Resource-Aware Virtual Network Parallel Embedding Based on

2016 17th International Conference on Parallel and Distributed Computing, Applications and Technologies

Resource-aware Virtual Network Parallel Embedding Based on Genetic Algorithm Zibo Zhou, Xiaolin ChangYang Yang, Lin Li School of Computer and Information Technology Beijing Jiaotong University, Beijing, P.R. China e-mail: {15120491, xlchang,16112082, lilin}@bjtu.edu.cn

to the same InP. Another example is that in a virtualized infrastructure, a single substrate failure may affect all the VNs sharing that resource. When the backup resources are absent, these VNs must be re-embedded or migrated. Both these two scenarios can be regarded as a special case of simultaneous arrival of multiple VNs requests (batch arrivals).

Abstract—Embedding virtual network requests in an underlying physical infrastructure, the so-called virtual network embedding (VNE) problem, has attracted significant research interests already. A realistic scenario might entail embedding multiple VN requests (MVNE) that arrive simultaneously (batch arrivals). The existing heuristic MVNE approaches neither consider the coordination among multiple VNR embeddings nor embed all the arriving VNRs simultaneously considering the available physical resources. This paper considers the MVNE problem in the scenario where the available physical resources may not be sufficient to satisfy the physical resource demands of all the VNRs in the batch. We explore applying genetic algorithm (GA) to handle the MVNE problem. We propose an algorithm to decide which VNRs could be mapped together. Extensive simulations are carried out to evaluate the performance of the proposed algorithms in terms of the VN acceptance ratio and the longterm revenue of the service provider.

The existing approaches to the MVNE problem did not consider the coordination between the node and link mappings in a VN [3] or did not consider the coordination among multiple VNR embeddings [3][5] or embedded all the arriving VNRs simultaneously without considering the current available substrate resources [7]. For the convenience of description, we use MVN-SE (MVN Sequential Embedding) to denote the first two kinds of embedding approaches and use MVN-CE-INS (MVN Coordinated Embedding Insensitive to the substrate Network State) to denote the third approach in the following.

Keywords-Network virtualization; Virtual network embedding; Optimization; Resource allocation.

I.

The MVN-SE approach improved the InP’s long-term revenue by embedding each VN in the batch in the descending order of their revenues (defined in Section II). Note that the MVN-SE approach may not maximize the InP’s revenue. We illustrate this by using the example shown in Fig.1. In this example, the three VN requests depicted in Fig.1 (a) are to be mapped to the substrate network of Fig.1 (b). When the algorithm proposed [3] or WiNE+R-ViNE/D-ViNE proposed [5] is applied, VNR1 must be mapped first with {aoC, boD}. The left two VNRs will be rejected and the revenue gained by InP is 20 units. However, if we map these VNs together in a coordinating way, we will get {coC, doD, eoC, foE} and the revenue is 24. Here we define revenue of serving a VN as the sum of the bandwidth and CPU required by this VNR.

INTRODUCTION

Network virtualization has been regarded as a promising technology for the future Internet [1]. The authors in [2] talked about the evolution of a future Internet architecture consisting of Infrastructure providers (InPs) and Service Providers (SPs). One of the most important issues in the network virtualization is the virtual network embedding (VNE) problem, which deals with the mapping/embedding1 of VN requests onto specific physical nodes and paths of the substrate network. Many efforts have been devoted to the VNE problem, see [4] and references therein. Most existing research deals with online VN requests (VNRs) one by one according to their arrival time. Some authors in [3][5][7] proposed to embed a batch of VNRs arriving in the time window in order to increase the InP’s long-term revenue and decrease InP’s embedding cost. This kind of VNE problems is denoted as multi-VNE (MVNE) problem. In a realistic network virtualization scenario, VN requests may arrive simultaneously. An obvious example is as follows. :KHQD YLUWXDO QHWZRUN PXVW EH SURYLVLRQHG DFURVV KHWHURJHQHRXV DGPLQLVWUDWLYH GRPDLQV PDQDJHG E\ PXOWLSOH,Q3Vthe VNR must be subdivided into subVNRs. It is possible that more than one sub-VNR is mapped

(a) Three VN requests

(b)Substrate network

1

The words ‘embed’ and ‘map’ are used interchangeably throughout this paper.

978-1-5090-5081-9/16 $31.00 © 2016 IEEE DOI 10.1109/PDCAT.2016.30

Fig.1

81

An example of three VN embeddings

The aforementioned example illustrates that coordination must not only exist between the node and link mappings in a VN but also exist among the multiple VNR embeddings. The MVN-CE-INS approach considers these two kinds of coordination. But it does not work well when there are insufficient substrate network resources for embedding the batch of VNRs, the VN requests are all rejected even if some of the VN requests can be embedded onto the substrate successfully.

power, storage and so on. Without loss of generality, this paper only considers the processing power. All the work presented in this paper can be applied directly to the environment where virtual nodes have other resource demands besides CPU demand. Each physical link e S (v, w)  E S between physical nodes (v,w) is associated with bandwidth capacity. All the physical resources (i.e. bandwidth and CPU) in GS are limited. Usually, the virtual node’s QoS (Quality of Service) requirements include the CPU demand and a preferred value V d n expressing how far a virtual node nV  N V can be placed from the specified location l (nV ) . The QoS

This paper aims to handle the MVNE problem in a resource-aware and coordinated manner in the scenario of peak resource demand, in which there are not enough physical resources to embed every arriving VNR. By resource-aware, we mean that the information of the available physical resources is applied to determine which VNs are to be simultaneously embedded. We propose two aspects to improve the InP’s long-term revenue from: ķ embed the batch of VNs in a way so as to improve the InP’s revenue generated by serving these VNs, and ĸ allocate the physical resources for the selected VNs in a way to accommodate more future VNRs.

requirements of a virtual link eV (v, w)  E V between virtual nodes (v,w) include the bandwidth requirement and a delay demand. Virtual network embedding for a VN request is defined as a mapping from GV to GS with the constraints: ķ Each virtual node is mapped to a physical node in a one-to-one manner, and the virtual node QoS requirements are satisfied.

In this paper, we propose a heuristic nested genetic algorithm (NGA), called VNE-NGA, which handles the batch embedding problem in a two-stage way. The first stage is called as the multiple VN selection (S-MVN) phase and the second is the multiple VN embedding (E-MVN) phase. Simulations are carried out to investigate the effect of the time window size on the performance of the MVN algorithms and to investigate the performance of the proposed algorithms in terms of the VN acceptance ratio and long-term revenue of the service provider.

ĸ Each virtual link eV (v, w) is mapped to a physical path (an unsplittable model) or a flow (a splittable model) in GS between physical nodes which host v and w, respectively, with at least two requirements. One is that the eV (v, w) bandwidth requirement is below the total available bandwidth of the physical path or the flow. The second is that the delay constraint of the virtual link is met.

The available CPU capacity AN ( n S ) of a physical

The rest of the paper is organized as follows. In Section II we first present the network model and the VN embedding problem. Then we present the related work on the MVNE problem. In Section III, we first present the MIP formulations of the S-MVN, then the VNE-NGA algorithm. We evaluate the performance of the proposed algorithms in Section V. Section VI presents the conclusions. II.

node nS is

defined

as AN (n S ) c(n S ) 

¦ V

n n n

c(nV ) , S

here nV n n S denotes that virtual node nV is hosted on the physical node nS . The available bandwidth AE (e S (v, w)) of a physical link e S (v, w) is defined as b(e S (v, w)) minus the total bandwidth used by virtual links that pass through e S (v, w) .

BACKGROUND AND RELATED WORK

Objective. We define the revenue R (GV (t )) of serving GV at time t as

In this section, we first describe the network model and problem definition, which form the basis for the MIP formulation in the subsequent section. Then we present the related work.

¦

R (GV (t ))

b(eV )  Z

eV EV

¦

nV N V

c (nV )

(1)

where Z is the weight to determine the relative importance of the CPU and bandwidth resources. From the InPs’ point of view, they hope to maximize their revenues in the long run. We define the long-term average revenue as

A. Network Model and Notation VN Embedding. Both the substrate network and the virtual network are modeled as weighted undirected graphs and are denoted by GS ( N S , E S ) and GV  N V , E V , respectively. Here N S / N V is the set of physical/virtual nodes and E S / EV is the set of physical/virtual links. Each physical node n S  N S is associated with CPU resources c ( n S ) and geographical location l ( n S ) . The system resources of a physical node include memory, processing

lim

T of

82

¦

T t 0

R (GV (t )) T

(2)

TABLE I VARIABLE DEFINITION

B. Related Work Significant studies have been carried out on the VNE problem. The following discusses the existing studies about the approaches for the MVNE problem.

Term

f

The authors in [3] proposed a method to process all VNRs arriving within a time window as well as in the request queue, in non-increasing order of their revenues. The virtual nodes of all the considered VN requests are mapped first, and then the virtual links for the requests that successfully finish the node mapping stage are mapped. The separation between the node mapping and link mapping may restrict the solution space and can result in poor performance [6]. Different from the batch processing proposed in [3], the authors in [5] consider to sequentially embed the VNRs in the batch in the non-increasing order of VN embedding revenues. These two algorithms either separated the node mapping from the link mapping, or separated one VN embedding from the other VN embedding.

xuuV

An integer decision variable. u  N S and uV  N V . Its value is 1 V

if virtual node u is mapped to physical node u ; otherwise, set to 0. An integer decision variable. k  ^1...K ` . Its value is 1 only if

yk

the kth VN is selected to be embedded; otherwise, it is set to 0.

Bu ,v

Denote the total bandwidth demands of the virtual links, each of which is mapped to a flow from physical node u to v.

J k ,u ,v

Denote the total bandwidth demands of the virtual links of the kth VN, each of which is mapped to a flow from physical node u to k ,u ,v Bu ,v . v. Thus, ¦ J k K

A real variable. Denote the total amount of the flows from

hekS,u(i,,vj )

The authors in [7] aim to handle the batch processing of VN requests by coordinating the mapping of all virtual nodes and the mapping of all virtual links. They formulated the batch processing problem as a MIP model and then applied the branch and bound algorithm to solve the MIP program. However, the number of VN requests to be embedded in the algorithm [7] is fixed, namely insensitive to the substrate network state. The disadvantage is that when there are insufficient substrate network resources for all the VN requests, the VN requests will be all rejected even if some of the VN requests can be embedded onto the substrate successfully. This paper aims to overcome the insufficiency of this approach. III.

Definition A real variable. Denote the total amount of the flows from physical node u to v on the physical link e S (i, j ) .

u ,v eS ( i , j )

physical node u to v on the physical link

e S (i, j ) for the kth

VN. An integer decision variable. Its value is 1 only if virtual link

g euV,v

eV is from u to v. otherwise, it is set to 0.

The challenge in the MIP formulation of the S-MVN problem is how to express the following features. (f1). Only one physical node is selected for each nV . (f2). No more than one virtual node for a VN is placed on a physical node but virtual nodes from different VNs can be mapped to the same physical node.

ALGORITHM DESCRIPTION

In this section, we first describe the MIP formulations. Then we present VNE-NGA algorithm.

We formulate the S-MVN problem as a linear integer program with integer constraints in the following manner.

A. MIP Formulation of S-MVN problem

S-MVN _MIP Objective:

Assume that there are K VNRs in a batch. Define GVk  N Vk , E Vk and GV GV ... ‰ GVk ... ‰ GVK . K (nVk ) represents nVk  N Vk in N V and H (eVk ) represents eVk  EVk in E . A set :  P ( n ) for each n V

Vk

Vk

^n

S

· c( w) ¸ ¹

(3)

Subject to: ¦ feuSc(,uvc,v) d AE  eS , eS (u, v)  E S

(4)

k

k

is created according to

the location and CPU computing constraints of nVk . : K ( nVk ) is defined as follows: :(K (nVk ))

§

¦ y ¨ ¦ b(e) Z ¦

max

wN

Vk

u c, vcN S

`

 N S dis  l (nVk ), l (n S ) d d n && c(nVk ) d c(n S ) Vk

© eE

Vk

¦ V

u N

TABLE I gives the definition of five variables, used in the following.

V

xuuV c(uV ) d AN (u ), u  N S

S

¦

S

S

¦

S

e ( u , w)E

e ( v , w)E

83

f euS ,(vu , w)  f euS ,(vv , w) 

S

¦

S

S

¦

S

e ( w,u )E

e ( w, v )E

(5)

f euS ,(vw,u )

Bu ,v , u, v  N S

(6)

f euS ,(vw,v )

 Bu ,v , u, v  N S

(7)

¦

eS ( i , w)E S

f euS ,(vi , w)

¦ b e g V

V

V

e E

¦g

vN S

u ,v eV

¦g

uN S

u ,v eV

¦

eS ( w, i )E S

f euS ,(vw,i ) ,

(8)

u, v  N S , w  N S \{u, v} u ,v eV

Bu ,v , u, v  N S

(10)

xvvV , eV (uV , vV )  EV , v  N S

(11)

¦

xuuV

¦

xuuV d 1, u  N S , k



u: u

uV N Vk

yk , uV  N Vk , k  K

(16)

x  ^0,1` ,u  N , u  N u uV

S

V

V

(18)

B u ,v t 0,u , v  N S

(19)

To avoid the exponential computation time of solving the large scale S-MVN_MIP problem by CPLEX solver, we propose a heuristic nested genetic algorithm, VNE-NGA. VNE-NGA consists of two loops: the outer-loop GA (described in Algorithm 2) and the inner-loop GA (described in [10]). The outer-loop GA seeks to find a nearoptimal VN list, such that the InP revenue brought by serving the batch of VNs is maximized with load balancing. The inner-loop GA aims to embed a VN with a minimized embedding cost as well as load balance. Some explanations about Algorithm 2 are given as follows.

Chromosome Representation. Assume that there are K VNRs in a batch. Each chromosome i in the outer-loop GA is associated with two binary vectors: Z i  zi1 , zi2 , ", ziK and Pi  pi1 , pi2 , " , piK . zik =0 means

3:

Get OpBest and update OgBest. Compute the fitness r cos t f outer (i ) and f outer (i ) of each chromosome i in the outer population and update OpBest. If OpBest  OgBest then OgBest = OpBest.

4:

Repeat step2-step3 until the maximum number of iterations is reached.

5:

Output the MVN embedding solution and stop. If r f outer (OgBest ) is 0, output there is no feasible solution. Otherwise, return OgBest as the MVN embedding solution.

Evolution. Both the inner-loop GA and the outer-loop GA apply the elitist selection scheme, the one-point crossover, and the flip-bit mutation to evolve. The innerloop GA applies the greedy method to map each virtual node. Whenever H i is updated, its feasibility must be checked by solving MFP (Multi-commodity Flow Problem) to map all the virtual links in the VN. H i is called as being feasible if all the virtual links finds their hosted physical paths; otherwise H i is unfeasible and then the ith chromosome is called unfeasible. The fitness function f inner (i ) of the inner-loop GA is defined as in Equation (36). If H i is unfeasible, f inner (i ) is set to +. The variable IpBest is defined to denote the local best solution, namely the solution with the smallest f inner (i ) value in the current

that the kth VN is selected to be re-embedded. Otherwise, it is not re-embedded. pik =1 means that the kth VN is reembedded successfully. Otherwise, its re-embedding fails. Each chromosome i in the inner-loop GA for handling GVk is associated with two vectors: ķ The host

 h , h ,", h , 1 i

2 i

N Vk

i

-

Generate new population. Apply selection, crossover and mutation to Z i vectors. For each Z i , if zik =0, then use the inner-loop GA to map the kth VN and update the corresponding pik .

B. VNE-NGA Heuristic Algorithm

vector H i

Vk

2:

(17)

yk  ^0,1` ,k  K

N Vk

i

Initialization. First initialize a population of the outerloop chromosomes by doing the following. Set each zik to 1 randomly. If zik =1, set pik =0. If zik =0, use the inner-loop GA to embed GVk . If the embedding is successful, set pik =1, otherwise, pik =0. For each r cos t chromosome i, compute f outer (i ) and f outer (i ) . Then set OpBest to the chromosome m such that OpBest  k , k belonging to the outer-loop population. Set OgBest = OpBest.

(14)

f euS , v t 0,u, v  N S , e S  E S

2 i

1:

(13)

(15)

1 i

Algorithm 2 (outer-loop GA): input=(a batch of GVk , GS )

(12)

g euV,v  ^0,1` ,u, v  N S , eV  EV

 s , s ,", s , which is a N

length bit vector. If sim =0, then the corresponding virtual node should be re-mapped. Otherwise, the current mapping of this virtual node remains.

(9)

xuuV , eV (uV , vV )  EV , u  N S

xuuV  xvvV  geuV,v d 1, eV (uV , vV )  EV , u, v  N S V

ĸ The state vector Si

which is a N Vk -length

integer vector. him denotes the physical node which hosts the virtual node m in the i th chromosome. Here, 1 d m d N Vk .

84

iteration. The variable IgBest is defined to denote the best value obtained so far.

¦

e S E S

De

¦

S

AE (e S )  H u , vN S

hekS,u , v 

¦

u N S

Eu AN (u )  H

¦

uV  N Vk

xuuV c(uV )

TABLE II COMPARED ALGORITHMS

r r cos t cos t f outer ( A) f outer ( B) and f outer ( A) d f outer ( B) . The variable OpBest is defined to denote the local best solution. The variable OgBest is defined to denote the best value obtained so far.

k i

§

· c( w) ¸ wN Vk ¹

k

© eEVk

D eS § · ¨ ¦ ¦ S hekS,u ,v ¸ S S S A (e )  H    e E u , v N E ¸ ¦k pik ¨¨ ¸ Eu u V ¨¨  ¦ ¦Vk xuV c(u ) ¸¸ S A (u )  H V u N © u N N ¹

IV.

Description

RViNE

Proposed in [7]. Map the batch of VNRs sequentially. Use MFP to map virtual links.

O-RViNE

First sort the batch of VNs based on the revenue and then call RViNE to maps the sorted VNs sequentially. Use MFP to map virtual links.

RW-PSO

Proposed in [11], but use MFP to map virtual links.

(20)

In the outer-loop GA, there are two fitness functions: r cos t f outer (i ) and f outer (i ) , defined in Equation (37) and (38), respectively. When we say chromosome A is better than B r r (denoted by A  B), we mean ķ f outer ( A) > f outer ( B) or ĸ

¦ p ¨ ¦ b(e) Z ¦

Notation

The metrics considered include (i) Acceptance ratio, which measures the percentage of total VNRs accepted by an algorithm over a given period. (ii) Average revenue, which measures the generated revenue (defined in Equation (2)) over time T.

(21)

The parameters used in RW-PSO are set as in [11]. In both outer-loop and inner-loop GAs of VNE-NGA, ķ pc is set to 0.8, ĸ pm is set to 0.05 according to the setting ranges suggested in [10], Ĺ the population size is set to 3, and ĺ the number of iterations is set to 4. D and E in Equation (20), and Z in Equation (1,3) are all set to 1. In this paper, we express the time window size in terms of VN number in a batch instead of time unit in order to compare OEM with the exact MVNE algorithms proposed in [7]. Unless other specified, the VN number in a batch is set to 4. Each simulation lasts 50000 time units.

(22)

PERFORMANCE EVALUATION

In this section, we compare the performance of the proposed algorithms with some existing exact MVNE algorithms and some heuristic state-of-the-art VNE algorithms. We first describe the simulation environment and the algorithms to be compared. Then we present the simulation results.

C. Comparative Performance We fix the average VN lifetime to 1000 time units and evaluate the algorithms by varying the VNR arrival rate from 4 to 8 VN requests per 100 time units. Each experiment is repeated 10 times and the average value of these repetitions is presented as the simulation results in the following figures. T is set to 50000 time units when computing average revenue.

A. Simulation Environment As in the existing VNE literature, we use synthetic network topologies to evaluate the proposed algorithms. We generate the substrate network topologies and virtual network topologies using the GT-ITM tool [8]. The substrate network is configured to have 50 nodes in (25u25) grids, which are randomly connected with probability 0.5. Both physical node CPU and link bandwidth capacities follow a uniform distribution from 50 to 100 units. CPU and bandwidth requirements of a VN are distributed uniformly from 0 to 20 units and from 0 to 50 units, respectively. Virtual nodes are also located on (25x25) grids. VNRs arrive in a Poisson process and the VNR lifetimes follow an exponential distribution.

We summarize the observation from the simulation results as follows: VNE-NGA provides higher acceptance ratio and average revenue compared with the other heuristic algorithms. Fig.2 and Fig.3 indicate that VNENGA performs better than the other heuristic algorithms, including RW-PSO. This is due to the outer-loop GA in VNE-NGA trying to make coordination among the batch embedding. Fig.2 and Fig.3 also show that RW-PSO provides higher revenue than RViNE, confirming the conclusion presented in [11]. Note that the algorithms evaluated in [5] applying k-shortest-path algorithm to map virtual links.

B. Compared Algorithms and Performance Metrics We compare VNE-NGA with the algorithms listed in Table II. We do not compare with the MVNE algorithm proposed in [3] because the algorithm implementation according to the paper description produces very lower long-term revenue. RViNE has been implemented in [9]. We implement the left algorithms.

85

VNE-NGA

0.7

RW-PSO

O-RViNE

algorithms in terms of acceptance ratio and the InP’s longterm revenue.

RViNE

ACKNOWLEDGMENT

Acceptance ratio

0.6

This research is supported in part by NSF 61572066 of China.

0.5 0.4

REFERENCES

0.3

[1]

T. Anderson, L. Peterson, S. Shenker, and J. Turner, “Overcoming the Internet impasse through virtualization,” In IEEE Computer, 2005. [2] N. Feamster, L. Gao, and J. Rexford, “How to lease the Internet in your spare time,” In SIGCOMM Computer Communication Reiew, 2007. [3] M. Yu, Y. Yi, J. Rexford, and M. Chiang, “Rethinking virtual network embedding: Substrate support for path splitting and migration,” In Proc. ACM SIGCOMM, 2008. [4] Xiaolin Chang, Xiuming Mi, Jogesh K. Muppala, Performance evaluation of artificial intelligence algorithms for virtual network embedding. Eng. Appl. of AI 26(10): 2540-2550 (2013). [5] N. M. M. K. Chowdhury, M. R. Rahman, and R. Boutaba, “ViNEYard: Virtual Network Embedding Algorithms with Coordinated Node and Link Mapping,” In IEEE/ACM Transaction on Networking, 2011. [6] I. Houidi, W. Louati, and D. Zeghlache, “A distributed virtual network mapping algorithm,” In Proc. IEEE International Conference on Communications (ICC 2008), 2008. [7] I. Houidi, W. Louati, W.B. Ameur, and D. Zeghlache, “Virtual network provisioning across multiple substrate networks,” In ELSEVIER Journal of Computer Networks, 2011. [8] E. Zegura, K. Calvert, and S. Bhattacharjee, “How to model an Internetwork,” In Proc. IEEE INFOCOM, 1996. [9] “ViNE-Yard,” http://www.mosharaf.com/ViNE-Yard.tar.gz. [10] Xiuming Mi, Xiaolin Chang, Jiqiang Liu, Longmei Sun, Bin Xing:Embedding Virtual Infrastructure Based on Genetic Algorithm. PDCAT 2012: 239-244. [11] X. Cheng, S. Su, Z.B. Zhang, K. Shuang, F.C. Yang, Y. Luo, and J. Wang, “Virtual Network Embedding Through Topology Awareness and Optimization,” In Elsevier Journal of Computer Newtorks, 2011.

0.2 









VNR average arrival rate (per 100 time units)

Fig.2

Acceptance ratio of heuristic algorithms

VNE-NGA

Average revenue

5000

RW-PSO

O-RViNE

RViNE

4000

3000

2000

4

5

6

7

8

VNR average arrival rate (per 100 time units)

Fig.3

Average revenue of heuristic algorithms

V.

CONCLUSION

This paper proposes an approach to handle the MVNE problem in a resource-aware manner to maximize the network service provider’s long-term revenue. We first present the problem as mixed integer programs and then propose a heuristic nested genetic algorithm. The simulation results indicate that VNE-NGA works better than the existing heuristic state-of-the-art VNE and MVNE

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