Reliability-aware virtual network function placement in carrier networks

Journal Pre-proof Reliability-aware virtual network function placement in carrier networks Lang Fang, Xiaoning Zhang, Keshav Sood, Yunqing Wang, Shui Yu PII:

S1084-8045(20)30010-2

DOI:

https://doi.org/10.1016/j.jnca.2020.102536

Reference:

YJNCA 102536

To appear in:

Journal of Network and Computer Applications

Received Date: 21 March 2019 Revised Date:

16 December 2019

Accepted Date: 11 January 2020

Please cite this article as: Fang, L., Zhang, X., Sood, K., Wang, Y., Yu, S., Reliability-aware virtual network function placement in carrier networks, Journal of Network and Computer Applications (2020), doi: https://doi.org/10.1016/j.jnca.2020.102536. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Elsevier Editorial System(tm) for Journal of Network and Computer Applications Manuscript Draft Manuscript Number: JNCA-D-19-00342R1 Title: Reliability-aware Virtual Network Function Placement in Carrier Networks Article Type: Research Paper Keywords: Network Function Virtualization; Service Function Chain; Reliability; Protection; Dynamic Programming; Lagrangian Relaxation Corresponding Author: Dr. xiaoning zhang, Corresponding Author's Institution: First Author: Lang Fan Order of Authors: Lang Fan; Xiaoning Zhang; Keshav Sood; Yunqing Wang; Shui Yu Abstract: Network Function Virtualization (NFV) is a promising technology that implements Virtual Network Function (VNF) with software on general servers. Traffic needs to go through a set of ordered VNFs, which is called a Service Function Chain (SFC). Rational deployment of VNFs can reduce costs and increase profits for network operators. However, during the deployment of the VNFs, how to guarantee the reliability of SFC requirements while optimizing network resource cost is still an open problem. To this end, we study the problem of reliabilityaware VNF placement in carrier networks. In this paper, we firstly redefine the reliability of SFC, which is the product of the reliability of all nodes and physical links in SFC. On this basis, we propose two reliability protection mechanisms: the All-Nodes Protection Mechanism (ANPM) and the Single-Node Protection Mechanism (SNPM). Following this, for each protection mechanism, we formulate the problem as an Integer Linear Programming (ILP) model. Due to the problem complexity, we propose a heuristic algorithm based on Dynamic Programming and Lagrangian Relaxation for each protection mechanism. With extensive simulations using real world topologies, our results show that compared with the benchmark algorithm and ANPM, SNPM can save up to 33.34% and 26.76% network resource cost on average respectively while guaranteeing the reliability requirement of SFC requests, indicating that SNPM performs better than ANPM and has better application potential in carrier networks.

Cover Letter

Professor: Xiaoning Zhang The School of Information and Communication Engineering University of Electronic Science and Technology of China Chengdu, China E-mail: [email protected] Mar.21, 2019 Dear Editor: We wish to submit an original research article entitled “Reliability-aware Virtual Network Function Placement in Carrier Networks” for consideration by Journal of Network and Computer Applications. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed. In this submission, we studied on how to guarantee the reliability of SFC requests while optimizing network resource cost in NFV-enabled carrier networks. Our work differs from all the previous works by considering not only the reliability of the nodes but also the reliability of the underlying links, and also optimizing network resource cost. We proposed two efficient algorithms to achieve our research objective. Extensive simulations are conducted to evaluate the performance of our proposed algorithms. And we analysis the simulation results from more aspects. Please

address

all

correspondence

concerning

[email protected]. Thank you for your consideration of this manuscript. Sincerely, Xiaoning Zhang

this

manuscript

to

me

at

*Detailed Response to Reviewers

Detailed Response to Reviewers Manuscript Title: Reliability-aware Virtual Network Function Placement in Carrier Networks Manuscript Number: JNCA-D-19-00342 Dear Editor, We hereby submit the revised version of our previously submitted above-mentioned paper. We would like to thank you for managing the review process of our paper, and to express our gratitude to the reviewers for their valuable comments and suggestions on the paper. We have revised the paper in accordance with the reviewers’ comments. Our responses to the reviewers’ comments are included in this letter. We hope that you and the reviewers find the revised version worthy of publication.

Best regards, Xiaoning Zhang, for all authors.

1

Reviewer 1 Reviewer Comments 1.1 It's indeed novel to consider the reliability of links when deploying VNF service chains. However, the problem setup is somewhat artificial as in my impression all services the VNF chain is still deployed in the same facility, just using different nodes. Intra data center links cannot justify the concerns for link reliability (there are other ways to do fault tolerance anyway). Therefore, the paper needs more justification (or statistics) to show that carriers are indeed deploying (or must need to deploy) different parts of their VNF chains into different physical locations.. Authors Response 1.1 We thank the reviewer for this comment. To prove that carriers are indeed deploying different parts of their VNF chains into different physical locations, we add multiple cited papers (i.e., [6]-[10]), which can describe this scenario. Reviewer Comments 1.2 The problem you defined is indeed NP hard, but it seems like the problem is already NP hard even without the extra parameters of link reliability and link cost (only considering node reliability and node cost); therefore, I can't find any deeper insight when the paper discusses the NP hardness, as the paper quickly jumps through it (rightfully for the sake of proving it's indeed NP hard, but the reader won't know where's the boundary at which the problem becomes intractable). Under the NFV reliability setup, what is the minimum to make the problem "hard"? E.g., If there's only node reliability constraint and link cost constraint, is the problem still polynomial? I would appreciate more discussion here, as the extra parameters that forces us to use heuristics need to be justified. Authors Response 1.2 Thanks for pointing out the importance of proving NP-hard of our problem. Following the reviewer’s suggestion, we add a detailed proof of NP-hardness of our problem in Section IV-E (Page 7). Reviewer Comments 1.3 The paper trivially made an artificial constraint that at most only one VNF can be put on any node, without further justification. This is an artificially constraint that the authors didn't justify well; I would assume that in some setup the optimal solution can have multiple VNFs putting on the same node. For example, if a node has really high reliability, we should definitely put as much as VNFs possible there (subject to capacity constraint). I understand that considering the overlapping placement will make the ILP formulation dirty, but please spell out this if it's a main reason for the no-overlapping constraint. Authors Response 1.3

2

We thank the reviewer for reminding us the mistake we made in this paper. We are sorry for such an imprecise representation mistake in our paper. In fact, we do not make a constraint that at most only one VNF can be put on any node. A node can deploy multiple VNFs as long as these VNFs belong to different SFCs and meet the capacity constraint of this node. In this regard, we add an explanation when describing Eq. (7). Reviewer Comments 1.4 Thirdly, the evaluation is comprehensive but missing some discussion about the performance of the heuristic algorithm. I would appreciate some results about the running time of the algorithm, and possibly a trend shown w.r.t the size of topology and the number of VNFs requested. This can also corroborate some discussion of the time complexity (w.r.t. both graph size and number of VNFs requested) in earlier sections. Authors Response 1.4 Thanks for pointing out the missing some discussion about the performance of our algorithms. To explain the performance of our algorithms, we add the results about the execution time of the algorithms in Section VI–B. Reviewer Comments 1.5 Finally, there are some small typos in the paper (e.g. last paragraph of section 4, "our problem dose not" -> should be "does not") that should be caught. Authors Response 1.5 Thanks for pointing out the mistake about typos, we have reviewed the entire paper carefully and corrected the related typos.

Reviewer 2 Reviewer Comments 2.1 There are many Grammar errors in the paper, here are some examples: At present, researches about the reliability of NFV only considers ... Our simulations results show that SNPM can saves up to .... Authors Response 2.1 Thanks for pointing out the mistake about grammar errors, we have reviewed the entire paper carefully and corrected the related errors.

3

Reviewer Comments 2.2 Recovering from single-node and multi-node failures is a classic network problem. The authors discuss the path protection VNF chains, however, I think this problem is just a re-formulation of the classic multi-node failure problems. My suggestion to the authors is to highlight the differences of their work compared to classic multi-node or multi-link failure problems in network literature and point out why we need new methods to solve this problem. Authors Response 2.2 We thank the reviewer for this comment. Following the reviewer’s comment, we reorganize and add some content in Section I. We detail the background of our problem in paragraph 3 of Section I. In addition, we highlight the differences of our work compared to previous researches in network literature and point out the novelty of our method in paragraph 3 of Section I-A. Reviewer Comments 2.3 It took me a while to understand Figure 1. It'd be best to show the requests first, then show the physical/logical layout of VNFs. Authors Response 2.3 Following the reviewer’s suggestion, we have improved the Figure 1 of our paper. We have corrected Figure 1 by showing the requests first, then showing the physical/logical layout of VNFs. Reviewer Comments 2.4 The paper uses a simulation to show the "total network resource cost" of ANPM and SNPM on different network typologies. While the results are encouraging, it is not clear how the proposed methods compare to the existing solutions. The paper cites recent works on this topic, it would be interesting to compare the cost of SNPM/ANPM to that of proposed solutions in [5], [10], [11], or [12] using the same network topology and SFC requests. I understand that it might not be possible to compare with every work on this topic, but you should provide at least one benchmark to compare your results against. It is not possible to comment on the performance of the proposed algorithms without any benchmarks or head-to-head comparisons with existing solutions. Authors Response 2.4 Thanks for pointing out the lack of benchmark algorithms. Following the reviewer’s comment, we add a benchmark algorithm and compare our algorithms with this benchmark algorithm in our simulation to evaluate our algorithms comprehensively in Section VI. Reviewer Comments 2.5 In section 4, the authors present their model. While the proposed model is solid, it is very hard to follow the equations to understand how the optimization problem is constructed. Table 1 helps to understand to notation and the variable names, but the text that follows 4

the equations does not help much. I think the authors need to explain the problem and what they want to achieve in plain language before they jump into the math. That helps readers better understand how the model works and what is the objective and constraints of the optimization problem at the core of this paper. Authors Response 2.5 We thank the reviewer for this comment. Following the reviewer’s suggestion, we describe the proposed problem and what we want to achieve in detail in first paragraph of Section IV. Reviewer Comments 2.6 This is minor, but Figure 2.a and 2.b seem to have different topologies. VNF1 is connected to the rest of VNF2s in 2.b, while in 2.a it is only connected to one. Is this intentional? Authors Response 2.6 Thanks for pointing out the mistake of Figure 2. Following the reviewer’s comment, we have corrected Figure 2. Reviewer Comments 2.7 From an editorial point of view, I think the paper needs some refinement in the language and its presentation. At its present state it is not an easy read. Sections 3 and 4 can be improved substantially with better word selection, clear sentences, and improved language. Authors Response 2.7 Thanks for the reviewer’s suggestion. We have improved the readability of our paper. We have reorganized language to describe problem definition of this paper in Section III and explained system model clearly in plain language in Section IV.

Reviewer 4 Reviewer Comments 4.1 In the introduction, this paper describes well the previous works. However, the object and subject of this paper are a little bit ambiguous. I hope the authors should add a more detailed and explicit purpose of this paper. Authors Response 4.1 We thank the reviewer for this comment. Following the reviewer’s suggestion, we have reviewed introduction and reorganized it. In Section I-A, we explain our motivation in detail, and we highlight the object and subject of this paper in Section I-B.

Reviewer Comments 4.2

5

If possible, the authors should mention about definite advantage and disadvantage for cited papers in previous works. Authors Response 4.2 We thank the reviewer for this comment. In Section II, We describe advantage and disadvantage for cited papers in previous works in detail and we highlight the novelty of our work. Reviewer Comments 4.3 A revision of English can improve the quality of the article. Authors Response 4.3 Thanks for pointing out the inadequacy of the English in this paper. We have reviewed the entire paper carefully and improved the English expression.

6

*Suggested List of Potential Referees

Professor: Xiaoning Zhang The School of Information and Communication Engineering University of Electronic Science and Technology of China Chengdu, China E-mail: [email protected] Dear Editor: The following is a list of suggested potential referees for your consideration: 1. Song Guo E-mail: [email protected] 2. Dapeng Oliver Wu E-mail: [email protected] 3. Guofei Gu E-mail: [email protected] 4. Nirwan Ansari E-mail: [email protected] Sincerely, Xiaoning Zhang

*Manuscript

Reliability-aware Virtual Network Function Placement in Carrier Networks Lang Fang1 , Xiaoning Zhang1 , Keshav Sood2 , Yunqing Wang1 , Shui Yu3 1

School of Information & Communication Engineering, University of Electronic Science and Technology of China 2 School of Information Technology, Deakin University 3 School of Software, University of Technology Sydney, Sydney, Australia

Abstract—Network Function Virtualization (NFV) is a promising technology that implements Virtual Network Function (VNF) with software on general servers. Traffic needs to go through a set of ordered VNFs, which is called a Service Function Chain (SFC). Rational deployment of VNFs can reduce costs and increase profits for network operators. However, during the deployment of the VNFs, how to guarantee the reliability of SFC requirements while optimizing network resource cost is still an open problem. To this end, we study the problem of reliabilityaware VNF placement in carrier networks. In this paper, we firstly redefine the reliability of SFC, which is the product of the reliability of all nodes and physical links in SFC. On this basis, we propose two reliability protection mechanisms: the All-Nodes Protection Mechanism (ANPM) and the Single-Node Protection Mechanism (SNPM). Following this, for each protection mechanism, we formulate the problem as an Integer Linear Programming (ILP) model. Due to the problem complexity, we propose a heuristic algorithm based on Dynamic Programming and Lagrangian Relaxation for each protection mechanism. With extensive simulations using real world topologies, our results show that compared with the benchmark algorithm and ANPM, SNPM can save up to 33.34% and 26.76% network resource cost on average respectively while guaranteeing the reliability requirement of SFC requests, indicating that SNPM performs better than ANPM and has better application potential in carrier networks. Index Terms—Network Function Virtualization, Service Function Chain, Reliability, Protection, Dynamic Programming, Lagrangian Relaxation

I. I NTRODUCTION Virtualization technology is changing the way network operators deploy and manage Internet services step by step. This has shown great advantages and potential compared with traditional hardware-based information technology in terms of improving resource utilization, maintaining management, and reducing energy consumption. Promoted by the European Telecommunications Standards Institute (ETSI), Network Function Virtualization (NFV) is currently seen as an essential technology for future generation network architecture [1]. The objective of NFV is to increase the scalability and flexibility of network service deployment to satisfy the increasing and ever-changing network services. Unlike traditional technologies in which network functions are implemented in expensive dedicated hardware, NFV [2] implements them with software on general servers. Therefore, traditional dedicated hardware are replaced by software-based

Virtual Network Function (VNF) [3]. In specific, NFV provides an efficient way to deploy network services using Service Function Chain (SFC) [4] that consists of a set of VNF nodes interconnected by physical links, as well as inject flexibility into service deployment to offer network as a service (NaaS) [5]. In a traditional network environment, the service chains can only be manually configured. In contrast, different types of VNFs can be dynamically created in NFV environment. VNFs in the same SFC can be all deployed in the same physical location (i.e., in the same data center) [6], [7] or in different physical locations in carrier networks [8]–[10]. NFV can significantly reduce the CAPital EXpenditures (CAPEX) and OPerating EXpenditures (OPEX) of telecom operators, shorten the deployment and delivery time of new services, and greatly improve the flexibility of telecommunication networks [11]. Despite NFV has many advantages over traditional network technologies, its highly shared approach to resource integration also poses a potential crisis for NFV environment. Reliability is an important problem in traditional networks as well as in NFV. Specially, reliability is especially significant for NFVenabled carrier networks. Traditional carrier-grade networks require the reliability of 99.999% or higher. However, due to both the Network Function Virtualization Infrastructure (NFVI) in the NFV architecture and the hardware and software components in VNFs may fail, software-based VNFs generally cannot meet the carrier-grade reliability requirement. For a variety of reasons, such carrier-grade requirements are extremely challenging to implement in NFV environment, and more indepth research is needed. For example, due to natural disasters, malicious attacks, or operational errors, the failure of any one of VNFs or physical links results in breaking down the SFC, and brings significant data losses, delays, and resource wastage [12]. Unlike traditional networks, NFV can flexibly use various resources in networks, thus the reliability problem solutions existing in traditional networks are not applicable in NFV, novel reliability problem solutions are urgently significant for NFV-enabled networks. In addition, reliability risks in NFV make service outages more likely to occur, potentially violating Service Level Agreement (SLA) between service providers and customers. Therefore, we observed and emphasize that it is emergent to investigate reliability-aware SFC chaining problem in carrier networks.

SFC1

SFC1

S

FW

IDS

NAT

D S

D

SFC2

S

FW

DPI CDN

D

SFC2

(a) Two SFC requests

(b) VNF placement

SFC1 (failed)

SFC1

S

D

D

SFC2 (failed)

SFC2

(c) Consequence of node failure Fig. 1.

S

(d) Consequences of link failure

Example of SFC failed caused by node or link failure.

A. Our Motivation So far, the use of VNF redundancy allocation technology to improve system reliability is frequently mentioned in NFV reliability studies, which as guided in ETSI VNF REL 003 of ETSI [13]. However, ETSI does not provide guidance for specific redundant allocation schemes. Recently, some researchers start to investigate the problem of reliability-aware VNF placement. Long et al. [12] considered redundancy-based VNF placement policies to achieve the service reliability. Fan et al. [14] used sufficient redundancy VNF to protecting the network services and considered three redundancy models: dedicated protection, shared protection and joint protection. The above works only consider the reliability of the nodes at networklevel. At present, researches about the reliability of NFV only involve the reliability of VNFs, but do not consider the factor of link reliability when calculating the reliability of SFC. In practice, the failure of physical links also leads to interruption in SFC, which is similar to the consequences of the failure of VNF nodes. As shown in Fig. 1, there are two SFC requests: SFC1 and SFC2. If some VNF node of SFC1 fails, the entire SFC1 will be failed. Similarly, if some physical link of SFC2 fails, the entire SFC2 will be failed. Thus, it can be seen that both the reliability of nodes and the reliability of physical link is identically critical to NFV. In SFC-level, if the reliability of links is not considered, it may be effortless to achieve the reliability required by the services, but the situation is different once the reliability of the link is taken into account. For instance, assume the SFC1 in Fig. 1 consists of 3 serially linked VNFs with service reliability requirement of 0.995, where the reliability of each VNF is 0.999, and the reliability of each link between nodes is also 0.999. If only the reliability of the VNF is considered, the reliability of the entire SFC is 0.997, which meets the reliability requirements. However,

if the reliability of the link is taken into consideration, the reliability of the entire SFC is 0.993, which obviously cannot satisfy the reliability requirements of service. As mentioned above, since the reliability of links is also very significant, we comprehensively consider the reliability of nodes and links in NFV to improve the overall reliability of SFC, which is different from previous researches. In addition, most studies at present propose to use only one protection path to improve system reliability [14]–[16]. However, we consider a working path and multiple protection paths to jointly guarantee the reliability requirement of SFC requests in this paper. Sufficient redundancy can protect network services in the event of failures, but it also greatly increases the use of link bandwidth resources and node computing resources, resulting in a significant increase of mapping costs. How to successfully map multiple service requests under the condition of satisfying reliability constraints while minimize the network resource cost is the problem to be solved in this paper. B. Our Contribution In this paper, we study the reliability-aware VNF placement (RAVP) problem in carrier networks. Our main objective of this research work is to propose a novel solution to revenue the reliability of SFC requests. Eventually this solution will also help to minimize the network resource cost. We study the reliability problem from two different aspects: reliability as well as resource cost optimization. We firstly redefine the reliability of SFC, which is the product of the reliability of all nodes and physical links in SFC. Then we propose two reliability protection mechanisms: the All-Nodes Protection Mechanism (ANPM) and the Single-Node Protection Mechanism (SNPM). The ANPM provides end-to-end protection for the entire SFC, while the SNPM only provides protection for one VNF with the lowest reliability in SFC. For each protection mechanism, we formulate the problem as an Integer Linear Programming (ILP) model and then propose an efficient heuristic algorithm based on Dynamic Programming and Lagrangian Relaxation for each protection mechanism. Extensive simulations by using real world topologies show that compared with the benchmark algorithm and ANPM, SNPM can save up to 33.34% and 26.76% network resource cost on average respectively while guaranteeing the reliability requirement of SFC requests, indicating that SNPM performs better than ANPM and has better application potential in carrier networks. The main technical contributions of this paper are summarized as follows. • For the reliability problem of SFC in NVF-enabled carrier networks, we propose two protection mechanisms, the ANPM and the SNPM. For each protection mechanism, we formulate the problem as an ILP model and prove the NPhardness of the studied problem. • Since the studied problem is NP-hard, we propose a heuristic algorithm based on dynamic programming and lagrangian relaxation for each protection mechanism respectively. • We evaluate the performance of two protection algorithms with extensive simulations. Our simulations results show

that SNPM can save up to 33.34% and 26.76% network resource cost on average than the benchmark algorithm and ANPM respectively while guaranteeing the reliability requirement of SFC requests. The remainder of this paper is organized as follows. In Section II, the related work is presented. After that, we explain the problem definition and present two protection mechanisms in Section III. In Section IV, we describe the system model and prove our proposed problem is NP-hard. Then, in Section V, we design an efficient heuristic algorithm for each protection mechanism, followed by extensive simulations in Section VI. At last, we give conclusion in Section VII.

0.9995 0.9991

0.9992 VNF2

A

0.9993 VNF3

0.9996

C

0.9991

S

0.9993

B

SFC

0.9993

D

0.9995

0.9994 VNF1

0.9994

0.9992

VNF2

0.9995

VNF3

0.9996 0.9997 G

F

E VNF1

0.9994

0.9992

VNF2

0.9995

VNF3

0.9996 0.9997

… … VNF1

0.9992

0.9994

VNF2

0.9995

VNF3

0.9996 0.9997

(a) Illustration of ANPM

II. R ELATED W ORK Recently, there have been some efforts on the reliabilityaware VNF placement problem. Cao et al. [5] proposed scalable and reliable joint topology design and mapping strategies that can significantly reduce the network reconfigurations and enhance the service reliability, respectively. Hmaity et al. [15] proposed three ILP models to solve the VNF placement problem of SFC. The authors also evaluated the influence of SFC delay on VNF distribution from VNF failure, and a heuristic algorithm is proposed. Xu et al. [16] established an ILP model for VNFs placement problem, and then proposed an enhanced VNF placing scheme based on layered graphs to achieve better reliability. In order to improve the reliability of SFC, the scheme avoided placing multiple VNFs of a service request on the same node to prevent SFC from being affected by a single node failure. Nejad et al. [17] proposed a genetic algorithm, the algorithm can optimize the placement cost while providing queue-aware dynamic placement schemes for VNFs. However, the above studies do not involve the reliability of underlying links. As mentioned above, some research efforts also applied redundant allocation techniques to improve the reliability of NFV. In order to protect the high availability of the application, Fan et al. [14] formulated an optimal usability-aware SFC mapping problem, and proposed a new online algorithm that performs redundant backup of VNF and minimizes physical resource consumption while satisfying high availability. In [18], the authors mentioned that sufficient redundancy can guarantee the normal use of network services in the event of physical failure, but doing so may reduce the efficiency of the physical resources, so the authors proposed a new method of joint protection. Compared with the traditional private protection and shared protection, the proposed algorithm can minimize the consumption of physical resources while feasible solution is obtained in polynomial time, and guarantee the high reliability required for service requests. Herker et al. [19] studied the importance of reliability guaranteed VNF deployment in Internet of Things (IoT) environment, and proposed an algorithm for VNF placement. The algorithm places primary VNFs in order, while recursively adding redundant VNFs until the placement meets the reliability requirements of SFC. In order to protect the high availability of the application, Machida et al. [20] proposed a strategy

0.9995

VNF1

0.9995 VNF1

0.9991

0.9995

0.9992 VNF2

A

0.9993

B 0.9991

0.9993 VNF3 C

0.9996

SFC

0.9993

S

D

0.9994

0.9995 VNF1

0.9994

0.9992

E

VNF1

0.9994

VNF1

0.9994

VNF2

0.9995 F

VNF2

VNF3

0.9996 0.9997 G VNF3

0.9992 0.9995 0.9996 0.9997

… …

0.9992

VNF2

0.9995

VNF3

0.9996 0.9997

(b) Illustration of SNPM Fig. 2.

Example of two protection mechanisms.

for configuring redundant virtual machines in the case of unpredictable failure of servers, which using a small number of servers to construct redundant configuration and estimate the required minimum number of redundant virtual machines according to the performance requirements of the application services, and determine the best virtual machines placement location to ensure system can provide the lowest performance required in the event of any k servers failures. Redundancy allocation technology is still applicable to reliability improvement of NFV, deploying backup VNFs can improve the reliability of the entire SFC to achieve SLAs between service providers and customers. However, traditional ways of redundancy allocation only focus on how to effectively deploy backup VNFs or servers to satisfy the reliability requirements. Our work in this paper differs from all the previous works by considering not only the reliability of the nodes but also the reliability of the underlying links, and also optimizing network resource cost, which is the performance assurance of practical application of high reliability NFV network for carrier operators. III. P ROBLEM D EFINITION In this section, we first discuss our proposed protection mechanisms and then state our problem. In NFV-enabled networks, reliability is especially important.

However the current researches about the reliability of NFV do not involve the impact of the underlying links. In this paper, we attempt to consider the underlying link failure impact in NFV domain in carrier networks. Following this, we attempt to alleviate the impact of node and link failure while minimizing the network resource cost. Now, we discus our proposed solution. If the primary path of a service request cannot guarantee the reliability requirement, we leverage two protection mechanisms (i.e., ANPM and SNPM) to improve the reliability of the SFC request. The main difference between the ANPM and the SNPM is the number of the protected primary VNFs. The ANPM provides protection for all VNFs on the working path, and the protection path is end-to-end path from the source node to the destination node, while SNPM only protects one VNF with the lowest reliability on the working path. We note that the ANPM and the SNPM may use multiple backup paths in order to meet the reliability requirement of SFC requests. To illustrate proposed protection mechanisms, we use an example as shown in Fig. 2. In this figure, the number next to links and nodes indicates their reliability, red dotted lines represent the SFC request and black solid lines represent the physical links. We suppose that the reliability requirement for service requests is 0.997. The SFC requests needs to pass through three VNFs (i.e., VNF1, VNF2, and VNF3) in order. The primary path is S→A→B→C→D, which is represented by a red solid line. The reliability of the primary path is approximately 0.9963, which is the product of the reliability of all VNF nodes and physical links in the primary path. Since the reliability of the primary path cannot meet the reliability requirement, we use two protection mechanisms to improve the reliability of the service request. As shown in Fig. 2(a), in ANPM the backup path is S→E→F→G→D, which is represented by a blue solid line. The reliability of the backup path is approximately 0.9959. Thus, the reliability of the service request is approximately 0.9999, which can meet the reliability requirement. As shown in Fig. 2(b), in SNPM the backup path is A→F→C, which is also represented by a blue solid line. The reliability of the backup path is approximately 0.9976. Thus, the reliability of the service request is approximately 0.9979, which can meet the reliability requirement. In addition, we consider the use of multiple protection paths to improve the reliability of SFC requests once one protection path can’t guarantee the reliability of SFC requests. The above protection mechanisms can indeed improve the reliability of NFV, but it also causes the problem of network resource cost. The heavy use of backup paths mean that network resource cost rise rapidly. How to optimize the network resource cost of two protection mechanisms is a significant problem. We describe this problem in detail in next section. IV. S YSTEM M ODEL In this section, we illustrate the system model of proposed problem. It is observed that the reliability requirement of service requests can be guaranteed with the two protection

TABLE I D EFINITIONS USED IN THIS PAPER Notation

Description

G(V, E)

the network topology, where V denotes the set of nodes, with m, n ∈ V and E denotes the set of physical links, with (m, n) ∈ E the set of service requests, with service request d ∈ D. the bandwidth requirement of service request d. the reliability requirement of d. the set of ordered VNFs for d, with i, j ∈ Fd . the set of virtual link between VNF for d, with (i, j) ∈ Ld . the number of protection paths, with k = {0, 1, 2, ..., Kd }. the computing resource requirement of VNF i. the reliability of VNF node m. the available computing resource of node m. the set of nodes adjacent to node m. the reliability of physical link (m, n), where (m, n) ∈ E. the available bandwidth of physical link (m, n). a coefficient denoting the relative importance of computing capacity a coefficient denoting the relative importance of link capacity a binary variable. It takes the value of 1 if primary VNF i of d is deployed on node m; otherwise 0. a binary variable. It takes the value of 1 if backup VNF i of d on the k-th backup path is deployed on node m; otherwise 0. a binary variable. It takes the value of 1 if the primary path of d from primary VNF i to primary VNF j goes through the physical link (m, n); otherwise 0. a binary variable. It takes the value of 1 if the k-th backup path of d from backup VNF i to backup VNF j goes through the physical link (m, n); otherwise 0. the primary path for d the k-th backup path for d a set of VNF nodes in Ppr,d k a set of VNF nodes in Pb,d the reliability of the primary path for d the reliability of the k-th backup path for d

D bd Rd Fd Ld Kd ci rm acm adjm r(m,n) b(m,n) α β xim,d xbi,k m,d (i,j)

y(m,n),d (i,j),k

yb(m,n),d Ppr,d k Pb,d Vpr,d k Vb,d Rpr,d k Rb,d

mechanisms from Fig. 2. However, both of these protection mechanisms require numerous backup paths to guarantee the reliability requirement of service requests. Thus, the two protection mechanisms accordingly consume large amount of network resources, such as physical links bandwidth resource and nodes computing resource. However, the resources in networks are limited, it is necessary to optimize the cost of network resource while improving the reliability of system. Our objective is to minimize network resource cost while guaranteeing the reliability of SFC requests. To this end, we formulate this problem as ILP models in this section. Specifically, we first illustrate the network model used in our problem. After that we present the SFC reliability model, then we formulate two ILP models for ANPM and SNPM. For clear presentation, all the notations used in this paper are summarized in TABLE I. A. Network Model We model the topology of network as an undirected graph G = (V, E), where V denotes the set of nodes, and E represents the set of underlying links. Let D denotes the set of SFC request, with SFC request d ∈ D, and Fd denotes the set

of ordered VNFs for SFC request d. For each node m ∈ V , let acm denotes its available computing resource. For each underlying link (m, n) ∈ E, let b(m,n) denotes its available bandwidth. Let Rd denotes the reliability requirement of SFC request d. Accordingly, the reliability of node m is rm , and the reliability of underlying link (m, n) is r(m,n) .

SFC requests. This is also a general constraint in the current researches [7], [12], [15]. In addition, the primary VNFs and the backup VNFs cannot be deployed on the same node. Eq. (7) guarantee the above constraints. X i∈Fd

B. SFC Reliability Model In this sub-section, we redefine the reliability of SFC requests, which is the product of the reliability of all VNF nodes and physical links in SFC. The reliability of the primary path for SFC request d can be obtained as follows. Y

Rpr,d =

(xim,d +

r(m,n) ∗

(m,n)∈Ppr,d

Y m∈Vpr,d

(1)

m∈Vb,d

RAN P M = 1 − (1 − Rpr,d ) ∗

(7)

k=1

Then, we have to satisfy the node computing resource requirements of primary VNFs and backup VNFs for service request d. X xim,d ∗ ci ≤ acm , ∀m ∈ V, i ∈ Fd (8) X

xbi,k m,d ∗ ci ≤ acm , ∀m ∈ V, i ∈ Fd , k = {0, 1, 2, ..., Kd }

d∈D

(9) We also have to satisfy the physical link bandwidth requirements of primary path and backup paths for service request d. X (i,j) bd ∗ y(m,n),d ≤ b(m,n) , ∀(m, n) ∈ E (10) (i,j)∈Ld

In the ANPM, the reliability RAN P M of service request d can be obtained as follows. Kd Y

xbi,k m,d ) ≤ 1, ∀m ∈ V

d∈D

rm

If the primary path cannot meet the reliability requirement of service request d, we must provide protection to improve the reliability of d. The reliability of the k-th backup path for d can be obtained as follows. Y Y k Rb,d = r(m,n) ∗ rm (2) k k (m,n)∈Pb,d

Kd X

X

bd ∗

(i,j),k

yb(m,n),d ≤ b(m,n) , (11)

(i,j)∈Ld k (1 − Rb,d )

(3)

∀(m, n) ∈ E, k = {0, 1, 2, ..., Kd }

k=1

In the SNPM, let b represent the protected primary VNF pro node, with b ∈ Vpr,d . Let Pb,d denote the protected primary path. So the reliability RSN P M of service request d can be obtained as bellow. Rpr,d Q ∗ (1 − (1 − rb ∗ RSN P M = (rb ∗ (m,n)∈P pro r(m,n) ) b,d (4) K Y Y k (1 − Rb,d r(m,n) ) ∗ )) (m,n)∈Pp,b

Besides, the flow conservation of primary path and backup paths should be satisfied for service request d. X X (i,j) (i,j) y(m,n),d − y(n,q),d = xjn,d − xin,d , (12) m∈adj(n) q∈adj(n) ∀n ∈ V, i, j ∈ Fd , (i, j) ∈ Ld X X (i,j),k (i,j),k i,k yb(m,n),d − yb(n,q),d = xbj,k n,d − xbn,d , m∈adj(n)

q∈adj(n)

∀n ∈ V, i, j ∈ Fd , (i, j) ∈ Ld , k = {0, 1, 2, ..., Kd } (13)

k=1

C. The ILP model of ANPM In this sub-section, we formulate the problem as an ILP model of ANPM. To deploy SFC requests in the underlying network, there are multiple constraints that need to be met. At first, for service request d, primary VNFs and backup VNFs must be deployed on the node. X xim,d = 1, ∀i ∈ Fd (5)

In addition, the primary path and the backup paths do not go through the same physical links. The k1 -th backup path and the k2 -th backup path do not go through the same physical links. (i ,j )

(i ,j ),k

1 1 2 2 y(m,n),d + yb(m,n),d ≤ 1, ∀(m, n) ∈ E,

(i1 , j1 ), (i2 , j2 ) ∈ Ld , k = {0, 1, 2, ..., Kd }

(14)

m∈V (i ,j ),k

X

xbi,k m,d

= 1, ∀i ∈ Fd , k = {0, 1, 2, ..., Kd }

(6)

m∈V

For each SFC request d, we have to guarantee that the VNFs it needs are deployed on different nodes. That is, each node deploys at most one VNF for each SFC request d. This is because if too many VNFs which belong the same SFC request are deployed on the same node, this node may not have too much resource to deploy the VNFs required by other

(i ,j ),k

1 1 1 2 2 2 yb(m,n),d + yb(m,n),d ≤ 1, ∀(m, n) ∈ E,

(i1 , j1 ), (i2 , j2 ) ∈ Ld , k1 , k2 = {0, 1, 2...Kd }, k1 6= k2

(15)

The reliability of the service request d in the ANPM should be satisfied: RAN P M = 1 − (1 − Rpr,d ) ∗

Kd Y

k (1 − Rb,d ) ≥ Rd , ∀d ∈ D

k=1

(16)

k where Rpr,d and Rb,d are shown in Eq. (1) and Eq. (2), respectively. Our objective is to minimize network resource cost while guaranteeing the reliability of service request. We give the cost of physical link bandwidth resource of service request d.

X

costb,d = β ∗ bd ∗

X

(i,j)

(y(m,n) +

Kd X

(pv,pv

X

next ys(m,n),d

next ,k xspv n,d

−

i∈Fd

(21)

k=1

We also have to ensure the computing resource constraints of the protected VNF backed up on the protection path. xspv,k m,d ∗ cpv ≤ acm , ∀m ∈ V, pv ∈ Fd , d ∈ D

(22)

Eq.(23) and Eq.(24) guarantee the link bandwidth constraint on the protection path. (pv

,pv),k

pre bd ∗ ys(m,n),d

(pv,pv

next bd ∗ ys(m,n),d

),k

,pv),k

≤ 1,

(27)

(i,j),k

(pv,pv

),k

≤ 1,

(28)

∀(m, n) ∈ E, (i, j) ∈ Ld , d ∈ D

As same as the ANPM, the k1 -th backup path and the k2 -th backup path do not go through the same physical link in the SNPM, Eq.(29)-(32) illustrates this constraint. (pv

,pv),k1

pre ys(m,n),d

(pv

,pv),k2

pre + ys(m,n),d

≤ 1,

(29)

∀(m, n) ∈ E, (i, j) ∈ Ld , d ∈ D, k1 6= k2 ,pv),k1

(pv,pv

next + ys(m,n),d

),k2

≤ 1,

(30)

∀(m, n) ∈ E, (i, j) ∈ Ld , d ∈ D, k1 6= k2

Eq.(21) ensures that at most one VNF is deployed on each node. xspv,k m,d ≤ 1, ∀m ∈ V, ∀d ∈ D

(26)

next y(m,n),d + ys(m,n),d

(pv

m∈V

xim,d +

(pv

pre ys(m,n),d

The ILP model of the SNPM is similar with that of the ANPM. The main difference is the number of protected primary VNF nodes and the reliability model. The two protection mechanisms have the same constraints: Eq.(5), Eq.(8), Eq.(10) and Eq.(12). The following describes the unique constraints of the SNPM. We have to guarantee that the protected VNF on each protection path can be mapped on the node. X pv,k xsm,d = 1, ∀d ∈ D (20)

Kd X

=

∀(m, n) ∈ E, (i, j) ∈ Ld , d ∈ D

(5) - (16)

D. The ILP model of SNPM

X

),k

∈ V, d ∈ D, (m, n) ∈ E

(i,j)

d∈D

Subject to:

xspv,k n,d , ∀n

pre y(m,n),d + ys(m,n),d

(17)

Finally, we get the ILP model to describe the problem of minimizing both computing and bandwidth resource cost as follow. X (costb,d + costc,d ) Minimize : (19)

ys(n,q),dnext

Eq.(27) and (28) indicate that the working path and the kth protection path do not pass through the same physical link.

(i,j),k

i∈Fd

(pv,pv

X q∈o(n)

yb(m,n),d )

Accordingly, we give the cost of node computing resource of service request d. X costc,d = α ∗ (1 + Kd ) ∗ ci (18)

−

m∈o(n)

k=1

(i,j)∈Ld (m,n)∈E

),k

(pv,pv

next ys(m,n),d

),k1

(pv

,pv),k2

pre + ys(m,n),d

≤ 1,

(31)

∀(m, n) ∈ E, (i, j) ∈ Ld , d ∈ D, k1 6= k2 (pv,pv

next ys(m,n),d

),k1

(pv,pv

next + ys(m,n),d

),k2

≤ 1,

(32)

∀(m, n) ∈ E, (i, j) ∈ Ld , d ∈ D, k1 6= k2

The reliability of the service request d in the SNPM should be satisfied according to Eq.(4): RSN P M =

Rpr,d (rb ∗

Y

Q

pro (m,n)∈Pb,d

r(m,n) ) ∗

K Y

r(m,n) )

∗ (1 − (1 − rb ∗ (33)

(1 −

k Rb,d ))

≥ Rd , ∀d ∈ D

k=1

(m,n)∈Pp,b

Compared with the ANPM, the cost of physical link bandwidth resource and the cost of node computing resource in SNPM formulated in different form as follows: X X (i,j) costb,d = β ∗ bd ∗ ( y(m,n),d + (m,n)∈E (i,j)∈Ld Kd X

(34) (pv

,pv),k

pre ys(m,n),d

(pv,pv

next + ys(m,n),d

),k

)

k=1

≤ b(m,n) , ∀(m, n) ∈ E, d ∈ D

(23) costc,d = α ∗

≤ b(m,n) , ∀(m, n) ∈ E, d ∈ D

(24)

Eq.(25) and Eq.(26) guarantee the flow conservation constraint of nodes in the k - th protection path. X X (pvpre ,pv),k (pvpre ,pv),k ys(m,n),d − ys(n,q),d = m∈o(n) q∈o(n) (25) pvpre ,k xspv,k − x , ∀n ∈ V, d ∈ D, (m, n) ∈ E n,d n,d

X X ( ci + Kd ∗ cpv )

(35)

d∈D i∈Fd

Accordingly, the objective function of the SNPM is as follows: X Minimize : (costb,d + costc,d ) (36) d∈D

Subject to: (5), (8), (10), (12), and (20) - (33)

E. Problem Analysis The RRVP problem can be proved NP-hard problem by reducing the standard Virtual Network Embedding (VNE) [21] problem in polynomial time. which is already proved as an NP-hard problem. To prove NP-hardness of our problem, we first illustrate VNE problem. Then the reliability-aware VNF placement problem can be redefined and reduced from the VNE problem. In VNE problem, the substrate network topology can be modeled as Gs (Vs , Es ), where Vs denotes the set of substrate nodes and Es denotes the set of substrate links. Each node ui ∈ Vs is assigned with a capacity Cs (ui ) and each link (ui , uj ) (where ui , uj ∈ Vs ) has a bandwidth capacity Bs (ui , uj ). Given another undirected graph Gv (Vv , Ev ) representing virtual network, where Vv denotes the set of virtual nodes, and Ev denotes the set of virtual links. Each virtual node wk ∈ Vv is assigned with a capacity Cv (wk ) and each link (wk , wl ) (where wk , wl ∈ Vv ) has a bandwidth capacity Bv (wk , wl ). The objective of the VNE problem is to solve the mapping problem of the virtual network. Specifically, it is to find a valid mapping from Gv to Gs under the two constraints: 1. Cv (wk ) ≤ Cs (ui ), and Cv (wl ) ≤ Cs (uj ); 2. Bv (wk , wl ) ≤ Bs (ui , uj ). Theorem 1: The RAVP problem is NP-hard. proof : To prove the above theorem, we first simplify our RAVP problem as an easier virtual network function placement (VNFP) problem without considering the constraint of reliability in polynomial time. First, we model the substrate network as an undirected graph G(V, E), where V is the set of nodes and E is the set of links. Each node and link has been assigned with the capacity C V (u) and C E (u,v), respectively. Then, we model a undirected graph Gr (Vr , Er ) for each request, where Vr is the set of virtual nodes (ie., VNF instances), and Er is the set of virtual links between virtual nodes. Each VNF instance is assigned with a capacity demand Cf to represent the capacity demand for holding the instance of function f ∈ Fv and Fv denotes the set of VNFs needed to be deployed. Each virtual link is assigned with a certain service chain bandwidth demand b(a,b) (u, v) which denotes the bandwidth demand of virtual link (a, b) on physical link (u, v) where a ∈ Vr , b ∈ Vr , u ∈ V , v ∈ V . When virtual nodes may be mapped to a single physical node of the substrate network, the constraint of capacity must be satisfied. That is, for each physical node u, the sum of the capacity demand of all the virtual nodes mapped to u must be less than or equal to the maximum capacity of u. Similarly, for each physical link (u, v), the total sum of the bandwidth demand of all virtual links mapped to (u, v) must be less than or equal to the maximum capacity of (u, v). Thus, we can summarize all the above as follows: for all virtual nodes a ∈ Vr mapped to u ∈ V , and all b ∈ Vr mapped to v ∈ V , and for all links (a, b) ∈ Er mapped to (u, v) ∈ E are required to satisfy P the following constraints: P V 1. f ∈FV Cf (u) P ≤ C V (u), and fP ∈FV Cf (v) ≤ C (v), ∀u, v ∈ V , where f ∈FV Cf (u) and f ∈FV Cf (v) are the

sum of capacity demands of all virtual nodes at physical node u and v respectively. P 2. P b(a,b) (u, v) ≤ C E (u, v), ∀(a, b) ∈ Er , ∀(u, v) ∈ E, where b(a,b) (u, v) is the sum of bandwidth demand of all virtual links mapped to physical link (u, v). Definition 1: X function f : δ1 → δ2 is called a mapping reduction from X to Y if f a) For any β ∈ δ1 , β ∈ X, if f (β) ∈ Y , b) f represents a computable function. From above definition, we can derive from the definition that if Y can be reduced from X then any instance of X can be transformed into an instance of Y in polynomial time and the solution to problem Y is the solution to problem X. Thus, after mapping the variables of VNE problem to the variables of our problem, we can obtain the relationship as follows:   Cs (ui ) → C V (u)      C (u ) → C V (v)      s j   P  C (w ) →  C (u) v k f f ∈F V P (37) Cv (wl ) → f ∈FV Cf (v)       E     B (u , u ) → CP (u, v)    s i j  Bv (wk , wl ) → b(a,b) (u, v) From Definition 1 and Eq.(8), we can map and reduce the VNE NP-hard problem to simplified VNFP problem [22]. Obviously, since our optimization problem does not consider the constraint of reliability, it is harder than VNFP problem. Hence, our EEVP problem is also NP-hard. V. H EURISTIC A LGORITHMS Since the problem to be solved in our study is NP-hard, it is difficult to find the optimal solution to map multiple service requests and minimize network resource cost under the condition of satisfying the reliability constraint. Therefore, we propose a heuristic algorithm to solve the problem. In addition, it is difficult to consider all service requests as a whole in static environment. In this paper, each service request is deployed one by one, and the problem to be solved will be transformed into mapping a single service request and minimizing network resource cost while guaranteeing the reliability of SFC requests. Based on this, the algorithms (ie., the ANPM and the SNPM) proposed in this paper is implemented based on Dynamic Programming [23] and Lagrangian Relaxation [24]. A. The ANPM Algorithm For a single service request d, the reliability of the service request d takes the partial derivative of the reliability of k working path, as shown in Eq.(37) , we know that 1−Rbd >0 is constant, then we derive that ∂RAN P M /∂Rpr,d > 0 is constant. Therefore, when other variables remain unchanged, RAN P M increases with the increase of Rpr,d . Similarly, the reliability of the service request d takes the partial derivative of the reliability of the kth protection path, as shown in Eq.(38) , k1 we know that 1−Rpr,d > 0 and 1−Rbd > 0 are constant, then k we derive that ∂RAN P M /∂Rbd > 0 is constant. Therefore,

when other variables remain unchanged, RAN P M increases k with the increase of Rbd . Kd Y ∂RAN P M k = (1 − Rb,d ) ∂Rpr,d

(38)

k=1

Kd Y ∂RAN P M k1 = (1 − R ) ∗ (1 − Rb,d ) pr,d k ∂Rbd k =1,k 6=k 1

(39)

1

Therefore, it can be seen from the above partial derivative functions, when designing our reliability protection algorithm, it is necessary to find a working path to meet the reliability constraints and minimize the network resource cost. When such a path exists, the deployment scheme of the service request is returned and the next service request is continued to be deployed. When such a path does not exist, select the path with the highest reliability as the working path, configure the protection path, and continue to solve a protection path that can meet the reliability constraints and minimize the network resource cost. The protection path and the working path are solved in the same way. When the reliability constraint of the service request is not satisfied, only the path with the highest reliability can be selected to improve the reliability of the service request more quickly, thus reducing the number of protection paths, link bandwidth resources and servers computing resource consumption, and ultimately achieving the objective of minimizing the network resource cost. The detail of the ANPM algorithm is shown in Alg. 1. In this algorithm, we sort the SFC requests in D according a descending order of its reliability requirement (line 1). We deploy each SFC request d to minimize network resource cost when guaranteeing the reliability (line 2-23). We first initialize P athd and Vd , where P athd denotes the set of primary path and backup paths, and Vd denotes the set of deployed VNF nodes (line 3-4), respectively. Then, we calculate the minimum network resource cost path Pcost and the set Vcost of VNF nodes in the Pcost by DP (Dynamic Programming) function (line 6). If the reliability of d after adding path Pcost meets the reliability requirement Rd , we add path Pcost to the set P athd , and deploy next SFC request in D (line 7-9). Otherwise, we calculate the most reliable path Pre and the set Vre of VNF nodes in the Pre by DP algorithm (line 10-11). If the reliability of d after adding path Pre can meet the reliability requirement Rd (line 12), it indicates that there is a path which can minimize network resource cost when guaranteeing the reliability of SFC request d. We calculate the path PLR by LR (Lagrangian Relaxation) algorithm, add path PLR to the set P athd , and deploy the next SFC request in D (line 1315). Otherwise, we add path Pre to the set P athd (line 17). We update Vd , deleted the links (which are consisted of by path Pre ) from E, and calculate a backup path in order to improving the reliability of SFC request d (line 18-22). In the ANPM algorithm, dynamic programming algorithm and Lagrangian relaxation algorithm are mainly used. In the following, the two sub-algorithms are described in detail.

Algorithm 1: The ANPM Algorithm Input: G(V , E), D Output: The set of path P athd for each d ∈ D 1: Sort the set D in a descending order of the reliability requirement 2: for each SFC demand d ∈ D do 3: Vd ← ∅ 4: P athd ← ∅ 5: while true do 6: Pcost , Vcost ← DP (d, cost, Vd ) 7: if the reliability of d after adding path Pcost can meet Rd then 8: add Pcost to P athd 9: break 10: else 11: Pre , Vre ← DP (d, re, Vd ) 12: if the reliability of d after adding path Pre can meet Rd then 13: PLR ← LR(Pcost , Vcost , Pre , Vre , d, Vd ) 14: add PLR to P athd 15: break 16: else 17: add Pre to P athd 18: Vd ← Vd ∪ Vre 19: G(V, E) ← G(V, E − Pre ) 20: end if 21: end if 22: end while 23: end for

1) DP Function: DP function is used to calculate the optimal deployment scheme of SFC request d. In this function, let w denote the weight used to obtain the optimal deployment scheme, where w(x,y) denotes the weight of physical link (x, y), and wx denotes the weight of node x. Let Pnj denote the path from the source node to node n where VNF j is deployed. Let Vnj denote the set of VNF nodes in the path i i of path Pm can be obtained as follow. Pnj . The weight wm X X i wm = w(x,y) + wx (40) i (x,y)∈Pm

i x∈Vm

In the essence of DP function, the optimal path Pnj can be calculated by the following recurrence relation: X i wnj = min{wm + w(x,y) + wn , ∀m ∈ Seti } (41) (x,y)∈Pm,n

where Pm,n denotes the optimal path from node m to node n, and Seti denotes the set of VNF nodes, which are available for deploying the VNF i. In addition, the weights in this paper are divided into two categories: one is network resource cost, which is represented by cost; the other is reliability, which is represented by re. i Here the network resource cost and reliability of path Pm are

Algorithm 2: DP Function Input: d, w, Vd Output: The path and the set of VNF nodes of d 1: for each VNF j ∈ Fd do 2: Setj ← the set of VNF nodes that are available for deploying VNF j 3: for each node n ∈ Setj do 4: wnj ← ∞ 5: i ← the previous VNF of j in d 6: for each node m ∈ Seti do 7: Pm,n ← P Dijkstra(m, n, w) i 8: if wm + (x,y)∈Pm,n w(x,y) + wn < wnj then P i 9: wnj ← wm + (x,y)∈Pm,n w(x,y) + wn i 10: Pnj ← Pm ∪ Pm,n j 11: Vn ← Vmi ∪ {n} 12: end if 13: end for 14: end for 15: end for 16: return the path and the set of VNF nodes of d

f 0  w0src   0 S

f2

n1 1

n 21

n12

n22

nL 2

f L 1  wLdes1 

D

nLV | f

des nLV| f | sL 1  wL

n2|Vf | SL

L

|

L

2

S1

Fig. 3.

……

sLdes1  wLnL1

……

1

fL

n L1

……

……

n1|V f | S0

……

f1

……

S L 1

Dynamic programming model in our study.

shown in Eq.(41) and Eq.(42), respectively. X X i cost(Pm , Vmi ) = cost(x,y) + costx i (x,y)∈Pm

i x∈Vm

(42)

Algorithm 3: LR Function Input: Pcost , Vcost , Pre , Vre , d, Vd Output: path PLR of SFC demand d 1: while true do 2: calculate the aggregated coefficient λ based on the cost and reliability of path Pcost and Pre 3: Pλ , Vλ ← DP (d, cost + λ ∗ re, Vd ) 4: if the aggregated weight of Pre is the same as of Pλ then 5: return Pre 6: else 7: if the reliability of d after adding path Pλ can meet Rd then 8: Pre , Vre ← Pλ , Vλ 9: else 10: Pcost , Vcost ← Pλ , Vλ 11: end if 12: end if 13: end while

2) LR Function: LR function provides a solution to minimize network resource cost when guaranteeing the reliability requirement of a SFC request. The function uses the concept of aggregated cost and provides an efficient method to find the optimal multiplier based on Lagrange Relaxation. Lagrange Relaxation is proven to be polynomial, and it is also efficient in practice. When solving the deployment scheme with the lowest network resource cost under the reliability constraint, the paths is set as P a, the nodes which mapping the VNFs is set as VN , and the reliability of the service request d is set as Rd , the problem can briefly described as Eq.(43), where the reliability parameters are logarithmically processed. Then, LR algorithm can be used to solve the required deployment solution. After Lagrange Relaxation, the problem description is as shown in Eq.(44), where λ represents the Lagrange multiplier, and the optimal deployment scheme is solved by adjusting λ. Minimize : {cost(P a, VN ) : re(P a, VN ) ≤ −lnRd }

(44)

(43)

Minimize : {cost(P a, VN ) + λ ∗ re(P a, VN ) + λ ∗ lnRd } (45)

The detail of DP function is shown in Alg. 2, and the dynamic programming model used in our study is given in Fig. 3. For each VNF j ∈ Fd , we establish a set of VNF nodes which are available for deploying the VNF j (line 2). Then, for each node n ∈ Setj , we initialize three parameters (line 4-5). We calculate the minimum weight path from the source node to node n based on Eq. (21) and update three parameters (line 6-13). In addition, Pn,m is calculated by the Dijkstra [25] algorithm with the weight w (line 7). At last, the function returns the VNF placement solution for the SFC request d (line 16).

The detail of LR function is shown in Alg. 3. In this function, we first calculate the aggregated coefficient λ based on the cost and reliability of path Pcost and Pre (line 2), which can be obtained by Eq.(41) and Eq.(42). Then, we calculate a path Pλ and a set Vλ by DP function with the aggregated weight (cost + λ ∗ re) (line 3). If the aggregated weight of Pre is the same as of Pλ , this function returns Pre (line 4-5). If the reliability of d after adding path Pλ can meet the reliability requirement Rd , this function updates Pre and Vre , and calculates a new solution (line 7-8). Otherwise, this function updates Pcost and Vcost , and calculates a new solution (line 9-12).

i re(Pm , Vmi ) =

X i (x,y)∈Pm

re(x,y) +

X i x∈Vm

rex

B. The SNPM Algorithm The SNPM algorithm is similar with the ANPM algorithm. As can be seen from above, the main difference is the number of protected primary VNFs and the reliability model (shown in Eq. (3) and (4)), which reflected in some parameters in the IPL model. The SNPM algorithm provides protection for only one VNF node with the lowest reliability, and also includes these two sub-algorithms of DP function and LR function. The SNPM only provides multiple dedicated protections for VNF pv which deployed on the working path, and each protection path is divided into two paths: the node mapping VNF pvpre to the node mapping backup VNF pv and the node mapping backup VNF pv to the node mapping VNF pvnext , so as to improve the reliability of service requests. In essence, the protection path can also be regarded as a service request: the source node is the node mapping VNF pvpre , and the destination node is the node mapping VNF pvnext , which only needs to go through VNF pv. When designing algorithms, similar to the ANPM, a working path should be obtained to satisfy the reliability constraint and minimize the network resource cost. If there is no working path satisfies the reliability constraint, the path with the highest reliability is taken as the working path, and the protection paths are configured for it. Then, one of the VNFs (the node with the lowest reliability) is selected for redundancy protection, and to solve the corresponding protection path. If the reliability constraint of the service request is not satisfied, only the path with higher reliability can be selected to better improve the reliability of the service request, so as to reduce the number of protection paths, links bandwidth resources and servers computing resource consumption, and the network resource cost is reduced ultimately. The details of the SNPM is described in Alg. 4. In this algorithm, we sort the SFC requests in D according a descending order of its reliability requirement (line 1). For each service request d, we calculate the work path that satisfies reliability with the lowest cost (lines 3-14). If there is no such working path, we calculate the protection paths that satisfy the reliability constraint with the lowest cost (lines 15-14). We first initialize P athd and Vd . Then, we calculate the deployment plan with the lowest network resource cost by DP (Dynamic Programming) function (line 5). If the reliability of d after adding path Pcost can satisfy the reliability requirement Rd , we add path Pcost to the set P athd , and deploy next SFC request in D (line 6-8). Otherwise, we calculate the most reliable deployment plan by DP algorithm (line 9-10). If the reliability of d after adding path Pre can satisfy the reliability requirement Rd (line 11), it indicates that there is a path which can minimize network resource cost while guaranteeing the reliability of SFC request d. We calculate the path PLR by LR (Lagrangian Relaxation) algorithm, add path PLR to the set P athd , and deploy the next SFC request in D (line 12-14). Otherwise, we add path Pre to the set P athd , and update Vd , delete the links (which are consisted of by path Pre ) from E (line 15-18). We select the VNF with the least reliability in

Algorithm 4: The SNPM Algorithm Input: G(V , E), D Output: The set of path P athd for each d ∈ D 1: Sort the set D in a descending order of the reliability requirement 2: for each SFC request d ∈ D do 3: Vd ← ∅ 4: P athd ← ∅ 5: Pcost , Vcost ← DP (d, cost, Vd ) 6: if the reliability of d after adding path Pcost can meet Rd then 7: add Pcost to P athd 8: break 9: else 10: Pre , Vre ← DP (d, re, Vd ) 11: if the reliability of d after adding path Pre can meet Rd then 12: PLR ← LR(Pcost , Vcost , Pre , Vre , d, Vd ) 13: add PLR to P athd 14: break 15: else 16: let Pre as the working Path and add Pre to P athd 17: Vd ← Vd ∪ Vre 18: G(V, E) ← G(V, E − Pre ) 19: Select the VNF pv with the least reliability in working path for protection. The protection path of pv is equivalent to a new service request d0 20: while true do 21: Pcost , Vcost ← DP (d0 , cost, Vd ) 22: if the reliability of d after adding path Pcost can meet Rd then 23: add Pcost to P athd 24: break 25: else 26: Pre , Vre ← DP (d0 , re, Vd ) 27: if the reliability of d after adding path Pre can meet Rd then 28: PLR ← LR(Pcost , Vcost , Pre , Vre , d0 , Vd ) 29: add PLR to P athd 30: break 31: else 32: add Pre to P athd 33: Vd ← Vd ∪ Vre 34: G(V, E) ← G(V, E − Pre ) 35: end if 36: end if 37: end while 38: end if 39: end if 40: end for

working path for protection. The protection path is equivalent to a new service request d0 (line 19). Then we calculate the

0

18

1

10

5

2

14

6

20

15

11

8

19

21

3 12 4

16

22

9

7

13 17

23

(a) USNET topology 10 11 1 8 3

7

0

13

6

4

12

2 5

9

(b) NSFNET topology Fig. 4.

Simulation topologies.

protection path (line 20-37), which is similar to lines 5-22 in the ANPM algorithm basically. C. Time Complexity Analysis Since the time complexity of Dijkstra algorithm is 2 O(|V | ), where |V | indicates the number of nodes in the 4 graph G, the time complexity of DP algorithm is O(|Fd ||V | ), where |Fd | indicates the number of VNFs required for the service request d. In addition, since |Fd | is much smaller than |V |, the time complexity of DP algorithm can be expressed 4 as O(|V | ). Since the time complexity of DP algorithm is 4 O(|V | ), that the time complexity of the LR algorithm is 4 O(|V | ). Finally, the time complexity of ANPM algorithm 4 is O(|D||V | ), where |D| represents the number of service requests, this is derived from the time complexity of the DP 4 algorithm and the LR algorithm both are O(|V | ). For the same reason, the time complexity of the DP 4 algorithm and the LR algorithm are both O(|V | ), the time 4 complexity of the SNPM algorithm is O(|D||V | ), where |D| represents the number of service requests. VI. S IMULATION A. Simulation Setting In our study, we test two typical telecom network, which is USNET topology (24 nodes, 43 links) and NSFNET topology (14 nodes, 21 links) in Fig.4. We assume that there are 5 types of VNFs (i.e., Firewall, Deep Packet Inspection, Intrusion Detection System, Network Address Translation, Content Delivery Network) to be placed in the network. The computing resource requirements of each VNF is uniformly distributed in the range of 15 units to 30 units. We set the bandwidth capacity of each physical link as 1000 Mbps and computing capacity of each node as 600 units. The SFC

requests are uniformly distributed among all node pairs, and sequentially at most traverse five VNFs. The length of each SFC request is uniformly distributed in the range of 2 to 5. We assume the bandwidth requirement of a SFC request is uniformly distributed in the range of 20 Mbps to 60 Mbps, the reliability of each physical link and each node are both uniformly distributed in the range of 0.999 to 0.9999, and the reliability requirement of each SFC demand is uniformly distributed in the range of 0.993 to 0.999. In addition, we set the coefficient α as 5 and set β as 1. Performance Metrics: we use the following five performance metrics to evaluate our proposed algorithms. (1) Execution time: the execution time is a significant index to evaluate the performance of our proposed heuristic algorithms, good execution time can reflect the efficiency of the algorithm. (2) T otal N etwork Resource Cost: this resource cost denotes the total network resource cost in the network for deploying all SFC requests, which consists of bandwidth resource cost and computing resource cost. (3) T otal Computing Resource Cost: this resource cost can be calculated by Eq.(18) and Eq.(35), which denotes the total cost of using the computing resource of nodes in the network for deploying all VNFs of all SFC requests. (4) T otal Bandwidth Resource Cost: this resource cost denotes the total cost of using the bandwidth resources for mapping all SFC requests in all link of the network, it can be calculated by Eq.(17) and Eq.(34). (5) Acceptance Ratio: the ratio of the number of successfully deployed SFC requests to the number of all SFC requests, which can be calculated as follows: Xsuc (46) Ya = Xall where Xsuc represents the total number of successfully deployed SFC requests, and Xall represents the number of all SFC requests. Note that a well-performing protection mechanism must be able to satisfy most SFC requests, i.e., the acceptance ratio must be high. Comparisons: we compare the two algorithms with the Shortest Path (SP) algorithm [26]. SP deploys a SFC request along the shortest path between the source node and the destination node. If the reliability of the calculated path can not guarantee the reliability requirement of SFC request, SP repeatedly calculates the shortest paths until the reliability meets the requirement. Since SP also requires that the working path and the backup paths can not overlap, this algorithm use large amounts of network resources to guarantee the reliability requirements of SFCs. B. Simulation Results 1) Execution time: Fig. 5 shows the execution time of two proposed algorithms using USNET and NSFNET topologies. We can see that with the increase in the number of SFC requests the execution time is increasing rapidly. However, the execution time of both algorithms is acceptable, because both

1 4 0 1 6 0

S

N

P

M

1 2 0

1 0 0

8 0

(

M

1 0 0

8 0

6 0

4 0

0

2 0

3 0

4 0

N

u

m

5 0

b

e

r

o

6 0

f

S

F

C

7 0

r e

q

u

e

8 0

s

9 0

1 0 0

1 0

2 0

3 0

Fig. 5.

4 0

t s

N

(a) Result of USNET topology

u

m

5 0

b

e

r

o

6 0

f

S

F

C

7 0

r e

q

u

e

8 0

s

9 0

1 0 0

t s

(b) Result of NSFNET topology

The execution time with different number of SFC requests. 8 0 0 0 0

1 0 0 0 0 0 P

M

S

N

P

M

S

P

7 0 0 0 0 c o s t

N

r e s o u r c e

8 0 0 0 0

A

p u tin g

6 0 0 0 0

4 0 0 0 0

T o ta l

c o m

c o m

c o s t

M

P

2 0

1 0

r e s o u r c e

P

N

m E x e c u tio n

4 0

0

p u tin g

N

S

e

e tim E x e c u tio n

6 0

2 0

T o ta l

A

1 2 0

s )

M

(

P

tim

N

m

s )

1 4 0

A

2 0 0 0 0

A

N

P

M

S

N

P

M

S

P

6 0 0 0 0

5 0 0 0 0

4 0 0 0 0

3 0 0 0 0

2 0 0 0 0

1 0 0 0 0

0

0 1 0

2 0

3 0

4 0

N

u

m

5 0

b

e

r

o

f

6 0

S

F

C

7 0

r e

q

u

e

8 0

s

9 0

1 0 0

1 0

2 0

3 0

4 0

N

t s

(a) Result of USNET topology

u

m

5 0

b

e

r

o

f

6 0

S

F

C

7 0

r e

q

u

e

8 0

s

9 0

1 0 0

t s

(b) Result of NSFNET topology Fig. 6.

Total computing resource cost.

are millisecond-level which can guarantee the requirements of carrier networks for network performance. In addition, since the sizes of the two network topologies are different, that is, there are more nodes in USNET topology than in NSFNET topology, the execution time of the two algorithms is a little longer in USNET topology. As expected, compared with ANPM algorithm, the execution time of SNPM algorithm is longer, this is because from the details of the two algorithms we can see that SNPM algorithm has more steps. 2) Computing resource cost: Fig. 6 shows the total computing resource cost of three algorithms using USNET and NSFNET topologies. We can see that computing resource cost increases as the number using SFC requests increases. As expected, SP consumes the most computing resources, followed by is ANPM algorithm and SNPM algorithm. In Fig. 6(a), compared with SP, SNPM algorithm reduces the computing resources cost by 42.15% in average in USNET; compared with ANPM algorithm, SNPM algorithm reduces the computing resources cost by 31.04% in average in USNET. In Fig. 6(b), SNPM algorithm reduces the computing resources cost by 39.46% in average than SP and reduces the computing resources cost by 33.35% in average than ANPM algorithm in NSFNET. We explain it as follows. Since SP does not consider the reliability of links and nodes, massive backup paths are required to guarantee the reliability requirement of

SFC requests. Therefore, the computing resource cost of this algorithm is the highest. As for the proposed algorithms, the main difference between these two algorithms is the number of protected primary VNFs. The ANPM algorithm provides end-to-end protection for the entire SFC, while the SNPM algorithm only provides protection for one VNF with the lowest reliability of SFC. Therefore, each node in ANPM needs backup nodes, whereas only one node in SNPM needs backup nodes. Obviously, ANPM requires more computing resource to operate these backup nodes than SNPM. Thus, ANPM algorithm uses more computing resource to improve the reliability of SFC requests than SNPM algorithm, namely SNPM algorithm can save up computing resource compared with ANPM algorithm. 3) Bandwidth resource cost: Fig. 7 shows the total bandwidth resource cost of three algorithms using USNET and NSFNET topologies. We can see that, as the number of SFC requests increases, the bandwidth resource cost also increases. As expected, SP consumes the most Bandwidth resources, followed by is ANPM algorithm and SNPM algorithm. In Fig. 7(a), compared with SP, SNPM algorithm reduces the bandwidth resource cost by 20.13% in average in USNET; compared with ANPM algorithm, SNPM algorithm reduces the bandwidth resource cost by 11.19% in average in USNET. In Fig. 7(b), SNPM algorithm reduces the bandwidth resource

1 8 0 0 0 N

P

M

S

N

P

M

S

P

r e s o u r c e

1 8 0 0 0

A

1 6 0 0 0 1 4 0 0 0

1 6 0 0 0

b a n d w

1 0 0 0 0 8 0 0 0 6 0 0 0 4 0 0 0

P

M

N

P

M

S

P

1 4 0 0 0

1 2 0 0 0

1 0 0 0 0

8 0 0 0

6 0 0 0

4 0 0 0

0

0 1 0

2 0

3 0

4 0

N

u

m

5 0

b

e

r

o

6 0

f

S

F

C

7 0

r e

q

u

e

8 0

s

9 0

1 0

1 0 0

2 0

3 0

4 0

N

t s

(a) Result of USNET topology

u

m

5 0

b

e

r

o

6 0

f

S

F

C

7 0

r e

q

u

e

s

8 0

9 0

1 0 0

8 0

9 0

1 0 0

t s

(b) Result of NSFNET topology Fig. 7.

Total bandwidth resource cost. 1 0 0 0 0 0

1 2 0 0 0 0 A

N

P

M

S

N

P

M

P

r e s o u r c e

S

c o s t

c o s t

1 0 0 0 0 0

8 0 0 0 0

A

N

P

M

S

N

P

M

S

P

8 0 0 0 0

6 0 0 0 0

o r k

6 0 0 0 0

n e tw

o r k

r e s o u r c e

N

S

2 0 0 0

2 0 0 0

T o ta l

4 0 0 0 0

T o ta l

n e tw

A

id th

1 2 0 0 0

T o ta l

T o ta l

b a n d w

id th

r e s o u r c e

c o s t

2 0 0 0 0

c o s t

2 2 0 0 0

4 0 0 0 0

2 0 0 0 0

2 0 0 0 0

0

0 1 0

2 0

3 0

4 0

N

u

m

5 0

b

e

r

o

f

6 0

S

F

C

7 0

r e

q

u

e

8 0

s

9 0

1 0 0

1 0

2 0

3 0

4 0

N

t s

(a) Result of USNET topology

u

m

5 0

b

e

r

o

f

6 0

S

F

C

7 0

r e

q

u

e

s

t s

(b) Result of NSFNET topology Fig. 8.

Total network resource cost.

cost by 19.65% in average than SP and reduces the bandwidth resource cost by 12.61% in average than ANPM algorithm in NSFNET. We explain it as follows. Since SP does not consider the reliability of links and nodes, massive backup paths are required to guarantee the reliability requirement of SFC requests. Therefore, the bandwidth resource cost of this algorithm is the highest. As for the proposed algorithms, there are more VNFs protected in ANPM, and more physical links are required to connect these alternate VNFs, resulting in a large amount of bandwidth resources are used. Thus, ANPM algorithm uses more bandwidth resource to improve the reliability of SFC requests than SNPM algorithm, namely SNPM algorithm can save up bandwidth resource compared with ANPM algorithm. 4) Total network resource cost: Fig. 8 shows the total network resource cost of three algorithms using USNET and NSFNET topologies. We can see that total network resource cost increases as the number of SFC requests increases. As expected, in Fig. 7(a), SP consumes the most network resources, followed by is ANPM algorithm and SNPM algorithm. In Fig. 8(a), compared with SP, SNPM algorithm reduces the total network resource cost by 33.34% in average in USNET; compared with ANPM algorithm, SNPM algorithm reduces the total network resource cost by 26.76% in average in USNET. In Fig. 8(b), SNPM algorithm reduces the total

network resource cost by 35.41% than SP and reduces the total network resource cost by 30.47% than ANPM algorithm in NSFNET. This is because network resource cost consist of computing resource cost and bandwidth resource cost. Since SP uses more bandwidth resource and computing resource, the total network resource cost of SP is the highest. 5) Results with different reliability requirements of SFC requests: Fig. 9 shows the total network resource cost vs reliability requirement of SFC requests using USNET and NSFNET topologies. In the simulation, we set the number of SFC requests as 100. We can see that the total network resource cost increases as the reliability requirement of SFC requests increase. As expected, SNPM algorithm performs better than SP and ANPM algorithm. As shown in Fig. 9(a), compared with SP, SNPM algorithm reduces the total network resource cost by 34.56% in average in USNET; compared with ANPM algorithm, SNPM algorithm reduces the total network resource cost by 29.73% in average in USNET. In Fig. 9(b), SNPM algorithm reduces the total network resource cost by 35.71% than SP and reduces the total network resource cost by 29.91% than ANPM algorithm in NSFNET. In addition, it can be seen that with the increase of reliability requirements, the network resource cost of ANPM increases faster than that of SNPM. We observe that the reason is as the reliability requirement increases, both protection mechanisms require

1

4

0

0

0

0

0

0

0

0

0

0

0

0

0

M

S

N

P

M

S

P

r a tio

0

P

0

0

n e tw

o r k

1

2

N

A c c e p ta n c e

r e s o u r c e

1

A

0

c o s t

1

6

0

0

0

6

4

0

0

0

0

0

0

. 0

0

0

. 9

8

0

. 9

6

0

. 9

4

0

. 9

2

0

. 9

0

0

. 8

8

0

. 8

6

0

. 8

4

0

. 8

2

0

. 8

0

0

. 7

8

. 9

9

3

0

. 9

9

4

0

. 9

9

5

0

. 9

9

6

0

. 9

9

7

0

. 9

9

8

0

. 9

9

R

0

2

e

l i a

b

i l i t y

r e

q

u

i r e

m

e

n

t

o

f

S

F

C

r e

q

u

e

s

0

0

0

0

1

0

0

0

0

0

8

0

0

0

0

N

P

M

S

N

P

M

S

P

r a tio

2

A

A c c e p ta n c e

c o s t

0

1

n e tw T o ta l

6

4

0

0

0

0

0

0

0

3

0

4

1

. 0

0

0

. 9

5

0

. 9

0

0

. 8

5

0

. 8

0

0

. 7

5

. 9

9

3

0

. 9

9

4

0

. 9

9

5

0

. 9

9

6

0

. 9

9

7

0

. 9

9

8

0

. 9

9

R

e

l i a

b

i l i t y

r e

q

u

i r e

m

e

n

t

o

f

S

F

C

r e

q

u

e

s

c o s r e s o u r c e o r k

r

o

0

f

6

S

F

0

C

7

r e

q

u

0

e

8

s

0

9

0

1

0

0

t s

A

N

P

M

S

N

P

M

S

P

. 9

9

3

0

1

5

0

0

0

0

1

4

0

0

0

0

1

3

0

0

0

0

1

2

0

0

0

0

1

1

0

0

0

0

1

0

0

0

0

0

9

0

0

0

0

8

0

0

0

0

7

0

0

0

0

2

A

N

P

M

S

N

P

M

S

P

. 0

2

. 5

3

L

e

n

. 0

g

3

t h

o

f

. 5

S

F

C

r e

q

4

. 0

u

e

4

s

. 5

5

. 0

t s

(a) Result of USNET topology 4

0

0

0

0

1

3

0

0

0

0

c o s

1

2

0

0

0

0

1

1

0

0

0

0

1

0

0

0

0

0

9

0

0

0

0

8

0

0

0

0

7

0

0

0

0

N

P

M

S

N

P

M

S

P

n e tw

1

A

2

. 0

2

. 5

3

L

e

n

. 0

g

3

t h

o

f

S

. 5

F

C

r e

q

4

. 0

u

e

4

s

. 5

5

. 0

t s

(b) Result of NSFNET topology Fig. 10.

e

. 9

9

l i a

4

b

0

i l i t y

. 9

r e

9

q

5

u

0

i r e

m

. 9

e

9

6

n

0

t

o

f

. 9

S

F

9

7

C

0

r e

q

. 9

u

9

e

8

s

0

. 9

9

9

t s

(b) Result of different reliability requirement of SFC requests.

Fig. 9. Total network resource cost vs reliability requirement of SFC requests.

n e tw

e

t s

(b) Result of NSFNET topology

T o ta l

5

b

9

R

r e s o u r c e

0

m

0 0

o r k

u

0

0

T o ta l

P

(a) Result of different number of SFC requests

o r k

r e s o u r c e

0

M

S

t s

(a) Result of USNET topology 0

M

P

9

N

0

P

N

0

1

4

N

S

0

0

1

A

0

T o ta l

8

1

Total network resource cost vs length of SFC requests.

Fig. 11.

Acceptance ratio with different parameter variations.

more backup paths to meet the reliability requirement of SFC requests. ANPM algorithm provides end-to-end protection for the entire SFC, while SNPM algorithm only provides protection for one VNF with the lowest reliability of SFC. Thus, compared with SNPM, the backup paths in ANPM contains more backup nodes and backup links, which means that SNPM needs more computing and bandwidth resources to operate backup paths. 6) Results with different length of SFC requests: Fig. 10 shows the total network resource cost vs length of SFC requests using USNET and NSFNET topologies. In the simulation, we set the number of SFC requests as 100. We can see that the total network resource cost increases as the length of SFC requests increase. As expected, SNPM algorithm performs better than SP and ANPM algorithm. As shown in Fig. 10(a), compared with SP, SNPM algorithm reduces the total network resource cost by 23.42% in average in USNET; compared with ANPM algorithm, SNPM algorithm reduces the total network resource cost by 19.25% in average in USNET. In Fig. 10(b), SNPM algorithm reduces the total network resource cost by 24.96% than SP and reduces the total network resource cost by 20.08% than ANPM algorithm in NSFNET. In addition, it can be seen that with the increase of length of SFC requests, the network resource cost of ANPM increase faster than that of SNPM. We observe that the reason is as the length of SFC requests is 2, the number of VNFs that ANPM needs to back up is 2, which is only one more than

the number of VNFs that SNPM needs to back up. However, when the length of SFC requests is 5, there are 3 more, and the number of links need to be backed up is also more. Obviously, the computing resources and bandwidth resources needed increase more. 7) Acceptance ratio: Fig. 11 shows the acceptance ratio of three algorithms with different parameter variations. It can be seen that no matter the increase of the number of SFC requests or the improvement of reliability requirements, acceptance ratio is on the decline. This is because the increase of both elements can increases network resource cost required by three algorithms, and resource in network are limited and cannot meet all the reliability requirements of SFC requests. When the number of SFC requests is very large or the reliability requirement of SFC requests is very high, SP requires the most backup paths, which can cause some links and nodes to carry more traffic exceed their maximum capacity, some SFC requests cannot be deployed successfully, thus the acceptance ratio of SP decline the fastest. In addition, the acceptance ratio of SNPM is still higher than that of ANPM. The reason is that SNPM uses fewer network resources than ANPM and SFC requests are more easily accepted by network system. VII. C ONCLUSION In this paper, we study on how to guarantee the reliability of SFC requests while optimizing network resource cost. We first redefined the reliability of SFC, and established SFC reliability model. Then, we proposed two protection mechanisms to improve the reliability of SFC requests: ANPM and SNPM. For each protection mechanism, we formulated the problem as an ILP model. Since the problem is NP-hard, we also proposed efficient heuristic algorithms based on Dynamic Programming and Lagrangian Relaxation to solve this problem. Extensive simulations by using real world topologies show that compared with the benchmark algorithm and ANPM, SNPM can save up to 33.34% and 26.76% network resource cost on average respectively while guaranteeing the reliability requirement of SFC requests, indicating that SNPM performs better than ANPM and has better application potential in carrier networks. R EFERENCES [1] J. Kang, O. Simeone, J. Kang, “On the trade-off between computational load and reliability for network function virtualization,” IEEE Communications Letters, vol. 21, no. 8, pp.1767–1770, 2017. [2] B. Han, V. Gopalakrishnan, L. Ji, and S. Lee, “Network function virtualization: Challenges and opportunities for innovations,” IEEE Communications Magazine, vol. 53, no. 2, pp. 90-97, 2015. [3] M, Xia, M. Shirazipour, Y. Zhang, H. Green, A. Takacs, “Network function placement for NFV chaining in packet/optical datacenters,” Journal of Lightwave Technology, vol. 33, no. 8, pp. 1565-1570, 2015. [4] T. Lin, Z. Zhou, M. Tornatore, et al. “Demand-aware network function placement,” Journal of Lightwave Technology, vol. 34, no. 11, pp. 25902600, 2016. [5] Z. Ye, X. Cao, J. Wang, H. Yu, C. Qiao, “Joint topology design and mapping of service function chains for efficient, scalable, and reliable network functions virtualization,” IEEE Network, vol. 30, no. 3, pp.81– 87, 2016. [6] K. Yang, H. Zhang, and P. Hong, “Energy-aware service function placement for service function chaining in data centers,” in Proc. IEEE Global Communications Conference (GLOBECOM), 2017.

[7] O. Soualah, M. Mechtri, C. Ghribi, and D. Zeghlache, “Energy efficient algorithm for vnf placement and chaining,” in Proc. IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID), 2017. [8] S. Van Rossem et al., “A network service development kit supporting the end-to-end lifecycle of NFV-based telecom services,” in Proc. IEEE Conference on Network Function Virtualization and Software Defined Networks (NFV-SDN), Berlin, 2017, pp. 1-2. [9] S. Van Rossem et al., “Deploying elastic routing capability in an SDN/NFV-enabled environment,” in Proc. IEEE Conference on Network Function Virtualization and Software Defined Network (NFV-SDN), San Francisco, CA, 2015, pp. 22-24. [10] B. Nmeth, J. Czentye, G. Vaszkun, L. Csikor and B. Sonkoly, ”Customizable real-time service graph mapping algorithm in carrier grade networks,” in Proc. IEEE Conference on Network Function Virtualization and Software Defined Network (NFV-SDN), San Francisco, CA, 2015, pp. 28-30. [11] R. Mijumbi, J. Serrat, J. Gorricho, N. Bouten, F. Turck, and R. Boutaba, “Network function virtualization: State-of-the-art and research challenges,” IEEE Communnications Surveys & Tutorials, vol. 18, no. 1, pp. 236-262, 2016. [12] Q. Long, C. Assi, K. Shaban, M. Khabbaz, “A reliability-aware network service chain provisioning with delay guarantees in NFV-enabled enterprise datacenter networks,” IEEE Transactions on Network and Service Management, vol. 14, no. 3, pp.554–568, 2017. [13] ETSI, Network Functions Virtualisation (NFV): Reliability. ETSI GSNFV-REL 003 v1.1.1., 2016 [14] J. Fan, C. Guan, Y. Zhao, C. Qiao, “Availability-aware mapping of service function chains,” in Proc. IEEE Conference on Computer Communications (INFOCOM), 2017. [15] A. Hmaity, M. Savi, F. Musumeci, M. Tornatore, A. Pattavina, “Virtual network function placement for resilient service Chain provisioning,” in Proc. IEEE International Workshop on Resilient Networks Design and Modeling (RNDM), 2016. [16] Y. Xu, V. Kafle, “Reliable service function chain provisioning in software-defined networking,” in Proc. IEEE International Conference on Network and Service Management (CNSM), 2017. [17] M. A. T. Nejad, S. Parsaeefard, M. A. Maddah-Ali, T. Mahmoodi, and B. H. Khalaj, “Vspace: Vnf simultaneous placement, admission control and embedding,” IEEE Journal on Selected Areas in Communications, vol. 36, no. 3, pp. 542-557, March 2018. [18] J. Fan, Z. Ye, C. Guan, X. Gao, K. Ren, C. Qiao, “GREP:Guaranteeing Reliability with Enhanced Protection in NFV,” in Proc. ACM SIGCOMM Workshop on Hot Topics in Middleboxes and Network Function Virtualization, 2015. [19] S. Herker, X. An, W. Kiess, S. Beker, and A. Kirstaedter, “Datacenter architecture impacts on virtualized network functions service chain embedding with high availability requirements,” IEEE Globecom Workshops (GC Wkshps), Dec 2015, pp. 1-7, 2015. [20] F. Machida, M. Kawato, and Y. Maeno. “Redundant virtual machine placement for fault-tolerant consolidated server clusters,” IEEE Network Operations and Management Symposium, 2010, 32-39 [21] A. Fischer, J. F. Botero, M. T. Beck, H. D. Meer, and X. Hesselbach, “Virtual network embedding: a survey,” IEEE Communications Surveys & Tutorials, vol. 15, no. 4, pp. 1888C1906, 2013. [22] B. Kar, H. K. Wu, and Y. D. Lin, “Energy cost optimization in dynamic placement of virtualized network function chains,” IEEE Transactions on Network & Service Management, no. 99, PP. 1-1, 2017. [23] H. Sakoe, and S. Chiba. “Dynamic programming algorithm optimization for spoken word recognition.” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 26, no. 1, pp.43–49, 1978. [24] A. Jttner, B. Szviatovski, I. Mcs, Z Rajko, “Lagrange relaxation based method for the QoS routing problem,” in Proc. IEEE Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 2, pp.859–868, 2001. [25] C. Yin, H. Wang, “Developed Dijkstra shortest path search algorithm and simulation,” in Proc. IEEE Computer Design and Applications (ICCDA), 2010. [26] T. W. Kuo, B. H. Liou et al., “Deploying chains of virtual network functions: On the relation between link and server usage,” in Proc. IEEE International Conference on Computer Communications (INFOCOM), 2016.

LaTeX Source Files Click here to download LaTeX Source Files: LaTeX Source Files.rar

*Author Biography

Lang Fan is currently pursuing the Master degree in electronic and communication engineering with the School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, China. His research interests include network optimization, software defined networks, and network function virtualization.

Xiaoning Zhang received the B.S., M.S., and Ph.D. degrees in communication and information engineering from the University of Electronic Science and Technology of China, Chengdu, China, in 2002, 2005, and 2007, respectively. He is currently an Professor with School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, China. His research interests include network design, software defined networks and network function virtualization.

Keshav Sood received the bachelor’s degree (Hons.) (with distinction) in electronic engineering and the master’s degree, majoring in optical fiber engineering from Punjab Technical University, India, in 2007 and 2012, respectively, and the Ph.D. degree in software-defined networking from Deakin University, Melbourne, in 2017. His research interests include software-defined networks, the Internet of Things, and cyber security. He is a recipient of the Professoriate of IT Award at Deakin University for outstanding research achievements.

Yunqing Wang is currently pursuing the Master degree in electronic and communication engineering with the School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, China. His research interests include network optimization, software defined networks, and network function virtualization.

Shui Yu received his B. Eng (Electronic Engineering) and M. Eng (Computer Science) degree from University of Electronic Science and Technology of China, P. R. China in 1993 and 1999, respectively. He also obtained an Associate Degree in Mathematics from the same university in 1993. He received his PhD (Computer Science) from Deakin University in 2004. He is currently a Senior Lecturer of School of Information Technology, Deakin University, Melbourne, Australia. Before joining Deakin University, Dr Yu was a Lecturer of Computer College in University of Electronic Science and Technology of China. He has a good experience of industry, especially in network design and software development organization and implementation. His research interests include Big Data Theory and Application, Networking Theory and Application, and Mathematical Modelling. He dedicates himself in advance human understanding of networks and information, including their measurement, representation, analysis, and application. As a semi-mathematician, he targets on narrowing the gap between theory and application using mathematical tools. Dr Yu is a Guest Professor of South West University of China, an overseas expert of the national 111 project at Beijing Jiaotong Univesity. Dr Yu is a Member of AAAS, ACM, and a Senior Member of IEEE.

*conflict of Interest Statement

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

*Author Contributions Section

Author Contributions Section Lang Fan and Xiaoning Zhang conceived and designed the study. Lang Fan and Yunqing Wang performed the simulations. Lang Fan Wrote the paper. Keshav Sood and Shui Yu reviewed and edited the manuscript. All authors read and approved the manuscript.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: