algorithm. In fact K = |{dij }|. The main idea consists in handling the above K commodities by assigning long paths in terms of the potential function φ to highly congested substrate links and short lengths to lightly congested ones. We define the SC i ’s potential function φi as: # $ * φi = di ∈SC i φ(dij ) (IV.7) j where φ(dij ) is the potential function of a virtual link dij ∈ SC i . We define it as: + ! ", d * ) φ(dij ) = ed ∈P Rl (ed , Ted ) · exp α · C(e (IV.8) ˆ d) C(e where P is a candidate embedding path to host the virtual link dij . α is analytically calibrated in order to guarantee the convergence to O(!)-optimal. Formally, α is defined as: α = 2 · (1 + !) ·

ˆ d) C(e C(ed )

· ln( m ! )

(IV.9)

where m is the number of substrate links within the Cloud’s backbone network (i.e., m = |E (G) |). The multi-commodity flow algorithm repeatedly modifies the assignment of flows (i.e., mapping decision of SC i ’s virtual links) until it becomes O(!)-optimal. In fact, in each iteration the algorithm calculates optimal value of α, hence the potential function φ induced. In [8], the authors prove that the process converges and is stopped when φ ≤ (1+!)φ∗ . Note that φ∗ is the minimal optimal potential value. PR-VNE limits the maximum number of iterations to NMCF . One the algorithm converges, our proposal embeds the SC i in the SN with respect to the final decision. As we can see, our proposal does not need any reservation of backup resources. Indeed, the reliability is maximised during the embedding of virtual nodes and links by taking into consideration the reliability of each used physical equipment within the SN . V. P ERFORMANCE E VALUATION In this section, based on extensive simulations, we will gauge the effectiveness of our proposal PR-VNE. For this aim, first we describe our discrete event VN embedding simulator with considering the reliability of the SN and the age of its equipments. Afterwards, we will define the main performance metrics in aim to compare our proposal with two related prominent survivable embedding virtual network strategies: i) SVNE [10] and ii) RMap [12]. At the end, based on the outputs of the above simulations, we will assess our proposal and comment the results obtained. A. Simulation Environment We implement a discrete event survivable VN embedding simulator. To do this, we make use of GT-ITM tool to generate random SN and VN topologies. Note that we model the arrival of VN requests by a Poisson Process with rate λA . We also model VN lifetime by exponential distribution with mean µL .

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As stated in our previous work [18], we set the SN size to 100. In this case, the ratio of access and core nodes is fixed to 20% and 80%, respectively. Furthermore, we set the VN size according to a discrete uniform distribution, using the values given in the interval [3, 10]. As in the SN , the proportion of access virtual routers is set to 20% in each VN . It is worth noting that in both cases (VN and SN ), each pair of nodes is randomly connected with a probability of 0.5. The arrival rate λA and the average lifetime µL of VN s are fixed to 4 requests per 100 time unit and 1000 time units respectively. We calibrate the capacity of substrate nodes and links (i.e., B (w), M (w) and Cˆ (e)) according to a continuous uniform distribution taking values in the interval [50, 100]. As well, we set the required virtual resources (i.e., B (v), M (v) and Cˆ (d)) according to a continuous uniform distribution, using the values given in the interval [10, 20]. Concerning the reliability of substate network, the parameters a and b of the Weibull distribution modelling the mean time between failures (MTBF) are set to 25×104 and 1.5 respectively. It is worth pointing out that a and b are calibrated in order to obtain expected lifetime of each physical equipment (≈ 6×105 ) approximately equal to 10 times the simulation duration (≈ 6 × 104 time units). Moreover, the proportional of young, adult and old equipments in the SN is defined in each scenario. Besides, the initial age of each physical equipment follows a uniform distribution within the bounds of its group (i.e., young, adult and old). In our simulator, we implemented our PR-VNE proposal alongside the related strategies: i) SVNE and ii) RMap. Based on extensive simulations, we calibrate the maximum number of iterations of the multi-commodity flow algorithm NMCF to 20. We fix the hop-range within local search area H of scout artificial bees to 1. We set the number of VN requests to 2000. It is worth noting that each performance value of pseudo-random strategies is equal to the average of 15 simulations. Moreover, simulation results are always presented with confidence intervals corresponding to a confidence level of 95%. Note that tiny confidence intervals are not shown in the following figures. B. Performance Metrics In this section, we will define the performance metrics used to assess our proposal. 1) Q: is the reject rate of VN requests during the simulation. In other terms, the rate of VN s which have not been mapped in the SN . 2) F: is the rate of deployed VN s which had been impacted by physical failures during the simulation. In fact, a VN is impacted if at least one of its components (i.e., virtual router and/or link) is impacted by the physical failure. 3) G: evaluates the SN provider’s profitability by calculating the total benefit G1 of all accepted VN requests minus the paid penalties G2 to the clients induced from the physical failures during all the simulation lifetime (G = G1 − G2 ).G1 is defined as in [10]. It depends on the amount of requested resources and the lifetime of the virtual network in the backbone T . We define the penalty G2 as the reimbursement to the clients. The cost is proportional to the residual time of a VN heightened by a penalty δ. Formally, for each VN denoted by D: G2 (D) =

(T −∆T ) T

× G1 (D) × δ

(V.10)

where ∆T is the hosting duration in the SN before the physical failure and δ is the penalty rate. In our simulations, we set the penalty to 5%.


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In this section, we will illustrate the performance of our proposal PR-VNE and the comparison with SVNE and RMap. For this aim, we consider two scenarios. In the first one, we vary the rate of young equipments in the SN while fixing the rate of old equipments to 10%. In the second scenario, we vary the proportion of adult equipments while setting the rate of young equipments to 30%. In the following, we will comment the results obtained. Finally, we will study the impact of NMCF on the performance of our proposal. 1) Variation of young physical equipments rate: Hereafter, we study the impact of varying young equipments population in the SN on the performance of our proposal PR-VNE. We simulated the Weilbull distribution for substrate nodes and links failures. The cumulative distributions of MTBF for physical equipments are depicted in Fig. 1. It is straightforward to see that when the rate of young equipments increases, the number of failures decreases within the SN . In Fig. 2, we notice that when the population of young equipments increases the performances are better in terms of i) reject rate of VN , ii) rate of VN impacted by physical failures and iii) revenue. On the other hand, we observe in Fig. 2.(a) and Fig. 2.(b) that PR-VNE outperforms both related strategies: RMap and SVNE. In spite of backup resources’ reservation performed by the related strategies, our proposal accepts more VN s in the backbone while the rate of VN s (i.e., clients) impacted by physical failures is approximately equal to RMap and lower than SVNE. In other words, whereas our proposal is preventive approach, it achieves at least the same performance of strategies based on backup mechanism in term of resilience against physical failures. Consequently, as shown in Fig. 2.(c), the revenue of cloud provider is increased with our proposal. Indeed, RMap and SVNE loses at least 15% and 5% of revenue compared to PR-VNE. 2) Variation of adult physical equipments rate: The impact of varying adult equipments on the performance is depicted in Fig. 4. The sampling of the MTBF Weibull distribution is illustrated in Fig. 3 for physical nodes and links. It is clear that when the physical network is older, the rate of physical failures growths. As depicted in Fig. 4, the increase of rate of adult equipments deeply deteriorates the performances in terms of i) reject rate of VN s, ii) rate of VN s impacted by substrate failures and iii) provider’s revenue. As in scenario 1 (i.e., varying the rate of young equipments), despite being a preventive approach, our proposal outperforms both related strategies RMap and SVNE. In fact, PR-VNE rejects less VN requests than the related approaches (see Fig. 4.(a)) while the proportion of VN s

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impacted by physical failures is approximately equal to RMap and lower than SVNE (see Fig. 4.(b)). In Fig. 4.(c), we illustrate the rate of CP’s loss compared with our proposal. In fact, RMap and SVNE lose respectively at least 30% and 10%, which is considerable. Based on results obtained in both scenarios, we can conclude that our proposal PR-VNE without any reservation of backup resources surpasses the related strategies. In fact, considering the reliability of physical equipments during the VN mapping process improves widely the revenue of Cloud providers. 3) Impact of NMCF : In Fig. 5, we evaluate the reject rate of VN s and the rate of VN impacted by physical failures while varying NMCF . It is clear that both performance are steady. It means that our proposal is not sensitive to this parameter. In other words, PR-VNE converges to !-optimal solutions quickly. VI. C ONCLUSION This paper studied the survivable virtual network embedding problem which is NP-hard and computationally intractable. In response, we proposed a novel preventive algorithm named PR-VNE. It is based on a artificial bee colony metaheuristic and

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multi-commodity flow. Our objective is to minimise the impact of physical failures within Cloud’s backbone and to maximise the revenue of providers. Based on extensive simulations, we have shown that PR-VNE makes embedding more effective and minimises the rate of clients impacted by physical failures. Moreover, PR-VNE outperforms related prominent strategies RMap and SVNE which make use of backup resources. ACKNOWLEDGMENT This research was supported by TILAS project funded by the European Union Celtic-Plus (2013-2015). R EFERENCES [1] S. Marston, Z. Li, S. Bandyopadhyay, J. Zhang, and A. Ghalsasi, “Cloud computing: The business perspective,” Decision Support Systems, vol. 51, pp. 176 – 189, 2011. [2] R. Buyya, C. S. Yeo, and S. Venugopal, “Market-oriented cloud computing: Vision, hype, and reality for delivering IT services as computing utilities,” pp. 5 –13, 2008. [3] N. M. M. K. Chowdhury and R. Boutaba, “A survey of network virtualization,” Computer Networks, vol. 54, 2010. [4] L. M. Vaquero, L. Rodero-Merino, J. Caceres, and M. Lindner, “A break in the clouds: towards a cloud definition,” ACM SIGCOMM Computer Communication Review, vol. 39, pp. 50–55, 2009. [5] NIST, “Definition of Cloud Computing v15,” csrc.nist.gov/groups/SNS/cloud-computing/cloud-def-v15.doc. [6] D. Karaboga and B. Basturk, “On the performance of artificial bee colony (abc) algorithm,” Elsevier Applied Soft Computing, vol. 8, 2008. [7] D. Karaboga, B. Gorkemli, C. Ozturk, and N. Karaboga, “A comprehensive survey: artificial bee colony (abc) algorithm and applications,” Springer, Artificial Intelligence Review, 2012. [8] T. Leong, P. Shor, and C. Stein, “Implementation of a combinatorial multicommodity flow algorithm,” Discrete Mathematics and Theoretical science, 1992.

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