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Green Survivable Collaborative Edge Computing in Smart Cities

Article  in  IEEE Transactions on Industrial Informatics · January 2018

DOI: 10.1109/TII.2018.2797922

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Green Survivable Collaborative Edge Computing inSmart Cities

Weigang Hou, Zhaolong Ning, and Lei Guo

Abstract—As an integrated environment deployed with wiredand wireless infrastructures, smart city heavily relies on theWireless-Optical Broadband Access Network (WOBAN). Theinformation flows captured by indoor devices are sent to opticalnetwork units through front-end Wireless Mesh sensor Networks(WMNs) and finally reach the optical line terminal for industri-al/commercial decision making via the passive optical networkbackhaul. To reduce the backhaul bandwidth saturated by thisconventional approach, edge devices are deployed at the front-endWMN to preprocess information flows. Based on collaborativeedge computing, home users or factory workers customize theircomputing services as virtual networks embedded onto thecommon WMN. In this paper, we propose the green survivablevirtual network embedding for the collaborative edge computingin smart cities. We mathematically formulate the problem andderive the corresponding bound. Extensive simulations with realtraces demonstrate the algorithm effectiveness.

Index Terms—Smart cities, wireless mesh sensor networks,green survivability, collaborative edge computing.

I. INTRODUCTION

The smart city is an integrated environment that heavilyrelies on the Wireless-Optical Broadband Access Network(WOBAN) [1]. As illustrated by Fig. 1, the front-end ofWOBAN is the Wireless Mesh sensor Network (WMN) [2, 3]where the data—captured by indoor devices—are transferredrouter-by-router along the wireless channel, and finally reachthe neighbor Optical Network Unit (ONU). The ONU receivesthe sensor data of the same community such as one factory’sdistrict, and the collected information flows are further sentto the Optical Line Terminal (OLT) via the Passive OpticalNetwork (PON). The Central Office (CO) connected to theOLT can be a public service infrastructure where someonemakes an effective industrial/commercial decision based oninformation flows.

Unfortunately, the amount of information flows becomesincreasingly numerous. According to the prediction of thecisco global cloud index [4], by 2019, the smart city including

Copyright (c) 2018 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

This research was sponsored by the National Nature Science Foundationof China (61401082, 61471109, 61502075) in part by the General ArmamentDepartment and Ministry of Education United Fund (6141A0224-003), andin part by the Fundamental Research Funds for the Central Universities(N150401002, N161604004, N161608001, DUT17RC(4)49).

W. Hou and L. Guo are with the School of Computer Science andEngineering, Northeastern University, Shenyang 110819, China.

Z. Ning is with the Key Laboratory for Ubiquitous Network and ServiceSoftware of Liaoning Province, School of Software, Dalian University ofTechnology, Dalian 116620, China.

The corresponding authors of this paper are Z. Ning (Email: zhaolongn-ing@dlut.edu.cn) and L. Guo (Email: guolei@cse.neu.edu.cn)

Fig. 1. WOBAN for smart city [7].

millions of people will generate 180 PB data coming fromsecurity, health and transportation everyday. It is not sustain-able to send so much information flows to the CO becausethe PON bandwidth will become saturated along optical fibercables. Edge Devices (EDs) should be deployed at ONUsand wireless routers so that the collaborative edge computingcan be performed at the front-end WMN [5-12], in order tomitigate the relative latency and the resource overprovisioningof the PON.

A. Motivation

Collaborative edge computing supports the ‘Infrastructure asa Service (IaaS)’ model where home/factory users customizetheir computing services through the common front-end WMNinfrastructure. Moreover, the Network Function Virtualization(NFV) [13-20] is an economical way to perform the above IaaSmodel. By using NFV, one user’s computing service can beabstracted into the virtual network that will be embedded ontothe underlying WMN infrastructure [7, 21-22]. As an exampleof the virtual network in Fig. 2, virtual node 1 is mapped onED b connected to the ONU, while virtual nodes 2, 3, 4 and5 are mapped onto EDs (e, c, a, and d, respectively) deployedat wireless routers. The computing resource of the mappedED is consumed for processing information flows, while theradio bandwidth is utilized to support inter-ED communicationalong relative wireless channels [7].

However, the network survivability cannot well be guar-anteed by the aforementioned Virtual Network Embedding(VNE) supporting collaborative edge computing. The networksurvivability is important because the failure of EDs prolongsthe delay of processing information flows without quick re-sponse measures. Especially in an industrial environment, the

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Fig. 2. Traditional VNE for collaborative edge computing in the WOBANsupporting smart cities [7].

EDs deployed at wireless routers are easy to loss efficiencydue to Inter-Channel Interference (ICI) [23].

B. Contribution

In this paper, we consider the realistic scenario where onlyone ED losses efficiency per time period. This realistic ED-failure scenario is seriously dangerous especially when theWOBAN has a very long running time. More important,in virtualization environment, a single physical node failurealso affects multi virtual networks with a mapping that spansover the disabled node. Based on this rational assumption,we propose a novel green survivable VNE framework forcollaborative edge computing in smart cities.

First of all, we divide every WMN into a pair of individualauxiliary graphs recording the usage of working and backupresources, respectively. For instance, in Fig. 3, after WMN 2is divided, among the initial 20 units of computing resources(can see ED c), 10 for working and 10 for backup (thescaling factor f = 10

20 = 0.5). This kind of equipartition maynot be optimal, so we achieve a more appropriate resourcedivision for each WMN. We firstly determine the number ofbackup EDs according to the WMN-level reliability. Next,we construct the backup graph for each WMN where thegeographical locations of k backup EDs are decided bythe heuristic strategy. As a result, the residual EDs do nothave to provide backup resource, avoiding some unreasonableresource-partition operations.

After dividing the WMN’s resource, we embed the virtualnetwork onto the working graph of the most qualified WMN,and then choose an appropriate backup ED on another graph.The backup ED should not be included in the set of workingEDs, so that it can quickly access the computing task previ-ously tackled by the disabled working ED. As an example ofFig. 3, the virtual nodes 1, 2 and 3 are respectively mappedonto EDs a, b, and c in the working graph. Since workingEDs communicate with each other via wireless channels, thetransmitting power assigned for them should be minimized.Next, on the premise that only one ED losses efficiency duringa time period, the backup resource can be shared by workingEDs disabled in different times. To maximize the sharingdegree of backup resource, the virtual nodes are embedded

Virtual network processed by

collaborative edge computing

in one WMN

Optical fiber cable

f g

CO Cloud

OLT

ONU ONU ONU

PON

WMN 1 WMN 3

WMN 2

WMN 2

working

graph

20

10

10WMN 2

backup

graph

c

3

1

2

1

c

c

a

b2

3

d

12

3

e

Fig. 3. Green survivable VNE for collaborative edge computing in theWOBAN supporting smart cities.

onto a single backup ED. In Fig. 3, the virtual nodes 1, 2and 3 are embedded onto the backup ED d functioned as thepublic candidate if one of the working EDs a, b and c becomesdisabled. In summary, we perform green survivable VNEoperation on the most qualified WMN where the maximalnumber of virtual networks can be served by consumingreasonable amount of the transmitting power assigned forworking EDs, and meanwhile, the maximal sharing degree ofbackup resource is also ensured.

But sometimes, a single WMN cannot well guarantee thesurvivability of the virtual network due to its limited resourceprovisioning. For this scenario, the backup ED coming fromthe different WMN can be utilized via the PON backhaul.As illustrated by Fig. 3, if the ED d in WMN 2 does nothave sufficient backup resource, the backup ED g—comingfrom WMN 3—can be chosen. In this case, if one of theworking EDs a, b and c becomes disabled, the backup carriersare consumed for the traffic migration from WMN 2 to g inWMN 3 along optical fiber cables. The main contributions aresummarized in the following.

• We mathematically define the WMN’s reliability so asto determine the number of EDs owning local backup-resource provisioning. The heuristic strategy is also de-signed for optimizing the geographical location of backupEDs in the WMN. By making extensive simulations,the optimal scaling factor, i.e., the most appropriatepercentage of the initial computing resource occupied bythe backup provisioning, is successfully determined forour resource-division method. Using the optimal scalingfactor, our resource-division method obtains the more rea-sonable usage of working and backup resources comparedwith the other resource-partition approaches.

• We make the green survivable VNE operation for virtualnetworks one-by-one. We select the most qualified WMNwhich serves the largest number of virtual networks whileensuring the maximal sharing degree of backup resource.

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We mathematically formulate the aforementioned opti-mization problem and derive the bound. If the singleWMN has the local bottleneck, the backup ED comingfrom the different WMN is utilized via the PON backhaul,and minimizing the number of consumed backup carriersbecomes the new objective where an appropriate optimalbound is determined.

• By analyzing extensive simulations for our green sur-vivable VNE framework, we discover some interest-ing phenomenon: 1) when all the virtual networks canbe successfully embedded onto front-end WMNs, ourmethod consumes an expected transmitting power as-signed for working EDs, with the average improvementratio of 26% over the benchmark; 2) when we havethe WMN’s local bottleneck, through the PON backhaul,our method—along with the optimal scaling factor—achieves the sharing degree of backup resource whichexactly matches the corresponding upper bound with theaverage convergence ratio of 92%; in addition, it alsoguarantees the survivability of more virtual networkswith the average improvement ratio of 50% over thebenchmark without considering the PON backhaul; 3) ourmethod well mitigates the consumption of backup carriersthrough the PON backhaul, which also well matches thecorresponding optimal bound with the average conver-gence ratio of 94%.

The rest of this paper is organized as follows. The networkmodel and the overview of our design framework are given insection II, and we formulate the problem in section III wherebounds are also deduced. To solve the problem within a shortspan of time, we develop the heuristic algorithm in sectionIV. We analyze numerical results in section V. We summarizethe related work in section VI before concluding the paper insection VII.

II. NETWORK MODEL AND DESIGN OVERVIEW

A. Network model

The WOBAN supporting smart cities has n WMNs, each ofwhich owns |M | EDs (ONU-level EDs) connected to the sameONU, and |P | wireless routers distributed in smart homes orfactory sites from the same community. The initial computingcapacity of the ONU-level ED is SCh, while each wirelessrouter owns the local ED which has a lower computingcapacity SCl, SCl < SCh. Correspondingly, the internalWMN structure can be represented by a weighted graphΓ(M

∪P,L), where L denotes the set of wireless channels

between EDs in the WMN Γ. The initial radio-bandwidthprovisioning of the wireless channel luv ∈ L between two EDsu and v is recorded as B(luv). The pre-determined wireless-channel weight Pu(v) denotes the transmitting power requiredfor directly sending information flows from u to v. Obviously,a longer physical distance between two linked nodes u and vcorresponds to a larger Pu(v). The wireless channel luv existsin Γ if the actually assigned transmitting power r(u) ≥ Pu(v).In the PON, one optical fiber cable is reserved between anONU and the OLT, and it has several carriers. ba is the initialbandwidth provisioning of each carrier. Only one ED losses

efficiency during a time period, and all the EDs have the samefailure probability Pr. The failure of the wireless channel oroptical fiber cable is not within the scope of this paper.

As mentioned in subsection I-B, the virtual network isembedded onto the working graph of the most qualified WMN,and then an appropriate backup ED is chosen on anothergraph. Firstly, the virtual network—which is processed by thecollaborative edge computing in the working graph of oneWMN—can be represented as a 4-tuple model vn(s, ϕ, wb, c).s is the virtual node mapped on the working ED connected tothe ONU, such as the virtual node 3 mapped on the WMN’sworking graph in Fig. 3. ϕ denotes the set of virtual nodesmapped onto the working EDs deployed at wireless routers,such as virtual nodes 1 and 2 mapped on the WMN’s workinggraph in Fig. 3. Since all the EDs collect information flows tocompute, we assume virtual nodes have the same requirementof computing resources c (c < SCl < SCh) to processinformation flows, and the virtual link between a pair of virtualnodes consumes the same radio bandwidth wb, wb < ba. Next,to make the survivable VNE operation for the same virtualnetwork—represented as a 2-tuple model vn(Ew(s, ϕ), c) thistime—on the backup graph. The virtual node s and the othervirtual nodes in the set ϕ are mapped onto the same backupED not included in the set Ew(s, ϕ). Here, Ew(s, ϕ) is theset of working EDs previously mapped by the virtual nodesin the 4-tuple model. Note that, since only one backup ED ischosen for the virtual network, it is not required to computethe backup path, thus eliminating wb in the 2-tuple model.

We list some important notations in the following.• n is the total number of WMNs in the front-end of the

WOBAN supporting smart cities;• M is the set of EDs connected to the same ONU in the

WMN;• P is the set of EDs deployed at wireless routers in the

WMN;• SCh is the initial computing capacity of the ONU-level

ED;• SCl is the initial computing capacity of the ED deployed

at each wireless router, and SCl < SCh;• Γ is the internal-structure graph of the WMN;• L is the set of wireless channels in the WMN;• luv is the wireless channel between two EDs u and v,

and luv ∈ L;• B(luv) is the initial radio-bandwidth provisioning of the

wireless channel luv;• RB(luv) is the residual available radio bandwidth of the

wireless channel luv , and RB(luv) ≤ B(luv);• Pu(v) is the transmitting power required for directly

sending information flows from u to v;• r(u) is the actual transmitting power assigned for the ED

u;• ba is the initial bandwidth provisioning of each carrier

on the optical fiber cable;• Pr is the failure probability of each ED;• vn is the virtual network;• s is the virtual node of vn, and it can be mapped on the

working ONU-level ED;• ϕ is the set of the virtual nodes in vn, and these virtual

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nodes can be mapped onto the working EDs deployed atwireless routers;

• wb is the radio bandwidth consumed for the wirelesschannel between two mapped working EDs serving the4-tuple mode of vn, and wb < ba;

• c is the computing resource consumed for the work-ing/backup ED serving vn, and (c < SCl < SCh);

• Ew(s, ϕ) is the set of working EDs mapped by the virtualnodes in the 4-tuple model of vn;

• k is the number of EDs that should have backup-resourceprovisioning in the WMN, and |M | < k ≤ |M

∪P |;

• f is the scaling factor, i.e., the percentage of the initialcomputing resource occupied by the backup provisioning,and 0.1 ≤ f ≤ 0.5;

• Γ∗ is the most qualified WMN;• Γ∗

w is the working graph of Γ∗;• Γ∗

b is the backup graph of Γ∗;• TPΓ∗

wis the transmitting power assigned for the working

EDs serving the virtual network on Γ∗w;

• SDΓ∗b

is the maximal sharing degree of the backup EDon Γ∗

b ;• SD(g ∈ Γ∗

b) is the maximal sharing degree of the backupED g on Γ∗

b ;• N1 is the number of successfully embedded virtual net-

works processed by front-end WMNs;• TP is the total transmitting power assigned for working

EDs;• αi

Γ∗w

is 1 if the ith virtual network is successfully em-bedded onto Γ∗

w, otherwise, it is 0;• SD is the maximal sharing degree of backup resource;• αi

Γ∗b

is 1 if the ith virtual network is successfully embed-ded onto Γ∗

b , otherwise, it is 0;• N2 is the number of virtual networks that can be suc-

cessfully processed by the PON backhaul;• N is the total number of virtual networks in the WOBAN

supporting smart cities.

B. Overview of our design framework

To give a clear description for the problem objective pre-sented later, we firstly introduce the design framework shownby Fig. 4 in general.

We divide the internal-structure Γ of each WMN into twosubparts: working and backup graphs, i.e., Γw and Γb. Sincethe initial computing capacity of one ED is the sum ofworking and backup subparts, we only need to determine theprovisioning of backup resource for Γb, and the residual is theworking assignment of Γw. To save the resource consumptionon Γb, only k (|M | < k ≤ |M

∪P |) EDs should have

backup-resource provisioning. k is determined by the WMN’sreliability function. Specifically, on Γb, |M | ONU-level EDsmust have backup-resource provisioning, and if the WMN’sreliability has been well guaranteed by k backup EDs, it isunnecessary for the residual (|M

∪P | − k) wireless routers’

EDs to offer backup resource.After deciding the value of k according to the WMN’s

reliability function, we perform the backup-ED location on Γb.For example, in Fig. 5(a) where SCh = 20 and SCl = 10,

*Γ

*Γ

Fig. 4. Our design framework.

Fig. 5. Selection and location of backup EDs.

|M | = 3 backup ONU-level EDs are considered on Γb, andeach of them provides 10 units of backup resources (thescaling factor fh = 10

SCh= 0.5). We continue to select the

other (k − |M |) = 6 − 3 = 3 backup EDs nearest to theseONU-level EDs on Γb, as shown in Fig. 5(b). In Fig. 5(b),each wireless router’s backup ED offers 5 units of computingresources (the scaling factor fl = 5

SCl= 0.5). We assume

fh = fl = f .Next, we embed each virtual network onto the most qual-

ified WMN Γ∗ through consuming the reasonable amountof assigned transmitting power while ensuring the maximalsharing degree of backup resource. The transmitting poweris assigned for the working EDs serving the current virtualnetwork. The maximal sharing degree denotes the maximalnumber of virtual nodes embedded onto the same backup ED.These virtual nodes come from the current and previouslyembedded virtual networks. Since only one backup ED ischosen for the virtual network, it is not required to computethe backup path.

If the single WMN has the local bottleneck, the backupED coming from the different WMN will be considered viathe PON backhaul. It should be noted that the link mappingbecomes unnecessary for the above survivable VNE operationbecause there is a constant path between the bottleneck WMNand another WMN owning the backup ED. As an example ofFig. 3, one path (green dotted line) is established and remainunchanged between the bottleneck WMN 2 and the ED g inWMN 3. Correspondingly, when we perform the survivableVNE procedure through the PON backhaul, the optimizationobjective is to minimize the number of consumed backupcarriers along fixed paths.

In summary, the green survivability is reflected from twoaspects: 1) we minimize the transmitting power assigned forworking EDs when we perform the local WMN embedding; 2)

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we minimize the number of consumed backup carriers whenwe perform the PON-backhaul embedding.

III. PROBLEM FORMULATION AND ANALYSIS

Based on the design framework, we mathematically formu-late our optimization problem in the following, and then theproblem bounds are also deduced.

A. Problem description

Given the most qualified WMN Γ∗, we first embed thecurrent virtual network vn(s, ϕ, wb, c) onto the working graphΓ∗w: 1) on Γ∗

w, we select an appropriate working ONU-levelED m ∈ M , so as to hold the virtual node s, i.e., themapping solution m = F (s) can be found; 2) we alsochoose a set of appropriate working EDs deployed at wirelessrouters, i.e., p ⊂ P , so as to hold the virtual nodes in ϕ.In other words, the mapping solution p = F (ϕ) can befound; 3) all mapped working EDs have available computingresource not smaller than c; 4) as to the link mapping, allthe wireless channels—traversed by the physical working pathPw—have available radio bandwidth not smaller than wb, i.e.,∀luv ∈ Pw, RB(luv) ≥ wb; 5) finally, after mapping thecurrent virtual network onto Γ∗

w, the assigned total transmittingpower TPΓ∗

w=

∑u∈Γ∗

wr(u).

Next, the current virtual network’s model is changed intovn(Ew(s, ϕ), c), and it is further embedded onto the backupgraph Γ∗

b where the location of k backup EDs has beendetermined: 1) eliminate the backup EDs included in Ew(s, ϕ)from k candidates, and choose only one backup ED g alongwith the highest sharing degree from the residual candidates.Then, the mapping solution g = F (s, ϕ) can be found;2) the mapped backup ED g has the available computingresource not smaller than c; 3) finally, after mapping thecurrent virtual network onto Γ∗

b , the maximal sharing degreeSDΓ∗

b= SD(g ∈ Γ∗

b). Here, SD(g ∈ Γ∗b) is the number of

virtual nodes that have been mapped onto the backup ED g.

B. Objective function

Let N1 record the number of successfully embedded vir-tual networks processed by front-end WMNs, then the to-tal transmitting power assigned for working EDs, TP =∑N1

i=1

∑nΓ∗w=1 α

iΓ∗w× TPΓ∗

w, where αi

Γ∗w

is 1 if the ith virtualnetwork is successfully embedded onto Γ∗

w; otherwise, it is0. On the other hand, the maximal sharing degree of backupresource, SD = argmaxi∈[1,N1],Γ∗

b∈[1,n]αiΓ∗b×SD(Γ∗

b), whereαiΓ∗b

is 1 if the ith virtual network is successfully embeddedonto Γ∗

b ; otherwise, it is 0.If no WMN bottleneck occurs, without using the PON

backhaul, we only need to embed each virtual network ontothe most qualified WMN through consuming the reasonableamount of transmitting power assigned for working EDs whileensuring the maximal sharing degree of backup resource. Theminimal assigned transmitting power represents the optimaleffect of greening the network, while the maximal sharingdegree reflects the best utilization of backup resource. Then,the comprehensive objective function is given below.

min

∑Nmax1

i=1

∑nΓ∗w=1 α

iΓ∗w× TPΓ∗

w

argmaxi∈[1,N1=N ],Γ∗b∈[1,n]α

iΓ∗b× SD(Γ∗

b), (1)

where N is the total number of virtual networks in theWOBAN supporting smart cities.

If there is the WMN bottleneck, the virtual networks arefirstly embedded to WMNs, and then residual virtual networksthat cannot be served by local WMNs will be embedded viathe PON backhaul. Thus, under this case, a more complexoptimization objective function is:

min

∑Nmax1

i=1

∑nΓ∗w=1 α

iΓ∗w× TPΓ∗

w

argmaxi∈[1,Nmax1 ],Γ∗

b∈[1,n]αiΓ∗b× SD(Γ∗

b)+⌈N

max2 × wb

ba⌉,

(2)where Nmax

1 and Nmax2 mean that we should serve virtual

networks as many as possible, and (Nmax1 +Nmax

2 ) ≤ N .Correspondingly, the first part of Eq. (2) is the optimization

objective for the local WMN embedding, i.e., Eq. (1), whilethe second part of Eq. (2) is the optimization objective for thePON-backhaul embedding.

The optimization objective for the PON-backhaul embed-ding is to minimize the number of consumed backup carriers.If the survivability cannot be well guaranteed by the singleWMN, the backup ONU-level ED coming from another WM-N, e.g., the ED g in WMN 3 of Fig. 3, will be considered.Since a different working ONU-level ED should also be foundin the new WMN so as to hold (1 + |ϕ|) virtual nodes ofthe virtual network vn(s, ϕ, wb, c), the ONU-level backup EDwill provide c · (1+ |ϕ|) units of computing resources. Let N2

record the number of virtual networks that can be successfullyprocessed by the PON backhaul, then the number of consumedoptical fiber cables is ⌈ N2

f·SChc·(1+|ϕ|)

⌉. Here, f ·SCh

c·(1+|ϕ|) denotes the

maximal number of virtual networks served by each opticalfiber cable. Since the maximal number of backup carriers

consumed by each optical fiber cable is ⌈(

f·SChc·(1+|ϕ|) )×wb

ba ⌉, thetotal number of consumed backup carriers serving N2 virtual

networks, ⌈ N2f·SCh

c·(1+|ϕ|)⌉ · ⌈

(f·SCh

c·(1+|ϕ|) )×wb

ba ⌉ = ⌈N2×wbba ⌉.

C. Bound analysis

First of all, we deduce the bound of Eq. (1) if no WMN’slocal bottleneck occurs. Under this case, the total assignedtransmitting power, i.e., the molecule of Eq. (1), becomesa constant TPconst(N

max1 ) =

∑Nmax1

i=1

∑nΓ∗w=1 α

iΓ∗w× TPΓ∗

w.

Therefore, the corresponding bound can be obtained if we havethe maximal sharing degree SDmax and a constant Nmax

1 .Thus, if no WMN’s local bottleneck occurs, the problem boundPB = Nmax

1 + SDmax.As mentioned in subsection II-B, within each WMN, (k −

|M |) wireless routers’ EDs have local backup-resource provi-sioning. In other words, for each WMN, (k − |M |) wirelessrouters’ EDs provide [(1−f)·SCl] units of working resources,and residual (|M

∪P | − k) wireless routers’ EDs offer SCl

units of working resources. We assume that these working EDsare replaced by a single one owning the aggregated working

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Algorithm 1 Pseudo code of our GSVNE

1: ∀Γ ∈ [1, n]: Pr(k)Γ ← (1− Pr)k × (Pr)

|P |−k;2: ∀Γ ∈ [1, n]: k ← Pr(k)Γ ≥ Prmax;3: for Γ = 1, 2, ..., n do4: k ← k − |M |;5: Update the set of located backup EDs: Φ← Φ+M ;6: while k! = 0 do7: for u ∈M do8: for v ∈ P do9: if minhop(u, v) ≤ h then

10: Φ← Φ+ {v};11: k ← k − 1;12: end if13: end for14: end for15: end while16: end for17: for Γb = 1, 2, ..., n do18: ∀u ∈M : SCb

h ← f · SCh;19: ∀v ∈ Φ

∩P : SCb

l ← f · SCl;20: ∀v /∈ Φ and v ∈ P : SCb

l ← 0;21: end for22: for Γw = 1, 2, ..., n do23: ∀u ∈M : SCw

h ← (1− f) · SCh;24: ∀v ∈ P : SCw

l ← SCl − SCbl ;

25: end for26: Initialize ℵ ← 0, W ← 0, SD ← 0, N1 ← 0, N2 ← 0;27: Initialize δ ← {vni|i ∈ [1, N ]};28: while δ ̸= Null do29: vni ← δ.top();30: for Γ = 1, 2, ..., n do31: Γw ← {RB(luv) ≥ wb, SC(u)w ≥ c, (u, v) ∈ Γw};

/*SC(u)w: available working resource of the ED u*/32: ∀Γw: Pu(v) → Pu(v) − argmin{Pu(x), (u, x) ∈

Γw};33: Γw ← {Pu(v) = 0};34: Γb ← {SC(u)b ≥ c, u ∈ Γb};

/*SC(u)b: available backup resource of the ED u*/35: end for36: Determine the most qualified WMN Γ∗: SD(Γ∗

b) ←argmax{SD(Γb)|Γb ∈ [1, n]}, and Γ∗

w is available;37: if Γ∗ can be found then38: Perform the corresponding resource allocation and

update SD;39: N1 ← N1 + 1;40: else41: if the available ONU-level ED g coming from the

different WMN can be found then42: ∀g : SCb

h ← SCbh − c · (1 + |ϕ|);

43: N2 ← N2 + 1;44: Update SD;45: else46: ℵ ← ℵ+ 1;47: end if48: end if49: δ.pop();50: end while51: Return W ← wb·N2

ba , ℵ.

resource [(k− |M |) · [(1− f) ·SCl] + (|M∪P | − k) ·SCl in

each WMN. Since |ϕ| virtual nodes of each virtual networkneed to be mapped onto wireless routers’ working EDs, themaximal number of virtual networks processed by front-endWMNs can be computed as follows.

Nmax1 =

n · [(k − |M |) · (1− f) · SCl + (|M∪

P | − k) · SCl]

c · |ϕ|.

(3)As the maximal number of virtual nodes embedded onto

the same backup ED, SDmax = ⌊ f ·SCh

c ⌋ · (1+ |ϕ|). Here, thenotation ⌊ f ·SCh

c ⌋ represents the maximal number of virtualnetworks that can be embedded on one single backup ONU-level ED. Note that, all the (1 + |ϕ|) virtual nodes of eachvirtual network share the same backup ED with consumingonly c units of computing resources.

Next, we deduce the bound of Eq. (2) if we utilize thePON backhaul. Given Nmax

1 determined by Eq. (3), we haveN ′

2 = N − Nmax1 virtual networks that will be processed

through the PON backhaul. Because N2 ≤ N ′2, here N2 is

the actual number of virtual networks prossed by the PONbackhaul, we have Nmax

2 = N ′2. Thus, the objective function

Eq. (2) is simplified as min TPconst(Nmax1 ) + ⌈N

′2×wbba ⌉.

Intuitively, the optimal bound for the number of consumedbackup carriers is Wbound = ⌈N

′2×wbba ⌉ = ⌈ (N−Nmax

1 )×wbba ⌉.

Proposition 1: The performance advantage brought by thePON backhaul becomes weak if the actual number of con-sumed backup carriers is less than Wbound.

Proof: If some virtual networks still cannot be embeddedthrough the PON backhaul, N2 < N ′

2. Then, the actual numberof consumed backup carriers W = ⌈N2×wb

ba ⌉ < ⌈N′2×wbba ⌉ =

Wbound. Therefore, the performance advantage brought by thePON backhaul deteriorates if W < Wbound. �

IV. HEURISTIC ALGORITHM

In this section, we describe our algorithm named as GreenSurvivable VNE for collaborative edge computing in smartcities (GSVNE) relying on the WOBAN, and then we analyzethe algorithm complexity.

A. Algorithm description

The pseudo code of our GSVNE is given in Algorithm 1.The corresponding procedure is detailed as follows.

Step 1: Initialize the information about the WOBAN andvirtual networks, based on the network model mentioned insubsection II-A.

Step 2: Backup-ED selection. As previously discussed, onlyk EDs should have local backup-resource provisioning at eachWMN, and k is determined by the WMN’s reliability function,∀Γ ∈ [1, n] : Pr(k)Γ = (1− Pr)

k × (Pr)(|M

∪P |−k). Here,

the ED-failure probability Pr < 0.5. Then, a bigger valueof k, i.e., deploying more backup EDs, results in a higherWMN’s reliability. Given the acceptable WMN’s reliabilityPrmax ≤ Pr(k)Γ, ∀Γ ∈ [1, n], an appropriate value of k canbe decided. (line 1-2 in Algorithm 1)

Step 3: Backup-ED location. In the backup graph ofeach WMN, in addition to |M | ONU-level EDs, the residual

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(k−|M |) wireless routers’ EDs nearest to ONU-level EDs arealso located. Thus, ∀u ∈ M, v ∈ P : minhop(u, v) ≤ h.Here, h is the maximal number of physical hops betweenthe geographical locations of the ONU-level ED and anotherwireless router’s one. As illustrated by Fig. 5(b) where h = 1,only three wireless routers’ EDs—that require one physicalhop to arrive at the ONU-level ED—can offer backup resource.Six backup EDs are located in Fig. 5(b), but it is not enoughto guarantee the WMN reliability if k = 9. As shown byFig. 6, six wireless routers’ EDs—that require at least twophysical hops to arrive at the ONU-level ED—have localbackup-resource provisioning. Then, the condition k = 9 issatisfied when h = 2. Obviously, we increase the value of huntil all k backup EDs are located. (line 3-16 in Algorithm 1)

Step 4: Resource division. For the ONU-level ED, given thescaling factor f , then the initial backup-resource provisioningSCb

h = f · SCh, while the residual SCwh = (1 − f) · SCh

is the working assignment. For the located ED deployed atthe wireless router, the initial backup-resource provisioningSCb

l = f · SCl, while the residual SCwl = (1 − f) · SCl

is the working assignment. For the unlocated ED deployed atthe wireless router, SCb

l = 0 and SCwl = SCl. (line 17-25 in

Algorithm 1)Step 5: Determine the most qualified WMN Γ∗ to serve

the virtual network one-by-one. As to the current virtualnetwork, for each WMN Γ, we delete the vertexes that haveavailable computing capacity lower than c on Γw and Γb,as well as delete the wireless channels that have availableradio bandwidth lower than wb on Γw. Furthermore, for theupdated Γw of each WMN, we make the following graph-cutting operation. Update the wireless-channel weight of Γw:Pu(v) → Pu(v) − argmin{Pu(x), (u, x) ∈ Γw}. Here,argmin{Pu(x), (u, x) ∈ Γw} is the minimal weight amongall outgoing wireless channels of the vertex u. For example,the weights of outgoing wireless channels (b, c) and (b, d)are 7 and 4, respectively. Thus, we have min{Pb(x), (b, x) ∈Γw} = 4; we then update the weights of (b, c) and (b, d) to3 and 0, respectively. After updating all wireless channels’weights, we reserve wireless channels whose weight is 0, e.g.,(b, d) in the example above, thus reducing the total assignedtransmitting power. Finally, the most qualified WMN Γ∗ isdetermined for the current virtual network if the correspondingavailable backup graph Γ∗

b has the maximal sharing degreeSD(Γ∗

b), and meanwhile, the working graph Γ∗w is also

available. (line 29-39 in Algorithm 1)

B. Complexity analysis

As shown by lines 3-16 in Algorithm 1, the maximalnumber of loop operations owned by the backup-ED locationis (n×k×|M |×|P |). As shown by lines 28-50 in Algorithm1, the maximal number of loop operations owned by thefollowing VNE operation is (n×N ).

V. SIMULATION RESULTS AND DISCUSSIONS

In this section, we firstly introduce the real test WOBANtopology supporting the smart university community andimportant simulation settings based on this real trace. We

Fig. 6. Location of backup EDs when h = 2 and k = 9.

Fig. 7. Real test topology for simulations.

then analyze the performance matrices of our approach undervarious conditions.

A. Real test topology and parameter settings

Our real test WOBAN topology is the UC Davis campusmap supporting the smart university community, and it has 3front-end WMNs. Note that, in the real simulation scenariomentioned in [22], at most 5 wireless routers form a front-end WMN, then only 5 × 3 = 15 EDs are deployed in theentire campus WOBAN. Taking the future ED-deploymentplan into account, in each WMN of our real test WOBANtopology shown by Fig. 7, we have 3 EDs deployed atONUs and 6 wireless routers along with local EDs (i.e.,n = 3, |M | = 3, |P | = 6). To ensure the clarity of Fig.7, some wireless channels are not shown. We can see that,all EDs are deployed in real locations, and a longer physicaldistance between two linked real places u and v correspondsto a larger pre-determined transmitting-power weight Pu(v).The initial radio bandwidth per wireless channel is assumed tobe rich. For the virtual network, |ϕ| = 2, c = 1 and wb = 1.We let |ϕ| = 2 to ensure that the total number of virtual nodesowned by the virtual network cannot exceed the total numberof WMNs, i.e., (1+|ϕ|) ≤ n. The wavelength capacity ba = 6,which is one-half of a small wavelength granularity OC-12.The Prmax is pre-given so that the WMN’s reliability can bealways guaranteed when h = 2 and k = 9.

Given SCl = 20, then SCh = 100 because we wantto ensure the condition SCh · fmin = SCl · fmax. Here,fmin = 0.1 and fmax = 0.5. In other words, we list all rep-resentative values of scaling factors, which covers the intervalof [0.5, 0.3, 0.1]. The scaling factor denotes the percentageof the initial computing resource occupied by the backupprovisioning. Therefore, the percentage value 0.5 means thateach ED provides equal amount of resources for workingand backup services; the percentage value 0.3 means thatthe working-resource provisioning plays a more dominatingrole, while the percentage value 0.1 means that the initial

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0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.5 (90) 0.4 (108) 0.3 (126)

Without graph cutting

Graph cutting

To

toa

l tr

an

smit

tin

g p

ow

er

Scaling factor (!"#$%)

Fig. 8. Total transmitting power.

border line:

N1max=90

0

20

40

60

80

100

120

140

160

180

200

90 100 110 120 130 140 150 160 170 180 190 200 210

GSVNE (f=0.5)

GSVNE without backhaul (f=0.5)

To

toa

l n

um

be

ro

f su

cce

ssfu

lly

em

be

dd

ed

v

irtu

al n

etw

ork

s

Total number of virtual networks in the system N

Fig. 9. Total number of successfully embedded virtual networks when f =0.5.

backup-resource provisioning has been very limited. We selectthe optimal scaling factor from the interval [0.5, 0.3, 0.1]according to the convergence between the actual maximalsharing degree of backup resource and the correspondingupper bound. The maximal sharing degree of backup resourcesrecords the maximal number of virtual nodes that have beenmapped onto the same backup ED. The upper bound of thesharing degree has been discussed behind Eq. (3). Hence, thehigher convergence ratio means that the corresponding scalingfactor is more appropriate because the backup resource can bewell utilized. In addition, we also evaluate the performancematrices including the number of successfully embedded vir-tual networks (N1+N2), and the actual number of consumedbackup carriers W .

border line:

SDmax

=150

0

20

40

60

80

100

120

140

160

90 100 110 120 130 140 150 160 170 180 190 200 210

SDmax (f=0.5)

GSVNE (f=0.5)

GSVNE without backhaul

(f=0.5)

Ma

xim

al sh

ari

ng

de

gre

e

Total number of virtual networks in the system N

Fig. 10. Maximal sharing degree when f = 0.5.

0

5

10

15

20

25

90 100 110 120 130 140 150 160 170 180 190 200 210

W GSVNE (f=0.5)

Wbound (f=0.5)

Nu

mb

er

of

con

sum

ed

ba

cku

p c

arr

iers

Total number of virtual networks in the system N

Fig. 11. Number of consumed backup carriers when f = 0.5.

5200

5400

5600

5800

6000

6200

6400

6600

6800

7000

110 120 130 140 150

GSVNE without backhaul

GSVNE

Sim

ula

tio

n t

ime

(m

s)

Total number of virtual networks in the system

Fig. 12. Runtime when f = 0.5.

B. Simulation results of total transmitting power

First, we evaluate the effectiveness of serving virtual net-works trough consuming an expected amount of the trans-mitting power assigned for working EDs. Assuming that allthe virtual networks can be successfully embedded onto front-end WMNs, we compare the consumed transmitting powerbetween our solution and the benchmark without consider-ing graph cutting. Satisfying the aforementioned assumptioncan avoid an unfair situation where few virtual networks—successfully embedded with bad use of radio resources—consume low transmitting power. For this end, we deter-mine the maximum number of successfully embedded virtualnetworks through front-end WMNs based on Eq. (3), i.e.,Nmax

1 = n·[(k−|M |)·(1−f)·SCl+(|M∪

P |−k)·SCl]c·|ϕ| = 90 when

f = 0.5, Nmax1 = 108 when f = 0.4, and Nmax

1 = 126 whenf = 0.3 (see the horizontal axis of Fig. 8). The total transmit-ting power is evaluated when all Nmax

1 virtual networks canbe successfully processed by front-end WMNs under the casesabove. Simulation results show that: 1) the total transmittingpower follows a rising trend with the increasing number ofsuccessfully embedded virtual networks, which is rational; 2)the graph cutting utilized in our solution effectively reducesthe total transmitting power with the average improvementratio of 11% over the benchmark without considering thegraph cutting. This is because that, using the graph cutting,we simplify the working graph for each WMN by reservingwireless channels along with lower weights.

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C. Simulation results when f = 0.5

First of all, in Fig. 9 where f = 0.5, we compare ourGSVNE solution and the benchmark that neglects the PONbackhaul, in terms of the total number of successfully embed-ded virtual networks, i.e., (N1+N2) = (N−ℵ). Here, the totalnumber of virtual networks in the system N starts from Nmax

1

determined in Eq. (3), i.e., N starts from Nmax1 = 90 when

f = 0.5. Thus, the virtual networks impossibly embeddedby front-end WMNs will emerge if N > Nmax

1 = 90,and then the PON backhaul will be invoked by our GSVNEsolution. We can see that, without using the PON backhaul, thebenchmark (GSVNE without the PON backhaul) always servesNmax

1 virtual networks via front-end WMNs along the borderline, due to the existence of the WMN’s local bottleneck.However, our GSVNE solution can further guarantee thesurvivability of more virtual networks because the backupONU-level ED coming from the available WMN still can bechosen via the PON backhaul. Moreover, the improvementratio brought by our GSVNE follows a rising trend with anincreasing N , and finally changes to stabilize after N = 190.The performance advantage peaks after N = 190, since theresource of the ONU-level backup ED is not unlimited afterall. Finally, the average improvement ratio over the benchmarkis approximately 69%.

Next, in Fig. 10 where f = 0.5, the maximal sharingdegree of backup resource is compared among the theoreticalupper bound, our GSVNE solution and the benchmark thatneglects the PON backhaul. The theoretical upper boundSDmax = 150 when f = 0.5. We can see that, the sharingdegree of the benchmark is always 30 which is much lowerthan the upper bound. It means that the usage of backupresource is not well maintained in the benchmark without thePON backhaul, because a relevant portion of the redundantbackup resource provided by ONU-level EDs becomes wasted.That well explains why the benchmark always serves at mostNmax

1 virtual networks in Fig. 9. However, by using thePON backhaul, the usage of backup resource can be furtherimproved in ONU-level EDs, thus resulting in the high sharingdegree which well matches the upper bound with the averageconvergence radio of 87%. Initially, the maximal sharingdegree does not quickly approach the border line becausethe PON backhaul is not urgently necessary when there areless virtual networks in the system. After N = 110, themaximal sharing degree of our solution tends to be stable,which well explains why the performance advantage broughtby our GSVNE peaks after N = 190 in Fig. 9.

Furthermore, given f = 0.5 in Fig. 11, we compare thenumber of consumed backup carriers between our GSVNEand the optimal bound wbound. Similar to Fig. 9, the numberof virtual networks N starts from Nmax

1 = 90 so that the PONbackhaul can be triggered to consume backup carriers if N >Nmax

1 . We can see that the number of backup carriers W usedby our GSVNE becomes larger with the increasing value ofN , which is rational. When N = [90, 180], the converge ratiobetween W and the optimal bound Wbound is 100% becausethe PON backhaul takes its full advantage of guaranteeingmore virtual networks’ survivability. However, after N = 190,

W becomes lower than the optimal bound. This means thatthe advantage brought by the PON backhaul has peaked andbecame increasingly weak when a high N continues to followa rising trend. This phenomenon has been demonstrated byProposition 1 mentioned in subsection III-C. In summary, theaverage convergence ratio is promisingly 97%.

Finally, given f = 0.5 in Fig. 12, we evaluate the runtimefor our GSVNE and the benchmark that neglects the PONbackhaul, on the computer configured with an Intel Core i5.Here, we let N starts from 110 > Nmax

1 = 90 so thatwe evaluate the running time when the PON backhaul isinvoked by our solution. The simulation results of Fig. 12show that the runtime follows a rising trend with the increasingnumber of virtual networks in the system, which is rational.When N becomes high, the runtime of our GSVNE is slightlyhigher than that of the benchmark, because the additional PONbackhaul could be triggered. Moreover, the maximal runtimeis approximately 7 seconds, which is acceptable.

D. Simulation results when f = 0.3

First of all, in Fig. 13 where f = 0.3, we compare ourGSVNE solution and the benchmark that neglects the PONbackhaul, in terms of the total number of successfully embed-ded virtual networks. Here, N starts from 125 (Nmax

1 =126when f = 0.3). Thus, the virtual networks impossibly em-bedded by front-end WMNs will emerge if N > Nmax

1 , andthen the PON backhaul will be invoked by our GSVNE. Wecan see that, with the help of the PON backhaul, our GSVNEstill guarantees the survivability of the more virtual networkscompared with the benchmark, and the corresponding averageimprovement ratio is 30%.

Next, in Fig. 14 where f = 0.3, the maximal sharing degreeof backup resource is compared among the theoretical upperbound SDmax = 90, our GSVNE solution and the benchmarkthat neglects the PON backhaul. The maximal sharing degreeof the benchmark is always 30 where a relevant portion ofthe redundant backup resource provided by ONU-level EDsbecomes wasted. However, by using the PON backhaul, theusage of backup resource can be further improved in ONU-level EDs, thus resulting in the high sharing degree which wellmatches the upper bound with the average convergence radioof 92%. It is worth noting that, after N = 145, the maximalsharing degree of our solution tends to be stable, and it exactlymatches the upper bound with the convergence ratio of 100%.But when f = 0.5 in Fig. 10, the maximal sharing degree isonly close to but never exactly matches the upper bound. Insummary, the optimal scaling factor should be f = 0.3.

Finally, given f = 0.3 in Fig. 15, we compare the numberof consumed backup carriers between our GSVNE and theoptimal bound Wbound. When N = [135, 175], W exactlymatches the optimal bound Wbound with the convergence ratioof 100%. However, after N = 175, W becomes lower thanthe optimal bound, then the advantage brought by the PONbackhaul has peaked and became increasingly weak when ahigh N continues to follow a rising trend. In addition, theaverage convergence ratio is 91%, which well demonstratesthe optimality of our algorithm.

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border line:

N1max=126

0

20

40

60

80

100

120

140

160

180

200

125 135 145 155 165 175 185 195 205

GSVNE (f=0.3)

GSVNE without backhaul (f=0.3)

To

toa

l n

um

be

ro

f su

cce

ssfu

lly

em

be

dd

ed

v

irtu

al n

etw

ork

s

Total number of virtual networks in the system N

Fig. 13. Total number of successfully embedded virtual networks whenf = 0.3.

!"#$%# &'(%)

SDmax

=*+

+

,+

-+

.+

/+

0+

1+

2+

3+

*+

,++

,-0 ,.0 ,/0 ,00 ,10 ,20 ,30 ,*0 -+0

45678 9:;+<.=

>4?@A 9:;+<.=

>4?@A B'CD"EC !7FGD7E&

9:;+<.=

H7

8'6

7& I

D7

#'(

J $

%J

#%%

K"C7& (E6!%# ": L'#CE7& (%CB"#GI '( CD% IMIC%6 N

Fig. 14. Maximal sharing degree when f = 0.3.

0

2

4

6

8

10

12

14

16

135 145 155 165 175 185 195 205

GSVNE (f=0.3)

Wbound (f=0.3)

Nu

mb

er

of

con

sum

ed

ba

cku

p c

arr

iers

Total number of virtual networks in the system N

Fig. 15. Number of consumed backup carriers when f = 0.3.

TABLE INUMBER OF SUCCESSFULLY EMBEDDED VIRTUAL NETWORKS WHEN

f = 0.1

N 175 185 195 205

Nmax1 162 162 162 162

Our GSVNE 68 68 68 68GSVNE without the PON backhaul 68 68 68 68

E. Simulation results when f = 0.1

In this subsection, we compare the number of successfullyembedded virtual networks between our GSVNE and thebenchmark that neglects the PON backhaul when f = 0.1.The simulation results in Table I show that the initial backup-

resource provisioning becomes very limited when f = 0.1.Therefore, even with rich working resource, whether ourGSVNE or the benchmark, there are far less than Nmax

1

virtual networks which have well guaranteed survivability.Another important reason is that the ONU-level backup EDcannot normally work due to very limited initial backup-resource provisioning, thus making the PON backhaul becomemeaningless. This phenomenon also demonstrates that theoptimal scaling factor should be f = 0.3.

VI. RELATED WORK

Currently, in virtualization environment, the effectiveschemes against the single physical node failure have beenutilized for virtual topology mapping or Virtual NetworkEmbedding (VNE). In terms of virtual topology mapping: theauthors in [25] focused on single-node failure and developeda remove-node algorithm to map IP links on lightpaths insuch a way that the IP topology remains connected after thefailure of any node in the Wavelength Division Multiplexing(WDM) topology. However, this algorithm is only applied tovirtual topology mapping instead of VNE. As to the VNE,the authors in [26] first pointed out that protecting against thesingle node failure was very important for VNE because thisrealistic scenario affected virtual networks with a mapping s-panning over the disabled node. They designed a p-cycle-basedprotection technique that minimized the backup resourceswhile providing a full protection scheme against a single nodefailure. In [27], the authors developed three different IntegerLinear Programming (ILP) models to solve the problem withservice chaining while guaranteeing resiliency against single-node failure. However, these schemes are not directly appliedto WOBAN supporting smart cities.

VII. CONCLUSION AND FUTURE WORK

In this paper, a novel design framework has been proposedto perform the green survivable VNE for the collaborativeedge computing in the WOBAN supporting smart cities. Foreach WMN, an appropriate resource-division method has beenproposed to determine the number and geographical locationsof backup EDs by using the heuristic strategy. Next, the greensurvivable VNE has been made for as many virtual networks aspossible on front-end WMNs through consuming an expectedamount of transmitting power while ensuring the maximalsharing degree of backup resource. Once the WMN’s localbottleneck occurs, the ONU-level backup ED has been chosenvia the PON backhaul. Simulation results have demonstratedthat: 1) our design framework can successfully embed morevirtual networks compared with the benchmark that neglectsthe PON backhaul; 2) our algorithm based on the optimal scal-ing factor has shown a good convergence between the maximalsharing degree of backup resource and the theoretical upperbound. Moreover, a blind setting of the scaling factor mayresult in a bad algorithm performance; 3) the actual numberof consumed backup carriers has well matched the theoreticaloptimal bound derived by us, which have demonstrated thealgorithm’s optimality.

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On the other hand, we must point out another realisticscenario where multiple EDs in the shared risk group simul-taneously become disabled. For example, multiple EDs willsimultaneously loss efficiency if they are located in the sameurban area suffering from power outage. However, it is notour focus, but it is an interesting problem which requires usto consume more time to investigate it in the near future.

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Weigang Hou (M’13) received the Ph.D. degree ininformation and communication system from North-eastern University, Shenyang, China, in 2013. He iscurrently an associate professor with the school ofcomputer science and engineering in NortheasternUniversity of China. His interests are in the areaof optical network with traffic grooming, opticalnetwork with data center, and optical network onchip.

Zhaolong Ning (M’14) received the M.S. and Ph.D.degrees from Northeastern University, Shenyang,China. He was a Research Fellow at Kyushu Univer-sity, Japan. He is an associate professor in the Schoolof Software, Dalian University of Technology, Chi-na. His research interests include social computing,edge computing, and Internet of vehicles.

Lei Guo received the Ph.D. degree from the U-niversity of Electronic Science and Technology ofChina in 2006. He is a Professor with NortheasternUniversity, Shenyang, China. His current researchinterests include communication networks, opticalcommunications, and wireless communications.

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