Decomposition-based VNF Placement Algorithm in ...

Decomposition-based VNF Placement Algorithm in TDM-WDM-based Optical Aggregation Network Takashi Miyamura

Akira Misawa

Jun-ichi Kani

NTT Network Service Systems Labs NTT Corporation Musashino, Tokyo, Japan [email protected]

Chitose Institute of Science and Technology Chitose, Hokkaido, Japan [email protected]

NTT Access Service Systems Labs NTT Corporation Yokosuka, Kanagawa, Japan [email protected]

Abstract—In this paper, we consider the design of an optical aggregation network with network edge functions virtualization in order to reduce network cost. Here, an optical aggregation network connects a server accommodating virtual network functions (VNFs) with optical line terminals (OLTs) via a time-division-multiplexing (TDM)-based point-tomultipoint (P2MP) wavelength path to aggregate traffic from access networks. Each VNF must be placed on an adequate server in consideration of the efficiency of wavelength paths to reduce network cost. However, existing VNF placement algorithms determines VNF placement without considering the efficiency of P2MP wavelength paths, which deteriorates network performance and increases network cost. To solve the problem, VNF placement must be carried out so that a P2MP wavelength path can be efficiently shared by multiple OLTs for reducing network cost. For this purpose, we propose a VNF placement algorithm, called decomposition-based VNF placement algorithm (DVA), in a TDM wavelength-division-multiplexing (WDM)-based optical aggregation network. The DVA can find approximate solutions of sufficient quality with practical computation time. Index Terms—NFV, VNF placement, aggregation network, network optimization, network design

I. Introduction Recent applications, such as mobile communications and Internet of Things, have imposed unpredictable largevolume traffic on communications networks. There has been clear and urgent need to provide a way of efficiently transporting such traffic. Considering the rapid increase in the number of terminals and 4G/5G base stations, the design of metro aggregation networks is of critical importance in terms of robustness and energy consumption [1]. An aggregation network enables us to efficiently transport traffic by using line multiplexing between optical line terminals (OLTs) located at access networks and edge routers at the edge of core networks, as illustrated in Fig. 1. An aggregation network is required to accommodate bursty and unpredictable traffic from numerous OLTs, so network design plays an important role regarding network cost and robustness against unpredictable traffic demand changes. In this paper, we thus investigate the design of c 2018 IEEE 978-1-5386-3416-5/18/$31.00 

Network edge VNF

Optical aggregation network

Edge Server Farm Core network

Access network OLT1

TDM/WDM ring

Optical fiber

OLT2

P2MP wavelength paths P2MP wavelength paths 1

1 OLT1

OADM

1

2

1

VNF ES Optical burst contention resolution through DBA

2

Edge server ROADM or OXC

OLT2

Fig. 1. Aggregation network architecture with network edge virtualization

an aggregation network that enables the accommodation of unpredictable large-volume bursty traffic. There have recently been extensive studies on an optical aggregation network architecture to efficiently accommodate large-volume bursty traffic while reducing network cost [2], [3], [4]. Carey et al. [3] proposed a dynamically reconfigurable time division multiplexing (TDM)wavelength division multiplexing (WDM) ring architecture using passive optical network technologies. To efficiently accommodate unpredictable bursty traffic from numerous OLTs, these aggregation network architectures basically enable the sharing of a common wavelength path by multiple OLTs through optical TDM technologies such as dynamic bandwidth allocation (DBA) [5]. So, the path topology forms point-to-multipoint (P2MP) connectivity. By introducing network functions virtualization (NFV) [6], [7] into network edge functions, we can further improve flexibility of network resource usage in conjunction with TDM/WDM-based optical aggregation networks. NFV enables network edge functions to be relocated from dedicated hardware (i.e. edge routers) to distributed pools of commodity servers. In network edge functions virtualization [8], [9], edge routers are replaced with edge servers (ESs) with virtual network functions (VNFs). Here, an optical aggregation network must connect an ES accommodating VNFs with corresponding OLTs via a P2MP wavelength path. Thus, VNF placement greatly affects the

efficiency of network resource usage. Designing VNF placement independently of an optical network topology increases the consumption of wavelength paths due to the lower utilization of the paths. Previous studies [2], [3], [4], [8], [9], [10] mainly focused on developing and demonstrating network and system architectures, but few have investigated the design of TDM-WDM-based optical aggregation networks. Each VNF must be placed on an adequate server in consideration of the efficiency of wavelength paths to reduce network cost. However, existing VNF placement algorithms [11], [12] determines VNF placement without considering the efficiency of P2MP wavelength paths. To solve the problem, VNF placement must be carried out so that a P2MP wavelength path can be efficiently shared by multiple OLTs for reducing network cost. In this paper, we thus propose a heuristic design algorithm, called decomposition-based VNF placement algorithm (DVA), that can find nearly optimal solutions in terms of network cost and robustness while reducing computational overhead for scalability. The basic idea of DVA is to decompose the whole network design problem into a) the VNF-placement phase and b) P2MP pathcomputation phase to reduce computational overhead. The main contributions of this paper are i) presenting a heuristic algorithm for finding approximate solutions of sufficient quality with practical computation time and ii) quantitatively evaluating the performance of the proposed algorithm compared with the optimal solution and other conventional algorithms in terms of network cost and robustness. II. Related Work We briefly review related work on i) the design of optical multicast networks and ii) virtual network design including VNF placement. In this paper, we consider a TDM-WDMbased aggregation network, where a wavelength channel is shared by multiple OLTs and the path topology forms P2MP connectivity. Therefore, the design of such networks is related to the design of optical multicast networks. To design a multicast network, Ahlswede et al. [13] presented a mathematical formulation of multicast trees in network cording. Algorithms for optical multicast network design were proposed by K¨oksal and Ersoy [14] and Hachisuka et al. [15]. They considered optical multicast that simply split optical signals at intermediate nodes, so their models cannot be applied to the TDM-based shared P2MP wavelength paths considered in this paper. In aggregation networks, as we described earlier, such capability is effective in efficiently accommodating bursty traffic from numerous OLTs through over-subscription and statistical multiplexing on the same wavelength channel. The optimization of VNF chaining problems in a packetbased network has recently been proposed [16], and heuristic algorithms for VNF placement have been proposed [11], [12]. However, these studies did not consider a shared

P2MP wavelength path network as a physical network. Basically, to achieve efficient and effective VNF placement, we need to use physical network information and requirements. In summary, few researchers have investigated VNF placement problems in consideration of recent progress in aggregation networks such as TDM-based P2MP wavelength paths. We previously proposed an opticalaggregation-network-design method with VNF placement, which is based on a mixed-integer linear programming (MILP) formulation [17]. Although it can find the optimal solution, it fails to ensure sufficient scalability in terms of the size of a network and the number of VNFs. In this paper, we thus propose a heuristic algorithm that improves scalability. III. Network Architecture A. Overview of Optical Aggregation Networks We now describe an optical aggregation network architecture with network edge VNF. The important feature of an optical aggregation network lies in i) highly efficient wavelength routing that eliminates electrical-tooptical conversion at intermediate nodes and ii) flexible network topologies that can adapt to unexpected traffic demand fluctuation. In a conventional aggregation network, electrical L2 switches forms fixed network topology and each edge router accommodates a group of OLTs. An edge router provides various network edge functions such as broadband access server and session border controller functions, and it plays a crucial role for quality of service (QoS) and service assurance. Each edge router accommodates a fixed group of OLTs, which are basically determined by geographical conditions. However, due to the addition or withdrawal of subscribers, some edge routers are heavily congested while others are underutilized in the same network. In the optical aggregation network considered in this paper, edge routers are replaced with ESs with network edge VNFs. Each VNF can run on any commodity server on a network, so it is able to be live-migrated from an over-loaded server to an under-utilized one in response to unpredictable traffic demand changes. Therefore, server resources are reallocated according to the variation in bandwidth demand of each OLT. The important thing here is that each server must retain enough residual resources to ensure robustness against unpredictable demand changes. Network functions virtualization enables us to efficiently accommodate unpredictable demand changes with limited network resources. Regarding VNF allocations, we assume each VNF has one-to-one correspondence to a specific OLT. The architecture requires a mechanism for providing connectivity between an ES accommodating a VNF and a corresponding OLT. For this purpose, we consider a shared P2MP wavelength path network that only requires a set of conventional optical add/drop multiplexer (ADM) modules

ĂƐĞϭ͗

ĂƐĞϮ͗

dǁŽK>dƐĂƌĞĂĐĐŽŵŵŽĚĂƚĞĚďLJ ĚŝĨĨĞƌĞŶƚ^Ɛ

dǁŽK>dƐĂƌĞĂĐĐŽŵŵŽĚĂƚĞĚďLJ ƚŚĞƐĂŵĞ^ • ŽŶƐƵŵĞĚŽŶůLJϱtDůŝŶŬƐ͘ • ^ĞƌǀĞƌŵĂLJďĞŽǀĞƌůŽĂĚĞĚ͘

• ŽŶƐƵŵĞĚϲtDůŝŶŬƐ͘ • ^ĞǀĞƌůŽĂĚŝƐǁĞůůďĂůĂŶĐĞĚ͘

ϭ





Ϯ

ϭ

Ϯ

dDͬtDƌŝŶŐ

ϭ





dDͬtDƌŝŶŐ

Ϯ

͗^ŽƵƌĐĞEŽĚĞ;^Ϳ

͗ĞƐƚŝŶĂƚŝŽŶEŽĚĞ;K>dͿ

͗ŽƌĞŶŽĚĞ;DͿ

͗tDůŝŶŬ

Ϯ

ϭ

͗sE&

͗&ŝďĞƌůŝŶŬ

͗^ŚĂƌĞĚǁĂǀĞůĞŶŐƚŚƉĂƚŚ

Fig. 2. Illustrative example of optical aggregation network design

for an intermediate node. A group of ADMs consists of a ring topology, and each wavelength in the network forms a P2MP wavelength path shared by multiple OLTs that have the same target ES. The bandwidth of each P2MP wavelength path can be shared by multiple OLTs in accordance with DBA; thus, we can improve the resource utilization of each wavelength channel through statistical multiplexing. Optical burst contention resolution in the same wavelength channel is executed through a DBA mechanism. Such mechanisms are implemented on burst sender/receivers at ESs and OLTs. From the viewpoint of network cost and robustness against unpredictable traffic demand changes, it is important to place each VNF to an adequate ES among server pools while considering bandwidth requirements and resource consumption in the TDM-WDM ring network. B. Problem Statement We now define a network design problem with VNF placement. We assume a TDM-WDM-based optical aggregation network with network edge functions virtualization. The aggregation network is attached with server farms containing numerous ESs. For the network design, we need to determine i) the placement of each VNF on an adequate ES in the network and ii) the route for each shared P2MP wavelength path connecting an ES and OLTs accommodated by the same ES. The objective of the network design is to improve robustness against unpredictable traffic demand changes and reduce network cost by improving the efficiency of shared P2MP wavelength paths. Network cost is defined as the total amount of WDM links occupied by all P2MP wavelength paths established on the physical network. For this purpose, our approach is to determine VNF placement to disperse server load, i.e., the minimization of the maximum server load, in the network design phase. Here, we must retain sufficient residual resources for ensuring robustness against unpredictable demand changes. However, minimizing the maximum server load tends to deteriorate the efficiency of P2MP wavelength paths. We thus use multi-purpose

optimization to minimize server load and physical network cost. Figure 2 illustrates an example of a TDM-WDM ring network with two ESs and two OLTs. In Case 1, two pairs of ESs and OLTs are connected via two P2MP wavelength paths, respectively. In Case 2, two VNFs, located at the same ES, are connected with the corresponding OLT via a common P2MP wavelength path. Whereas Case 1 consumes more wavelength link resources than Case 2, the server load in Case 1 is adequately dispersed between two ESs. Thus, Case 1 is more tolerant of unexpected demand changes due to residual server resources. As illustrated in the above example, by adequately designing VNF location as well as shared P2MP wavelength paths, we can improve network resource efficiency and robustness against unpredictable demand changes. What is important here is how to place each VNF on an adequate server among pools in consideration of efficient route selection between ESs and OLTs. We now describe the problem we are attempting to solve: to establish an algorithm that determines VNF placement and network resource allocations in order to minimize network resource consumption as well as the maximum load of ESs on a given physical network while reducing computational overhead. IV. Mathematical Formulation First, we describe the notations used in our formulation and mathematical formulations before presenting our proposed algorithm. The network consists of ESs, OLTs, intermediate nodes (ADMs), and physical WDM links connecting two adjacent nodes. We introduce the following notations: Given: • Dj : Traffic demand generated at OLT j • Eλ : maximum number of wavelengths per link • Cλ : capacity of a wavelength channel (in Gbps) Variables: i • cmn : required capacity of a P2MP path from ES i k • xij : traffic from node i to node j r.w.t. VNF k We model a physical network as a directed graph. Second, we present just a part of the mathematical formulations of a shared P2MP wavelength path network with VNF placement since the full version is described in our previous paper [17]. The objective of our design is to minimize network resource consumption while avoiding an increase in the maximum load of ESs on a given physical network. This is because we can allocate residual bandwidth or server resources in case of sudden traffic demand changes. In the design, we need to determine how to do the following: • Place a VNF to an adequate ES considering the bandwidth requirement and capacity of ESs. • Find routes for P2MP wavelength paths that minimize physical network resource consumption. • Define a group of OLTs that are accommodated by the same P2MP path.

An outline of the MILP formulation is described below.

ϭ͘>ŽŐŝĐĂůƚŽƉŽůŽŐLJĚĞƐŝŐŶƉŚĂƐĞ KǀĞƌͲůŽĂĚĞĚ hŶĚĞƌͲƵƚŝůŝnjĞĚ hŶĚĞƌͲƵƚŝůŝnjĞĚ

Objective: Minimizing network cost and maximum server load ⎞ ⎛   (1) min ⎝ ckmn + α · max Dj · xkij ⎠ k

mn

i

k

A. Design Goal The goal of developing DVA is to reduce computational overhead while providing sufficient quality of solutions in designing an optical aggregation network with VNF placement. The previously proposed method fully depends on MILP to find a solution. So, the method failed to ensure scalability regarding the size of a network including the number of VNFs. From the results of our performance evaluation (discussed in the next section), the bottleneck lies in the VNF placement calculation instead of P2MPpath computation. Our DVA avoids this issue. The basic idea is to decompose a network design problem into i) the logical topology design phase, which includes VNF placement, and ii) P2MP path computation phase. DVA is a heuristic algorithms for resolving the VNF placement problem. Regarding the P2MP path routing design phase, we use an MILP-based approach because the computational overhead is relatively light-weight. We developed DVA regarding VNF placement to find practically accurate solutions while reducing computational overhead for network scalability. B. Overview We now give an overview of DVA. A schematic of the algorithm is illustrated in Fig. 3. The objective function of DVA is to minimize the weighted summation of the total network cost and maximum ES load, as described in Equation (1). Therefore, we need to find adequate VNF placement that efficiently disperses hot spots of ES load while i) improving the efficiency of shared P2MP wavelength paths and ii) reducing total hop counts between an ES and OLTs. However, the total network cost is traded-off with the maximum ES load, as we found in our previous study [17]. To reduce the maximum ES load, we should place VNFs on an ES accommodating fewer VNFs with less demand. This strategy may degrade the efficiency





Ϯ ŚŽƉƐ

'ĞŽŐƌĂƉŚŝĐĂůůŽĐĂƚŝŽŶ

Ϯ ŚŽƉƐ

Ϯ

ϯŚŽƉƐ

;ŚŽƉĐŽƵŶƚďĞƚǁĞĞŶ^ ĂŶĚK>dͿ

Ϯ͘WϮDWƉĂƚŚƌŽƵƚŝŶŐĚĞƐŝŐŶƉŚĂƐĞ WŚLJƐŝĐĂůŶĞƚǁŽƌŬ ϭ





V. Proposed Algorithm We now present our proposed algorithm, called DVA, which dramatically decreases the computation overhead while providing sufficient quality of solutions. It can be applied to a large-scale network or short-term reoptimization (e.g., every hour). In this section, we first describe a design goal of DVA, followed by an overview. We then present a detailed description of DBA.

Ϯ



j

In Eq. (1), the first term corresponds to the total wavelength resource consumption and the second term indicates the maximum load of ESs.

ŽŵƉƵƚĞsE&ƉůĂĐĞŵĞŶƚ ĐŽŶƐŝĚĞƌŝŶŐ^ůŽĂĚĂŶĚ ŐĞŽŐƌĂƉŚŝĐĂůůŽĐĂƚŝŽŶ͘

^ůŽĂĚ

WĂƚŚͲϭ

00 0 0 0 0 0 0 0 0000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

ϭ

00 00 00 00 00 00 00 00 00000000 000 000 000 000 000 000 000 000

000 000 000 000 000 000 000 000 000 000 000 000 000 000 00000000000000

000 000 000 000 000 000 000 000 00 00 00 00 00 00 00 00 00000000 00000000 00000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

Ϯ

Ϯ

>ŽŐŝĐĂůƚŽƉŽůŽŐLJ 

ϭ

Ϯ

 ^ŚĂƌĞĚWϮDW ƉĂƚŚƐͲϭΘϮ WĂƚŚͲϮ

dƌĂĨĨŝĐϭнϮŝƐƌĞƐƚƌŝĐƚĞĚďLJďĂŶĚǁŝĚƚŚ ŽĨƐŚĂƌĞĚǁĂǀĞůĞŶŐƚŚ ƉĂƚŚƐ

>ŽŐŝĐĂůƉĂƚŚͲϭ dƌĂĨĨŝĐϭ

ϭ

ŽŵƉƵƚĞŽƉƚŝŵĂůƌŽƵƚŝŶŐŽĨ ƐŚĂƌĞĚWϮDWǁĂǀĞůĞŶŐƚŚ ƉĂƚŚƵƐŝŶŐD/>W͘

>ŽŐŝĐĂůƉĂƚŚͲϮ dƌĂĨĨŝĐϮ

Ϯ

͗^

͗K>d

͗KD

͗sE&

Fig. 3. Overview of proposed algorithm

of a shared P2MP wavelength path because the path is less likely to be shared by other OLTs. To avoid this, DVA disperses ES load in VNF placement in consideration of geographical information of ESs and OLTs in order to reduce network cost. The basic idea is as follows; we first select candidate ESs geographically closer to an OLT according to hop count information; we then preferentially select one ES among candidates in consideration of residual resources of the ES. This can achieve adequate loadbalancing among ESs while suppressing the increase in total network cost. C. DVA: Decomposition-based VNF Placement Algorithm We now give details of DVA. We define the following functions and parameters to describe the algorithm: • T Ri : Total resource usage at ES i • ES evaluate(i, j): evaluation value of ES i to VNF j • V N F list: group of VNFs to be allocated to an ES • h cnt(i, j): minimum hop count from OLT j to ES i • h penalty(i, j): hop penalty of ES i to an OLT associated with VNF j • Hth : threshold of hop count penalty • SD : scale parameter that reflects traffic demand Dj in evaluation function ES evaluate(i, j) The ES evaluate(i, j) plays an important role in DVA, as it indicates the preference of ES i in placing VNF j. A smaller ES evaluate(i, j) means that ES i is more preferable than other ESs to VNF j. The initial ES evaluate(i, j) is determined by function h penalty(i, j), which reflects the minimum hop count from an OLT corresponding to VNF j to each ES. SD is another key parameter used in updating evaluation function ES evaluate(i, j) when a VNF with traffic demand Dj is assigned to ES i. As the absolute magnitude of h penalty(i, j) and Dj are totally different, we adjust the scale by introducing parameter SD . We discuss how to choose an adequate SD in the next section. Please note that SD plays an important role in adjusting the trade-off

between the network cost and maximum ES load. Function h penalty(i, j) is given by h penalty(i, j) ⎧ 1 ⎪ ⎪ ⎪ ⎨h cnt(i, j) = ⎪ ⎪ ⎪ ⎩ h cnt(i, j)2

if h cnt(i, j) − minl h cnt(i, l) ≤ 1 else if h cnt(i, j) − minl h cnt(i, l) ≤ Hth otherwise

The pseudo-code of DVA is presented in Table I. In Step 1, we first choose a VNF with the maximum traffic demand Dk in V N F list. Then, in Step 2, we update function ES evaluate(i, k), which determines the preference of ES i in placing VNF k, based on the minimum hop information from an OLT. After that, we select one ES based on the value of function ES evaluate(i, k) in Step 3. In Step 4, we check the residual capacity of the chosen ES l. If the ES is able to accommodate the VNF, we update function ES evaluate(l, k) and residual capacity T Rl . We then move to the next VNF placement. If the ES cannot accommodate the VNF, we add a penalty on ES evaluate(l, k) to decrease the preference of ES l in placing VNF k. We then go back to Step 1. In the next round, we can choose ESs with longer hop counts. In this way, we can place all VNFs to ESs. After completing the logical network design phase, we move to the P2MP path computation phase by using MILP. TABLE I Pseudo-code of DVA 1: 2: 3: 4:

5: 6: End.

DVA Select k s.t. Dk indicates the maximum demand in V N F list. if V N F list is empty, go to End. For k update ES evaluate(i, k) ES evaluate(i, k) = h penalty(i, k) for i in Ves Choose l s.t. ES evaluate(l, k) has the minimum value Evaluate residual capacity of ES l if T Rl + Dk ≤ Ces then go to 5. otherwise update ES evaluate(l, k) = h cnt(l, k)2 then go to 1. Update residual capacity T Rl + = Dk and then remove k from V N F list. Update evaluation function ES evaluate(l, k) = SD · Dk , then go to 1

VI. Performance Evaluation We conducted intensive mathematical experiments to quantitatively evaluate the effectiveness of DVA. We explain some of the results in this section. A. Aims and Conditions We had three objectives for the mathematical experiments: • to demonstrate the effectiveness of DVA in terms of computational overhead reduction, • to clarify how to design the scale parameter SD in DVA, and

TABLE II Comparison of computation time between DVA and Optimal (in seconds) Algorithm DVA Optimal

•

Multi-ring topology 0.028 364.9

Torus topology 0.065 1419.9

to evaluate the quality of solutions with DVA compared with the optimal solutions.

We now describe the experimental conditions. We implemented our MILP-based formulation on GLPK [19]. A 10node multi-ring network topology and twelve-node torusform network topology were deployed in the experiments. Traffic demand of OLTs was generated in accordance with the Zipf distribution [20]. The experiments had two shared conditions: • •

number of wavelengths per link Eλ : 16 capacity of a wavelength channel Cλ : 100 Gbps

B. Reference Algorithms We compared the performance of DVA with two conventional sever selection algorithms (Nearest and Round robin) [18]. In Nearst, VNFs are always placed on the nearest ES from an OLT among four ESs. Thus, Nearst basically provides the best solution among the three algorithms in terms of network cost. In Round robin, each VNF is placed among four ESs in round robin order without considering network cost, which can efficiently distribute server load among the four ESs. We evaluated network cost and maximum server load while varying traffic demand. As a benchmark of the computational overhead and optimality of solutions, we also used an MILP-based optimal solution (Optimal [17]). C. Reduction in Computational Overhead We compared the computation time of DVA and Optimal in multi-ring network and torus-form network topologies. In these experiments, the average traffic demand Di was set to 40 Gbps. The results are listed in Table II. In Optimal, it took more than 6 minutes, even for the relatively small multi-ring network topology. For the torusform network topology that contained more nodes and VNFs, it required more than 20 minutes to obtain the optimal solution. Thus, we conclude Optimal failed to ensure network scalability. With DVA, it took less than 1 second for both network topologies. We also investigated the computation time of the logical network topology design phase and P2MP path computation phase. The former was less than 10 ms for both network topologies, so DVA ensures network scalability. The reduction is achieved with our decomposition-based approach, which detaches heavy-weight VNF placement computation from the MILP formulation and implements DVA as a heuristic algorithm.

 ϭϬϯ͘ϴ

ϭϬϬ ϴϬ

ϳϯ͘Ϭ

ϳϯ͘Ϭ

ϳϯ͘ϭ

ϳϯ͘Ϭ

ϲϬ ϰϬ ϮϬ

ϭϳ͘ϭ

ϭϵ͘Ϭ

ZŽƵŶĚƌŽďŝŶ

0D[LPXPVHUYHUORDG

1HWZRUNFRVW

ϭϵ͘ϰ

ϮϬ͘ϯ

sͺϭϬ

sͺϭϬϬ

s



Network cost

Maximum server load /Network cost

ϭϮϬ



KƉƚŝŵĂů EĞĂƌĞƐƚ



ϭϲ͘ϰ

 Ϭ

sͺϬ͘ϭ

sͺϭ



KƉƚŝŵĂů







Traffic demand





(a) Comparison of network cost

DVA scale parameter s

Fig. 4. Impact of parameter SD on performance in terms of reducing network cost and server load

D. Design of Scale Parameter Next, we investigate how scale parameter SD affects network cost and maximum server load and clarify an adequate value of SD . Parameter SD , which is given in Table I, indicates the weight of traffic demand to hop counts in selecting an ES. If we set SD to 0, DVA just places each VNF on an ES that is geographically nearest to a corresponding OLT without considering the load of the ES. Thus, DVA tends to reduce network cost. A larger SD indicates an increased weight of the maximum server load in placing VNF to an ES. Therefore, DVA is more likely to reduce the maximum server load. We compared both performance indices while varying SD from 0.1 to 100. The average traffic demand of each VNF was set to 40 Gbps. The results are listed in Fig. 4. When parameter SD was relatively low, DVA tended to optimize network cost instead of server load. As parameter SD increased, DVA tended to optimize the maximum server load. Network cost is traded-off with maximum server load, as the results show. By setting SD to 1.0, we can efficiently reduce network cost while adequately dispersing server load. E. Performance comparison for various traffic demand We now compare the performance of DVA with that of two conventional algorithms in terms of reducing both network cost and maximum server load while varying traffic demand. We also evaluate the quality of our approximate solutions obtained from DVA compared with that of Optimal. On the basis of the above investigation into parameter SD , we set SD to 1.0 in this experiment. The results are listed in Fig. 5. The horizontal line indicates relative traffic demand normalized by the capacity of wavelength channel. Traffic demand 0.3 means 30 Gbps of average traffic demand from each OLT. In the multi-ring network topology, compared with Round robin, DVA reduced the maximum server load and network cost by up to 11 and 12%, respectively (see Fig. 5). This is because DVA adequately uses traffic demand information as well as physical topology information in calculating VNF placement in order to maximize the sharing of each P2MP wavelength path among OLTs.

Maximum server load



EĞĂƌĞƐƚ



ZŽƵŶĚƌŽďŝŶ

 

s KƉƚŝŵĂů

  











Traffic demand (b) Comparison of maximum server load

Fig. 5. Comparison of network cost and maximum server load in multi-ring network topology

Moreover, DVA indicated a slight increase in network cost by about 14% compared to Nearest, which we used as a benchmark of network cost in our evaluation. Regarding the quality of solutions with DVA, DVA increased network cost by just 11% on average compared with Optimal and showed almost the almost same performance regarding the reduction of the maximum server load. We also compared the performance in a different network topology (twelve-node torus-form topology); the results indicate the same tendency. DVA increased network cost by about 5% on average compared with Optimal, and showed almost the same performance in terms of the maximum server load. Thus, we concluded that both resource efficiency and robustness against traffic demand changes can be improved by adequately selecting the locations of VNFs and wavelength path routing. VII. Concluding Remarks We studied the design of optical aggregation networks with network edge virtualization, where a P2MP wavelength path is shared by multiple OLTs through TDM, and the location of network edge functions can be selected flexibly among commodity server pools. In this paper, we proposed a heuristic algorithm called DVA that provides solutions of sufficient quality with light-weight computational overhead. References [1] Hidetoshi Takeshita, Daisuke Ishii, Satoru Okamoto, Eiji Oki, Naoaki Yamanaka, “Highly Energy Efficient Layer-3 Network Architecture Based on Service Cloud and Optical Aggregation Network,” IEICE Transactions on Communications, Vol. E94-B, No. 4, pp. 894-903, Apr. 2011.

[2] Kyota Hattori, Toru Homemoto, Masahiro Nakagawa, Naoki Kimishima, Masaru Katayama, and Akira Misawa, “Optical Layer 2 Switch Network with Bufferless Optical TDM and Dynamic Bandwidth Allocation,” IEICE Transactions on Electronics, Vol. E99.C No. 2, pp. 189-202, Feb. 2016. [3] Daniel Carey, Nicola Brandonisio, Stefano Porto, Alan Naughton, Peter Ossieur, Nick Parsons, Giuseppe Talli, and Paul Townsend, “Dynamically Reconfigurable TDM-DWDM PON Ring Architecture for Efficient Rural Deployment,” Proc. ECOC 2016, Sep. 2016. [4] A. Kotsugai, T. Sato, H. Takeshita, S. Okamoto, and N. Yamanaka, ʠ TDMA-based OLT sharing method to improve disaster tolerance in Elastic Lambda Aggregation Network, ʡProc. ECOC 2014, pp. 13, Sep. 2014. [5] IEEE P802.3av Task Force, ʠ 10Gb/s Ethernet Passive Optical Network, ʡ http://www.ieee802.org/3/av/ [6] ETSI, GS NFV001,ʠ Network Functions Virtualisation (NFV); Use Cases, ʡ1 V1.1.1, Oct. 2013. http://www.etsi.org/standards [7] Rashid Mijumbi, Joan Serrat, Juan-Luis Gorricho, Niels Bouten, Filip De Turck, and Raouf Boutaba, ”Network Function Virtualization: State-of-the-Art and Research Challenges”, Communications Surveys & Tutorials IEEE, Vol. 18, pp. 236-262, Sep 2015. [8] Joon-Myung Kang, Hadi Bannazadeh, Hesam Rahimi, Thomas Lin, Mohammad Faraji, and Alberto Leon-Garcia, “SoftwareDefined Infrastructure and the Future Central Office,” 2013 IEEE International Conference on Communications (ICC) Workshops, Jun. 2013. [9] Akira Misawa, Konomi Mochizuki, Hideo Tsuchiya, Masahiro Nakagawa, Kyota Hattori, Masaru Katayama, and Jun-ichi Kani, “Virtual Edge Architecture with Optical Bandwidth Resource Control,” IEICE Transactions on Communications, Vol. E99.B No. 8, pp. 1805-1812, Aug. 2016. [10] G. Talli, S. Porto, D. Carey, N. Brandonisio, A. Naughton, P. Ossieur, F. Slyne, S. McGettrick, C. Blum, M. Ruffini, D. [18] Shigeyuki Yamashita, Daiki Imachi, Miki Yamamoto, Takashi Miyamura, Shohei Kamamura, and Koji Sasayama, “A New Content-Oriented Traffic Engineering for Content Distribution: CAR (Content Aware Routing)” IEICE Trans. Commun., Vol. E98-B, No.4, pp. 575-584, Apr. 2015.

[11]

[12]

[13]

[14]

[15]

[16]

[17] [19] [20]

Payne, R. Bonk, T. Pfeiffer, N. Parsons, and P. Townsend, ”Demonstration of SDN Enabled Dynamically Reconfigurable High Capacity Optical Access for Converged Services,” Proc. Optical Fiber Communication Conference 2017 Postdeadline Papers, Mar. 2017. Mari Otokura, Kenji Leibnitz, Yuki Koizumi, Daichi Kominami, Tetsuya Shimokawa, and Masayuki Murata, ʠ Application of evolutionary mechanism to dynamic virtual network function placement, ʡ The IEEE 24th International Conference on Network Protocols (ICNP), Workshop: Control Operation and Application in SDN protocols (CoolSDN Workshop), Nov. 2016. Tachun Lin, Zhili Zhou, Massimo Tornatore, and Biswanath Mukherjee, “Demand-Aware Network Function Placement,”, IEEE Lightwave Technology Journal of, Vol. 34, pp. 2590-2600, Feb. 2016. Rudolf Ahlswede, Ning Cai, Shuo-Yen Robert Li, and Raymond W. Yeung, “Network Information Flow,” IEEE Transactions on Information Theory, Vol.46, No.4, Jul 2000. F. K¨ oksal and Cem Ersoy, “Multicasting for all-optical multifiber networks,” OSA Journal of Optical Networking, Vol. 6, No. 2, 219-238, Feb. 2007. Y. Hachisuka, H. Hasegawa, and K. Sato, ʠ Impairment-aware multicast tree design for hierarchical optical path networks, ʡ Photonics in Switching 2012 (PS 2012), Th-S33-O08, Corsica, Sep. 2012. Bernardetta Addis, Dallal Belabed, Mathieu Bouet, and Stefano Secci, “Virtual Network Functions Placement and Routing Optimization,” CloudNet 2015 - IEEE 4th International Conference on Cloud Networking, Niagara Falls, ON, Canada. IEEE, pp. 171-177, Oct. 2015. Takashi Miyamura, Akira Misawa, and Jun-ichi Kani, “Design of Optical Aggregation Network with Carrier Edge Functions Virtualization,” APNOMS 2017, Sep. 2017. “GNU Linear Programming Kit,” https://www.gnu.org/ software/glpk/ L. Breslau, P. Cao, L. Fan, G. Phillips, and S. Shenker, ”Web Caching and Zipf-like Distributions: Evidence and Implications”, Proc. INFOCOM’99, Mar. 1999.