Replication of Virtual Network Functions: Optimizing Link Utilization and Resource Costs

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1 Repication of Virtua Network Functions: Optimizing Link Utiization and Resource Costs Francisco Carpio, Wogang Bziuk and Admea Jukan Technische Universität Braunschweig, Germany Emai:{f.carpio, w.bziuk, arxiv: v1 [cs.ni] 23 Feb 2017 Abstract Network Function Virtuaization (NFV) is enabing the softwarization of traditiona network services, commony depoyed in dedicated hardware, into generic hardware in form of Virtua Network Functions (VNFs), which can be ocated fexiby in the network. However, network oad baancing can be critica for an ordered sequence of VNFs, aso known as Service Function Chains (SFCs), a common coud and network service approach today. The pacement of these chained functions increases the ping-pong traffic between VNFs, directy affecting to the efficiency of bandwidth utiization. The optimization of the pacement of these VNFs is a chaenge as aso other factors need to be considered, such as the resource utiization. To address this issue, we study the probem of VNF pacement with repications, and especiay the potentia of VNFs repications to hep oad baance the network, whie the server utiization is minimized. In this paper we present a Linear Programming (LP) mode for the optimum pacement of functions finding a trade-off between the minimization of two objectives: the ink utiization and CPU resource usage. The resuts show how the mode oad baance the utiization of a inks in the network using minimum resources. I. INTRODUCTION Network Function Virtuaization (NFV) is a new paradigm that virtuaizes the traditiona network functions and paces them into generic hardware and couds, as opposed to the designated hardware. The pacement of the virtua network functions (VNFs) can happen either in remote data centers or by depoying singe servers or custers of servers. Pacing VNFs in remote data center can ower the cost of depoyment, but is known to typicay increasing the deay and create churns of network oad, due to the fix and often remote ocation. Instaing new services (or, mini data centers) inside the network can mitigate the distance-to-datacenter probem. At the same time, the depoyment of new servers forming sma data centers in reguar nodes requires new investment costs, which requires a gradua upgrade of the network. Therefore, the optima pacement of these servers in the network is a must for network operators to reduce the operationa costs. Whie most of the current work concentrates on the optima pacement of VNFs under some specific objective minimizing the network costs under some specific resources constraints, e.g. costs of power consumption or the number of physica servers, ess effort has been on addressing the network oad baancing probem with VNF pacement. In this paper, we address, jointy, the network oad baancing and resource cost probem with VNF pacement, where the concept of VNF repications is used to find a trade-off between network oad baancing and network costs. The Fig. 1 iustrates the idea, whereby we assume a service chain which is composed by non-repicabe VNFs and, depending on the number of repicas, may be spitted to one or more parae sets of an ordered sequence of VNFs towards the service end-point. The VNF repicas in a service chain can be impemented as many time as needed in the network. The major advantage is to spit the traffic fows in a controed way such that network traffic oad baancing can be optimized when the service is running. As commony in network services, the service chain starts with a non-repicabe VNF, e.g. a oad baancer or gateway, and is aocated in a dedicated data center which generates service requests. Whie the rest of the functions are aocated on sma servers, maintaining the sequence order. To find the optimum pacement of servers required for the depoyment of VNFs, we formuate the probem as a Integer Linear Programming (ILP) mode. The rest of the paper is organized as foows. Section II presents reated work. Section III describes the reference architecture. In Section IV, the reated optimization mode is described. Section VI anayzes the performance, and Section VII concudes the paper and discusses future research. II. RELATED WORK Eary work in [1] studies the optima VNFs pacement in hybrid scenarios, where some network functions are provided by dedicated physica hardware and some are virtuaized, depending on demand. They propose an ILP mode mode with the objective to minimize the number of physica nodes used, which imits the network size that can be studied due to compexity of the ILP mode. In [2], a context-free anguage is proposed for the specification of VNFs and a Mixed Integer Quadraticay Constrained Program (MIQCP) for the chaining and pacement of VNFs in the network. The paper finds that the VNF pacement depends on the objective, such as atency, number of aocated nodes, and ink utiizations. In mobie core networks, [3] discuss the virtuaization of mobie gateways, i.e., Serving Gateways (S-GWs) and Packet Data Network Gateways (P-GWs) hosted in data centers. They anayze the optimum pacements by taking into consideration the deay and network oad. In [4] aso propose the instantiation and pacement of PDN-GWs in form of VNFs. Unike previous work, we sove the VNF pacement probem by considering VNF repications which is the nove idea that we aready proposed in [5]. In this work, we extend [5] to sove the optimum pacement of VNFs by minimizing the network

2 enb S-GW Internet P-GW + Services Legacy system VNF1 S-GW P-GW LB Service Function Chain VNF4 LB FW NAT enb VNF1 S-GW LB P-GW VNF4 LB FW NAT VNF1 VNF4 S-NE Physica ocation Fig. 1: Use case on Mobie Core Networks P-NE cost whie maximizing oad baancing with constraints on the avaiabe resources in mobie core networks. Therefore, we propose a more reaistic approach to enabe an scaabe growth of the mobie data traffic over years. This paper aso incudes a new traffic mode which aso considers the end-user traffic generated in the Radio Access Network which previous paper did not consider. We aso consider mutipe VNFs pacement per node with repications, which is new. III. REFERENCE ARCHITECTURE The NFV architecture is basicay described by three components: Services, NFV Infrastructure (NFVI) and NFV Management and Orchestration (NFV-MANO). A Service is the composition of VNFs that can be impemented in virtua machines running on operating systems or on the hardware directy. The hardware and software resources are provided by the NFVI that incudes connectivity, computing, storage, etc. Finay, NFV-MANO is composed by the orchestrator, VNF managers and Virtuaized Infrastructure Managers responsibe for the management tasks appied to VNFs. In NFV-MANO, the orchestrator performs the resource aocation based on the conditions to perform the assignment of VNFs chains on the physica resources. The sub-task running in the orchestrator, known as VNF Forwarding Graph Embedding (VNF-FGE) or VNF pacement probem, tries to find the optimum pace to aocate VNFs with regard to some specific objective, such as minimization of computation resources, minimization of power consumption, network oad baancing, etc. A. Gateway Virtuaization: The EPC Use-Case In the focus area of VNF pacement probem, we propose to study a concrete scenario from egacy mobie systems, namey the Evoved Packet Core (EPC) networks, where we beieve that the VNF pacement in Service Function Chaining can bring most benefits. The proposed case study is shown in Fig. 1. The Serving Gateway (S-GW) and PDN Gateway (P-GW) are connected to e-nodeb and send the end-user traffic towards Internet. This traffic usuay requires various additiona services, currenty depoyed using traditionay enb Background traffic End-user traffic Fig. 2: Network traffic considerations Data Center traffic embedded network functions, such as oad baancers, TCP optimizers, firewas and NATs. Considering the virtuaization of the S-GW and P-GW on sma data centers, as proposed in [3], both the data-pane and contro-pane functions of the current egacy gateways are moved to an operator s datacenter. At the paces of the egacy gateways, an off-the-shef network eement (NE) is used to redirect the traffic from the origin access point of the Radio Access Network (formey done by the S-GW) to the DC and from the DC to the externa backbone interface, which is, in the most cases, the former pace of the P-GW. Typica VNFs reated to contro-pane functionaities of the S-GW and P-GW can not be further distributed on the network. In contrast, due to the arge traffic voumes handed by the data-pane, parae transmission paths can be used in the transport network, and thus, VNFs reated to datapane functions with high intensives tasks, e.g. TCP optimizers (TCP opt) or Performance Enhancement Proxies (PEP), may aso be repicated and be used in parae at different network ocations, as proposed in [6]. Thus, we study the chaining and virtuaization of the additiona functions reated to the datapane on different physica ocations (sma data centers) in the mobie core network. The number of required repicas wi be in reation with the network traffic demands. Therefore, by knowing how many repicas are necessary we can pace them to maintain a good network oad baancing. On the other hand, the usage of additiona network ocations can increase the number of required servers and DCs, which potentiay wi increase the network costs. To this end, we define the probem as finding the optimum pacement for these functions subject to the network costs in form of used DC ocations whie at the same time oad baancing the network. B. Network Traffic Mode In a rea network, not a services wi be virtuaized at once. Thus in this paper, we assume two kinds of network traffic, defined as the background traffic and data center traffic. This is iustrated in Fig. 2. The background traffic is reated to the egacy not virtuaized services and the traffic is

3 generated from each core node to the rest of nodes and routed by a traditiona network core protoco, e.g. IP routing. The virtuaized services are responsibe for the data center traffic. This traffic is generated at the S-NEs (former S-GW paces) and has to be transported towards the Internet gateways (P- NE s at former P-GW ocations), as shown in Fig. 1. Since the atter category of traffic, usuay TCP connections, is generated by end users, it has to traverse a set of network functions to match the required service before accessing to Internet. In our approach, we assume that the background traffic can be generated randomy and forwarded foowing the rues of a specific Traffic Engineering (TE) mode defined by the traditiona singe path destination oriented IP routing. The TE mode written in form of ILP formuation (detaied in the next section) minimizes the ink utiization of a inks in the network using a inear cost functions approach. Once the background traffic is oad baanced, it wi not be affected by the contro of the data center traffic, but it has to be considered as a fixed input parameter for the next mode caed Resource Aocation (RA). This mode is used to aocate optimay VNFs in the network trying to minimize the cost associated to the used resources, maximizing the network oad baancing. The optimum pacement of VNFs and repicas can provide the optimum ocations for the data centers, which wi be responsibe for the instantiation of VNFs in the network. IV. OPTIMIZATION MODELS This section formuates the Link Capacity Dimensioning, TE and RA modes as optimization probems subject to a set of constraints, as described next. The notation of a parameters and variabes is summarized in Tabe I. A. Link Capacity Dimensioning Mode This mode aows the initia ink dimensioning with the aim to minimize the required capacities for a given topoogy and a given traffic matrix. Then: Minimize: C L t T t (1) The constraint (2) assures that for the given ink traffic (eft side) the capacity of each ink is dimensioned according to an over-provisioning factor ϑ. So, L: λ R p t p P p ϑ C λ t T t t (2) λ Λ b To be sure that every ink is of exacty one bandwidth type: L : Ct = 1 (3) t Finay, the next constraint assures that every traffic demand exacty uses one admissibe path: λ Λ b : R p P p λ = 1 (4) λ B. Traffic Engineering Mode The TE mode minimizes the utiization cost of a inks in the network given as Parameter N = {n 0, n 1,..., n (N 1) } L = { 0, 1,..., (L 1) } P = {p 0, p 1,..., p (P 1) } T = {t 0, t 1,..., t (T 1) } Y = {y 0, y 1,..., y (Y 1) } S = {s 0, s 1,..., s (S 1) } V s = {v 0, v 1,..., v (Vs 1)} Λ = {λ 0, λ 1,..., λ (Λ 1) } Λ b Λ Λ s Λ P λ P P s P t p {0, 1} r v {0, 1} r max w max c ϑ Variabe TABLE I: Notation Meaning set of a nodes set of a inks set of a paths set of a bandwidths types set of inear cost functions set of service chains set of VNFs in service chain s set of a traffic demands subset of background traffic demands subset of demands of service chain s subset of paths for a specific λ subset of paths for service chain s 1 if path p traverses ink 1 if function v can be repicated maximum number of aowed repicas per service chain maximum number of VNFs per DC maximum capacity of ink over-provisioning capacity ratio Meaning K utiization cost of ink Rp λ {0, 1} 1 if traffic demand λ is using path p Ct {0, 1} 1 if ink is of of bandwidth type t Rp s {0, 1} 1 if service chain s is using path p Rp λ,s {0, 1} 1 if traffic demand λ from service chain s is using path p Fn v,s {0, 1} 1 if VNF v from service chain s is aocated in node n F n {0, 1} 1 if node n is running some VNF Minimize : L K (5) where the cost of every ink is reated to its ink utiization U T E and defined by the resuting vaue from a inear cost functions y i (U T E ) = a i U T E b i as foows: ( ) L, y Y : K y U T E where constants a i and b i are chosen in a way that the sope of the incrementa cost vaues y i Y approximatey foows an exponentia function [7]. The ink utiization is given by U T E = λ Λ b p P λ (6) λ R λ p t p c (7) The summation takes into account each traffic demand λ out of the set of a background demands Λ b whose specific path p P λ is traversing ink, divided by the ink capacity. The ony routing constraint for this mode assures that every traffic demand exacty uses one admissibe path: λ Λ b : R p P p λ = 1 λ

4 C. Resource Aocation Mode The second optimization mode, caed RA mode, uses a simiar objective function than the previous one, but adding a new term using the binary variabe F n (1 means the node is used by at min 1 VNF, 0 no VNF is assigned) which minimizes the number of nodes that are aocating VNFs subject to the constraints expained beow: ( ) ( ) Minimize : α K + β F n (8) L n N Both terms are weighted by α and β parameters to enabe the desired tradeoff between oad baancing and network costs. In this paper we restrict to use them as seection parameter for one of the objective functions. The RA traffic mode is different to the TE mode and defined as foows. For each service chain s S a tota number of Λ s traffic demands λ Λ s are defined, where each of them coud not be spitted and have to be forwarded over one service chain specifc path p P s, which is taken (is ony 1 if path p is used by demand λ). Furthermore, the number of paths P s may be different than the number of demands. Thus, without the usage of VNF repicas a demands of a service chain must use the same path. As a resut, the ink utiization due to the RA mode is given by: into account by binary variabe R λ,s p U RA = s S λ Λ s p P s λ Rp λ,s t p (9) c In the RA mode, the inear utiization cost functions take into account the superposition of the fix given background TE traffic with the RA traffic specified as: ( ) L, y Y : K y U T E + U RA (10) Because each demand has to be assigned to a path, the routing constraint is given by s S : R λ #» p P p λ,s = Λ s (11) s Λ s Then, to know if an specific node is being used or not, the binary variabe F n wi ony be 1 if 1 VNFs are assigned to a node n, which is assured by the constraint n N : s S v V F v,s n W F n s S v V F v,s n (12) where the binary variabe Fn v,s indicates, if VNF v from service chain s is aocated to node n. W is a arge constant to assure, that the eft side of the equation is aways ess than 1. The next constraint (13) assures that a certain traffic demand λ can ony use a path p if the requested service chain is aso using the same path. Thus (13) takes into account, that more than one demand can use the same path. On the other hand, constraint (14) guarantees, that a service schain s can not estabish an active path without traffic assigned to it. V1 p1 p2 V2 V2_rep Node n V3 Fig. 3: VNF repication strategy s S, p #» P s, λ #» Λ s : R λ,s p R s p (13) s S, p #» P s : R s p R λ,s λ Λ #» s V4 p (14) Furthermore, the number of admissibe paths for each service chain s is constrained by the number of repicas. Then, for [0, 1, 2,..., r max ] repicas, each service chain can use at maximum [1, 2, 3..., (r max + 1)] paths to forward traffic, i.e., s S : 1 p #» P s R s p r max + 1 (15) Therefore, with no repicas, a certain service chain can ony use one path, whie increasing number of repicas, the number of admissibe paths proportionay increases. Then, for each activated path in service chain s defined by Rp, s the next constraint aocates a VNFs of the service chain: s S, p P s, v Fn v,s (16) V s : R s p n p On the other hand, the sequence order of VNFs in the service chain has to be maintained. Then, for a certain path p, the function v can not be aocated in the node n, if the previous function v 1 is not aready aocated in any of the previous nodes of the same path. So, v V s, p P s, n p: ( n ) m=0 F (v 1),s m F v,s n R s p 1 when v > 0 (17) The next two constraints imit the maximum number of VNFs that can be aocated in the network. First, the maximum number of VNFs aocated in some specific node n is constrained by the parameter w max : n N : F s S v V n v,s w max (18) s Second, if a certain function v can be repicated r v, then, the maximum number of repicas is constrained by the maximum number of active paths Rp. s If the function can not be repicated, then can ony be paced once. So, s S, v V s : Fn v,s r v R n N p P p s + 1 r v (19) s To improve the oad baancing feature using repicated VNFs, we introduce an additiona constraint. In the proposed repication mode, we excude the case where two seected

5 Fig. 4: Janos-us network paths p 1 and p 2 from the service chain s are choosing the same shared node n to pace the same function (origina and repica). So, foowing the exampe shown in Fig. 3, v 2 and v 2 rep can never be aocated in the same node n. Then, for v V s, p 1 P s, p 2 P s, n 1 p 1, n 2 p 2 : R s p 1 + R s p 2 + 2F v,s n r v 3 { n1 = n 2 = n v 0 V s 1 (20) To be noted that, this constraint is added for a possibe pairs of admissibe paths of each service chain. To reduce the computing compexity we restrict, in this work, to ink disjoint paths. V. PERFORMANCE EVALUATION In this section, we show the resuts for four different optimization scenarios: 1) network oad baancing (minlb), 2) minimization of network costs (minnc) given by the number of required data centers (DCs), 3) minimization of network costs with imited number of VNFs per DC (minnc constr) and4) network oad baancing with imited number of DCs to pace VNFs and imited number of VNFs per DC (minlb constr). The LP modes are impemented using the Gurobi Optimizer [8] and the topoogy (26 nodes and 84 inks) is chosen from SNDLib website [9] and shown in Fig. 4. The background traffic is generated for each sourcedestination node pair randomy within the interva [1, 4] Gbps. Since the aocation of VNFs is known to be NP-hard, we restrict to 9 S-GWs and 3 P-GWs paced in the network, which are responsibe for the data-center traffic (see Fig.4). Unike other proposas, where the traffic between the S-GW and P- GW is assumed to be non-spittabe, each S-NE generates 10 traffic demands of 4.4 Gbps to its associated P-NE, which can be routed aong different path. For the ink dimensioning, the background and data-center traffic is optimay oad baanced by soving the TE mode, where the GWs are not virtuaized and paced at the origina ocations. Based on the traffic fows, we assume an overprovisioning factor of 1.2 to cacuate the ink capacities c, which are chosen from different granuarities (2.5, 10, 40, 100 and 200 Gbps). For the RA mode the background traffic is routed over the singe path derived above, which yieds the partia ink utiization U T E. Ony the DC traffic is now optimay routed, possiby using parae paths. A traffic demands of one S/P- NE are handed by one service chain. The service chain anayzed is shown in Fig. 2, which is composed by V NF 1 (i.e. S-GW, P-GW, LB), which can not be repicated, V NF 2 (i.e. TCP-optimizer) and V NF 3 (i.e. PEP), which can be repicated, and finay, V NF 4 (i.e. LB, FW, NAT), which again can not be repicated. Depending of the optimization objective, a VNFs may be paced in the same or in different DCs, where aso the S/P-NEs are possibe ocations. Repicated VNFs can be paced ony at DCs on different paths. We assume the ocation of the DCs and the assignment of the VNFs to DCs are the variabes to optimize. A. Network Load Baancing vs Minimum Network Node Costs We study optimization resuts obtained for the excusive minimization of the oad baancing (minlb, α = 1, β = 0) and excusive minimization of the network costs (minnc, α = 0, β = 1). In the Fig. 5, we show the comparison of the average ink utiization, maximum ink utiization, number of used DCs and maximum number of VNFs per DC with no repication, with one and two repicas, respectivey. Due to Eq.(15) the number of repications are restricted to the maximum vaue r max, ater shown in the figures as repicas. For the minnc scenario we observe expected resuts. Due to the cost optimization a VNFs are paced in 3 DCs which are reated to the number of P-NEs and ony singe paths between the S-NEs and P-NEs are used. Thus the average and maximum ink utiization is maintained constant for any case. The maximum number of VNFs per DC for the NC scenario changes if one VNF repication can be used (see Fig. 5c ) athough the optimized vaue of the objective function remains the same. This comes from the fact that the soution is ony unique with respect to the number of used DCs and not to the number of assigned VNFs per DC, which is an important behavior and for further studies. Whie, in the minlb scenario, the average ink utiization increases with repication (Fig. 5a) because the optimization mode tries to decrease number of overoaded inks using onger paths with underutiized inks, which can be seen from the reduction of the maximum ink utiization (Fig. 5b). In more detai Fig. 6 shows a histogram of the ink utiization, which verifies, that an increment of the avaiabe parae paths to forward traffic decreases the number of overoaded inks due to repication. The improvement between one and two repicas is not significant, but it is totay dependent on the chosen topoogy. The effect on the objective function?? is quite arger, as can be seen from the chart embedded in Fig. 6. On the other hand, as shown in (Fig. 5c), the number of used DCs increases because of onger paths more DCs are required to aocate repicas. Accordingy the maximum number of VNFs assigned to a DC decreases. B. Network Optimization under DC and VNF Constraints In the minnc case, the objective is to minimize the number of used DCs without restricting the number of VNF per DC. However, in a reaistic DCs the number of VNFs aocated to a virtua maschine (VM) wi be restricted due to performance

6 Percentage of inks Percentage of inks a) Average Link Utiization b) Maximum Link Utiization c) Max. num of VNF per DC - max. num. of used DCs No repication 1 repica 2 repicas Load Baancing Network Cost No repication 1 repica 2 repicas Load Baancing Network Cost 5 0 No repication 1 repica 2 repicas LB - max VNF LB - used DCs NC - max VNF NC - used DCs Fig. 5: Comparison between Load Baancing and Network Cost modes No repication Normaized cost 1 repica 2 repicas No repication 1 repica 2 repicas No repication Normaized cost 1 repica No repication 1 repica Link utiization Fig. 6: Link Utiization of minlb Mode TABLE II: Node Cost mode with at most 8 VNFs per node Case avg utiization path ength avg vnf No repication With repication boundaries of the avaiabe computation resources, e.g. the service processing time. Furthermore the number of VMs per DC wi be constrained as we. Due to our sma scae exampe we wi dea with this probem by simpe constraining the maximum number of VNFs per DC to 8 VNFs. The soution of the constraint optimization probem minnc constr resuts into 6 DCs, which doubes the network costs as shown in Fig.5. Due to the increased number of DCs the use of VNF repications offers some advantages, as shown in Tabe II. The constraint reduces the average number of VNFs (avg-vnf) per node and further, the usage of repicas aows to use some aternative paths in parae, which reduces the average path ength (in hops). As a consequence, the tota network traffic decreases as we as the average ink utiization. Finay we want to optimize the oad baancing under constraints given by the maximum number of usabe DCs as we as the maximum number of VNFs per DC, where the constraints are taken from the optima resuts given by the minnc constr probem. In the Fig. 7, we show the resuts for the histogram of the ink utiization. Here, we can see that one repica is sti abe to improve the oad baancing, but due to the sma exampe with ess effect. VI. CONCLUSIONS As VNFs can ony be paced onto servers ocated in data centers, the traffic directed to these DCs has not ony Link utiization Fig. 7: Link Utiization of minlb constr mode significant impact on the network costs but aso on the oad baancing. To enabe a cost efficient DC pacement by jointy improve the oad baancing we introduce the VNF pacement with repications in this paper, and especiay show how the repications of VNFs can hep to oad baance the network. ACKNOWLEDGMENT This work has been performed in the framework of SENDATE-PLANETS (Project ID C2015/3-1), and it is party funded by the German BMBF (Project ID 16KIS0470). REFERENCES [1] H. Moens and F. De Turck, VNF-P: A mode for efficient pacement of virtuaized network functions, Proceedings of the 10th Internationa Conference on Network and Service Management, CNSM 2014, [2] S. Mehraghdam, M. Keer, and H. Kar, Specifying and pacing chains of virtua network functions, 2014 IEEE 3rd Internationa Conference on Coud Networking, CoudNet 2014, pp. 7 13, [3] A. Basta, W. Keerer, M. Hoffmann, H. J. Morper, and K. Hoffmann, Appying NFV and SDN to LTE mobie core gateways, the functions pacement probem, AThingsCeuar 14, pp , [4] M. Bagaa, T. Taeb, and A. Ksentini, Service-aware network function pacement for efficient traffic handing in carrier coud, IEEE Wireess Communications and Networking Conference, WCNC, [5] F. Carpio, S. Dhahri, and A. Jukan, VNF Pacement with Repication for Load Baancing in NFV Networks, pp. 1 6, [Onine]. Avaiabe: [6] W. Haeffner, J. Napper, M. Stiemering, D. Lopez, and J. Uttaro, Service Function Chaining Use Cases in Mobie Networks, Internet-Draft, [Onine]. Avaiabe: [7] M. Caria, T. Das, A. Jukan, and M. Hoffmann, Divide and conquer: Partitioning OSPF networks with SDN, in IFIP/IEEE Internationa Symposium on Integrated Network Management, [8] Gurobi, Gurobi Optimizer. [Onine]. Avaiabe: [9] SNDib. [Onine]. Avaiabe: