Mobile Networks and Applicationshttps://doi.org/10.1007/s11036-018-1032-0

Contract-theoretic Approach for Delay Constrained Offloadingin Vehicular Edge Computing Networks

Ke Zhang1 · Yuming Mao1 · Supeng Leng1 · Sabita Maharjan2 · Alexey Vinel3 · Yan Zhang4

© Springer Science+Business Media, LLC, part of Springer Nature 2018

AbstractMobile Edge Computing (MEC) is a promising solution to improve vehicular services through offloading computationto cloud servers in close proximity to mobile vehicles. However, the self-interested nature together with the high mobilitycharacteristic of the vehicles make the design of the computation offloading scheme a significant challenge. In this paper,we propose a new Vehicular Edge Computing (VEC) framework to model the computation offloading process of the mobilevehicles running on a bidirectional road. Based on this framework, we adopt a contract theoretic approach to design optimaloffloading strategies for the VEC service provider, which maximize the revenue of the provider while enhancing the utilitiesof the vehicles. To further improve the utilization of the computing resources of the VEC servers, we incorporate task prioritydistinction as well as additional resource providing into the design of the offloading scheme, and propose an efficient VECserver selection and computing resource allocation algorithm. Numerical results indicate that our proposed schemes greatlyenhance the revenue of the VEC provider, and concurrently improve the utilization of cloud computing resources.

Keywords Vehicular network · Cloud · Mobile edge computing · Contract theory

1 Introduction

The advancements in Internet of Things (IoT) and wire-less technologies bring us pervasive smart devices suchas smart vehicles that can facilitate realizing many novel

� Ke Zhangzhangke@uestc.edu.cn

Yuming Maoymmao@uestc.edu.cn

Supeng Lengspleng@uestc.edu.cn

Sabita Maharjansabita@simula.no

Alexey Vinelalexey.vinel@hh.se

Yan Zhangyanzhang@ieee.org

1 School of Information and Communication Engineering,University of Electronic Science and Technology of China,Chengdu, China

2 Simula@OsloMet and University of Oslo, Oslo, Norway

3 Halmstad University, Halmstad, Sweden

4 Department of Informatics, University of Oslo, Oslo, Norway

and powerful mobile applications [1]. Some of such appli-cations include interactive infotainment, traffic cognitionand automatic driving [2–6]. However, with the drasti-cally increasing needs for resources along with stricterrequirements on performance for advanced vehicular appli-cations, supporting large computing intensive applica-tions is a big challenge for the resource constrainedvehicles.

To cope with the explosive application demands of thevehicular terminals, cloud-based vehicular networking iswidely considered as a promising approach to improvethe performance of the services [7–9]. In cloud-enablednetworks, computation processing and storage for vehicularapplications are provided as services on the cloud [10].Thus, the complicated computing tasks can either runlocally on the vehicular terminals or be offloaded to theremote computation cloud.

By leveraging rich computational resources from cloud,both the performance of the vehicular applications as wellas the resource utilization of the cloud can be improved.However, the long distance between mobile vehiclesand remote cloud servers may incur significant networktransmission delay as well as considerable overhead [11,12]. This latency and overhead seriously impairs theperformance of delay-sensitive mobile applications and the

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computation offloading efficiency. A new architecture andtechnology known as Mobile Edge Computing (MEC) hasemerged to address the above challenges, which pushescloud services to the edge of the radio network, and providesa cloud-based computation offloading in close proximity tothe mobile vehicular terminals [13].

Due to proximity to mobile vehicles, the network latencyaccessing to cloud computing services can be greatlyreduced, which enables MEC to provide fast interactiveresponse in the computation offloading service. However,compared to the traditional cloud servers located in thebackbone network with powerful computation platforms,MEC servers may suffer from resource limitation. Further-more, unlike handheld mobile devices that always moveslowly within a relatively small range, smart vehicles havea unique feature in terms of their high mobility [14]. Con-sidering the limited coverage area of each RoadSide Unit(RSU), a vehicle may pass by several RSUs within the delaytolerance time of its applications. In MEC systems, serversare always equipped with the RSUs. Thus, in order toimprove the computation offloading efficiency while ensur-ing the performance constraints, it is imperative to jointlyinvestigate MEC server selection strategies for offload-ing data transmission as well as the MEC cloud resourceallocation schemes.

Intuitively, mobile computations can be migrated effec-tively in MEC systems with well-designed offloading mech-anisms. However, in practice, MEC service is always pro-vided by operators, and vehicles should pay to use thisservice. Since vehicle users are self-interested and want tomaximize their own profit, it is unrealistic to assume thatthey follow the control instructions from the MEC serviceproviders unconditionally. This factor poses a significantchallenge on the design of an optimal offloading scheme.

To address this challenge, we turn to contract theory,which is a powerful framework from economics andmakes the rational trading participants act accordingto the contractual arrangements [15]. In this paper,we investigate the characteristics of edge computing invehicular cloud networks, and design an optimal contracttheoretic computation offloading scheme, which maximizesthe revenues gained by the cloud service providers. Themain contributions of this paper are listed below:

– We propose a new Vehicular Edge Computing (VEC)offloading framework, where both the computingresource capacity of the VEC servers and the high-speed mobility of vehicles are considered.

– We model the VEC offloading process with a con-tract theoretic approach, and design a contract-basedoffloading scheme, which maximizes the revenue of theVEC provider while also improving the utilities of thevehicles.

– To further improve the computing resource utilizationof the VEC servers while also ensuring the delayconstraints of the vehicular applications, we proposean efficient algorithm for VEC server selection andcomputing resource assignment.

The rest of the paper is organized as follows. In Section 2,we review related works. The system model is presented inSection 3. The contract-based VEC offloading schemes aredescribed in Section 4. In Section 5, we propose an effectivedelay-constrained VEC server selection and computingresource allocation algorithm. We present performanceevaluation in Section 6 and conclude the paper in Section 7.

2 Related work

Vehicular cloud networks, an integration of vehicularcommunication and mobile computing, possesses thepotential to handle massive computing in a flexible andvirtualized manner [16–18]. The authors in [19] formulatedthe computation resource allocation of a vehicular cloudcomputing system as a semi-Markov decision process, andproposed an optimal decision-making scheme to maximizethe expected reward. In [20], the authors introduced acollaborative traffic information sharing system, wheretraffic images provided by a vehicular cloud are utilizedto assist drivers for route planning and route decisions.The authors in [10] proposed a backoff-based wirelessresource scheduling method in mobile cloud computingnetworks, where the average queueing delay of themultiuser applications is minimized. The authors in [14]proposed a coalition game for resource management amongcloud service providers, where the resources of the cloud-enabled vehicular network are effectively utilized.

Compared with core-based cloud platform, MEC canprovide lower computing delay and higher data throughput,which makes it a promising cloud networking solution [21,23]. Driven by this fact, MEC has recently been explored forvarious applications. The authors in [24] formed a tree hier-archical distributed edge cloud server deployment, whichimproves the utilization of the cloud resources serving thepeak loads from mobile users. To optimize energy con-sumption of mobile devices while minimizing applicationlatency, the authors in [25] incorporated dynamic voltagescaling technology into partial computation offloading forMEC, and proposed a locally optimal algorithm with theunivariate search technique. In [26], the authors focused onthe tradeoff between the gain and the cost of live avatarsmigration, and proposed a profit maximization avatar place-ment scheme for the edge cloudlet networks. In [27], theauthors exploited fog computing and mobile edge comput-ing to detect abnormal or critical events, and demostrated

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that these technologies are helpful in improving the ser-vices readiness required in case of time-critical events. In[28], the authors utilized mobile edge computing to man-age smart grid data, where the large data sets generated byvarious smart grid devices are disseminated efficiently withthe aid of cloud mechanisms. In [29], the authors formu-lated edge computation offloading decision as multi-usergame, and designed a distributed algorithm to achieve aNash equilibrium.

Among the aforementioned studies, only [19] and[28] have taken into account the impacts of vehiclemobility on MEC server choosing and recently in operationmanagement. In addition, the effectiveness of incentive-based approaches in the design of MEC offloadingmechanisms has been ignored in these work. As theoffloading nodes are rational and self-interested, they willperform computation offloading in a way that maximizestheir revenues. The nodes may not follow the optimaloffloading strategies without any incentive. To improve theoffloading efficiency, an incentive-based MEC offloadingscheme is required.

Contract theory incentivizes two rational entities ina trading system to reach agreements, and has beenwidely applied in economic control, resource allocation andoperation management recently. For example, in [30], theauthors modeled the spectrum trading process in cognitiveradio networks as a monopoly market, and designed anoptimal quality-price contract, which maximizes the utilityof spectrum owners. Observing the dominant positionof content providers in publish-subscribe networks, theauthors in [31] adopted contract theory to optimize thedistribution strategies for the content delivery process. In[32], the authors proposed a contract theoretic approachfor motivating user equipments to participate in device-to-device communications in cellular networks. In [33],contract theory is introduced as a economic incentiveapproach for energy trade in the smart grid. However, noneof these work have incorporated contract-based strategiesinto the VEC offloading schemes.

Different from these studies, in this paper we concentrateon the computation offloading process in a vehicular edgecloud network and propose the optimal contract-basedoffloading schemes to improve the revenues of the cloudservice providers while guaranteeing the required delayconstraints.

3 Systemmodel

Figure 1 shows our proposed VEC network. We consider atwo-way road, which has M Road Side Units (RSUs). EachRSU is equipped with a VEC server. We denote the set ofthese VEC servers as M = {1, 2, ..., M}. The computation

resources of each VEC server are limited [34]. The amountof the computation resources for VEC server m is bm units,m ∈ M. All the RSUs and the VEC servers along theroad belong to the same service provider. The resources ofthe VEC servers together constitute a virtual computationresource pool, which is charged by the provider, along withthe wireless access of the vehicular terminals.

Due to the variation in transmission power and thewireless environment, the RSUs may have different wirelesscoverage areas [35]. Each vehicle accesses the RSU withthe strongest signal. Thus, the road can be divided into M

segments, whose length is {R1, R2, ..., RM}, respectively.The vehicles running within the mth segment can onlyaccess RSU m and offload their tasks to VEC server m.

We consider that there are Q1 and Q2 vehicles arrivingat the two ends of the road, respectively. All the vehiclesmove at a constant speed h, and have identical onboardcomputation resource, which is denoted as d0. Each vehiclehas a computation task, which is denoted as T ={d, tmax}. Here, d is the amount of computing resourcesrequired to accomplish the task, and tmax is the maximumallowed end-to-end latency for the task [36, 37]. Eachcomputation task can be accomplished either locally onthe vehicle or remotely on a VEC server through taskoffloading.

In our model, there are N types of computation tasks ofthese vehicles, whose resource requirements are denoted as{d1, d2, ..., dN }, respectively [38–40]. Thus, the tasks of thevehicular terminals can be presented as Ti = {di, t

maxi },

i ∈ N = {1, 2, ..., N}. Without loss of generality, weassume that d1 < d2 < ... < dN .

According to their computation task types, these vehiclescan be correspondingly classified into N types. Let γi bethe proportion of vehicles with task Ti in all the arrivingvehicles, and

∑Ni=1 γi = 1. Each vehicle knows its own

type. However, as the types of the vehicles are privateinformation of each vehicle, the computation offloadingservice provider may not be well aware of this information[41]. Thus, we can see that an information asymmetry hasoccurred between the service provider and the vehicles.Although the service provider can not accurately determinethe type of each vehicle, it can obtain the probabilitydistribution of the vehicle types through some statisticalinformation.

Both the service provider and the vehicles are rationaland self-interested [42]. Each vehicle can offload itscomputation task to a VEC server with payment to theservice provider. Thus, to maximize its revenue, the serviceprovider derives the optimal amount of the computationresources allocated to offload the tasks and determines thecorresponding payment. The information of these servicesis broadcasted to the vehicles running on the road incontract forms via wireless communication. According to

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Fig. 1 The computationoffloading in a cloud-basedvehicular network

the contract information, each vehicle offloads its task tomaximize its own utility.

4 Contract theoretic computation offloading

In this section, we first formulate the computationoffloading process as a contract problem. Then we derivethe optimal contract solutions, which maximize the utility ofthe VEC service provider while satisfying the requirementof the vehicles.

4.1 Contract problem formulation

As there are N types of vehicles according to theircomputation tasks, the provider needs to offer N kinds ofcontracts correspondingly. Let (qi, pi) denote the contractdesigned for the vehicle that belongs to type i (i ∈ N ).Here qi is the amount of computation resources provided bythe VEC servers for offloading the computation task from atype i vehicle. pi is the payment that type i vehicle shouldpay to the provider for using the offloading service.

Each vehicle can obtain the contract information throughthe wireless broadcast from the provider. After that, thevehicle chooses to accept the contract that brings maximalutility to it. Here we define the utility of a type i vehiclegained from offloading its task based on the contract (qi, pi)

as

Uiv(qi, pi) = λ

di

d0ln(αqi + β) + (1 − λ)e0qi − pi,

qi ≤ di, i ∈ N .(1)

In Eq. 1, the first item represents the utility of saving com-putation resource by task offloading. The utility is affectedby the original resource utilization di/d0. α and β are coef-ficients, and α > 0, β > 0. In the second item, e0 is theutility gained from saving energy for running a task on aremote unit computation resource. λ is the weight factor,and 0 < λ < 1. The inequality qi ≤ di ensures that theamount of the resources defined by the contract is less thanor equal to the total resources required by the task. LetG(di, qi) = λ

di

d0ln(αqi + β) + (1 − λ)e0qi . Then, Eq. 1

can be rewritten as

Uiv(qi, pi) = G(di, qi) − pi . (2)

As the vehicles are rational, they will not choose thecontract which brings negative utilities to them. Thisproperty is called Individual Rationality (IR), and can bemathematically expressed as Ui

v ≥ 0 (i ∈ N ). Besides thisproperty, according to the contract theory, a feasible contractshould satisfy the Incentive Compatible (IC) constraint [43].This constraint indicates that type i vehicles are incentivizedto choose the contract specifically designed for their owntype, but not the contracts of the others. The IC constraintcan be represented as Ui

v(qi, pi) ≥ Uiv(qj , pj ), i �= j ,

i, j ∈ N .The utility of the provider providing computation task

offloading service based on these contracts is defined as

USP = Q

N∑

i=1

γi(pi − cqi), (3)

where c is the cost for the VEC servers running acomputation task on a unit resource.

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Based on the utility functions of the vehicles andthe service provider while considering the IR and ICconstraints, the contract theoretic optimization problemof the computation offloading can be formulated asfollows,

max{pn,qn} U′SP =

N∑

n=1γn(pn − cqn)

s.t . C1 : G(di, qi) − pi ≥ 0, i ∈ NC2 : G(di, qi) − pi ≥ G(di, qj ) − pj

i �= j, i, j ∈ NC3 : 0 ≤ qi ≤ di, i ∈ N

. (4)

It is noteworthy that, compared to Eq. 3, Q is omitted inEq. 4, as this parameter does not affect the design of thecontracts.

4.2 Optimal contract design

As there are N(N + 3)/2 constraints, it may be complex tosolve Eq. 4, especially for a large N . Thus, to solve Eq. 4more efficiently, some constraints should be removed [44].In this subsection, we first present the steps to simplifythe optimization problem. Then, we propose an efficientalgorithm to get the optimal contract solutions.

Lemma 1 Monotonicity: Both the computation resourcesqi and the offloading payment pi of the feasible contract{qi, pi} designed for type i vehicles are monotonicallyincreasing in terms of i, i ∈ N , i.e., for contracts {qi, pi}and {qj , pj }, we have qi ≥ qj and pi ≥ pj , if and only ifi > j , i, j ∈ N .

Proof According to the IC constraints of type i and type j

vehicles, where i �= j and i, j ∈ N , we have

G(di, qi) − pi ≥ G(di, qj ) − pj , (5)

and

G(dj , qj ) − pj ≥ G(dj , qi) − pi . (6)

Adding Eqs. 5 and 6, we can get G(di, qi) + G(dj , qj ) ≥G(di, qj )+G(dj , qi). By substitutingG(·, ·), the inequationis equally changed to (di −dj ) ln(

αqi+βαqj +β

) ≥ 0. Given i > j ,according to the vehicle type definition, we have di > dj ,which implies that between the feasible contracts, qi ≥ qj

if i ≥ j . Next we will prove that qi ≥ qj should holdwhenever pi ≥ pj . Given the condition pi ≥ pj , accordingto Eq. 5, we have λ

di

d0ln(αqi + β) + (1 − λ)e0qi − pi ≥

λdi

d0ln(αqj + β) + (1 − λ)e0qj − pj . By rearranging the

inequation, we can get λ di

d0ln( αqi+β

αqj +β)+(1−λ)e0(qi −qj ) ≥

pi − pj ≥ 0. Due to 0 < λ < 1, we can get qi ≥ qj .Similarly, the inequality pi ≥ pj can be proved under thecondition qi ≥ qj .

Lemma 2 IR Constraints Reduction: If the IR constraint oftype 1 vehicles is satisfied, then other IR constraints of typei, 1 < i ≤ N , do automatically hold [43].

Proof Based on the IC constraints, we can get G(di, qi) −pi > G(di, q1) − p1. Furthermore, according to thedefinition of the vehicle types, we have di > d1, where 1 <

i ≤ N . As G(di, qi) is a monotonically increasing functionin terms of di , we get G(di, q1) − p1 > G(d1, q1) − p1.The inequality indicates that the IR constraint of type i

vehicles, 1 < i ≤ N , is automatically satisfied whenever IRconstraint of type 1 vehicles holds.

Definition 1 Local Downward Incentive Constraint (LDIC)and Downward Incentive Constraint (DIC): Consideringtwo adjacent types, namely type i and type (i − 1), theIC constraint of the contracts between these two types isdefined as LDIC, which can be formally presented as

Uiv(qi, pi) ≥ Ui

v(qi−1, pi−1), i ∈ {2, 3, ..., N}. (7)

By extending the definition of LDIC to the IC constraintsbetween type i and type j , where j ∈ {1, ..., i −1}, we havethe DICs, which are shown as

Uiv(qi, pi)≥Ui

v(qj , pj ), i ∈{2, 3, ..., N}, j ∈{1, ..., i −1}.(8)

Definition 2 Upward Incentive Constraint (UIC) and LocalUpward Incentive Constraint (LUIC): Similar to Definition1, the definition of UIC and LUIC are formally given asUi

v(qi, pi) ≥ Uiv(qj , pj ), where i ∈ {1, 2, ..., N − 1}, j ∈

{i + 1, ..., N}, and Uiv(qi, pi) ≥ Ui

v(qi+1, pi+1), wherei ∈ {1, 2, ..., N − 1}, respectively.

Lemma 3 Given the LDICs hold, all DICs do automaticallyhold and can be reduced. Similarly, under the condition thatLUIC holds, all the UICs can be removed.

Proof According to the definition of G(·, ·), it is easy toget G(di+1, qi)−G(di+1, qi−1) ≥ G(di, qi)−G(di, qi−1).Given that LDIC holds, according to Eq. 7, we haveG(di, qi) − G(di, qi−1) ≥ pi − pi−1. From these twoinequations, we get

G(di+1, qi) − G(di+1, qi−1) ≥ pi − pi−1. (9)

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Based on Eq. 9 and the LDIC definition between type(i + 1) and type i contracts, we have

G(di+1, qi+1) − pi+1 ≥ G(di+1, qi) − pi

≥ G(di+1, qi−1) − pi−1.(10)

The Eq. 10 can be extended to prove that all the DICs dohold, i.e.,

G(di+1, qi+1) − pi+1 ≥ G(di+1, qi−1) − pi−1 ≥ ...≥ G(di+1, q1) − p1, i ∈ {1, 2, ..., N − 1}. (11)

Hence, we come to the conclusion that all the DICs hold andcan be reduced. The feature that all the UICs hold can beproved in a similar way.

Lemma 4 All the LDICs are binding at the optimalcontracts obtained from problem (4).

Proof For the contract designed for type i vehicles,an LDIC is not binding, when G(di, qi) − pi >

G(di, qi−1) − pi−1. Under this condition, the serviceprovider can adapt the contract by raising all pj (j ≥i) to make the LDIC binding. This method can improvethe maximum utility of the provider while not affectingthe LDICs for the contracts of the other types ofvehicles.

The fact that all the LDICs are binding for the optimalcontracts, together with the monotonicity proved in Lemma1, leads all the LUICs to be satisfied [32]. Thus, we canrewrite optimization problem (4) as

max{pn,qn} U′SP =

N∑

n=1γn(pn − cqn)

s.t . C1 : G(d1, q1) − p1 = 0C2 : G(di, qi)−pi =G(di, qi−1)−pi−1, 1<i ≤N

C3 : 0 ≤ q1 ≤ q2 ≤ ... ≤ qN

C4 : 0 ≤ qi ≤ di, i ∈ NC5 : pi ≥ 0, i ∈ N

.

(12)

Let �k = G(dk, qk) − G(dk, qk−1), where 1 < k ≤ N

and �1 = 0. Combining constraints C1 and C2 in Eq. 12,pi can be expressed as

pn = G(d1, q1) +n∑

k=1

�k, n ∈ N . (13)

Now replacing pn in Eq. 12 with Eq. 13, the objectivefunction can takes the form

max{qn} U ′SP =

N∑

n=1γn(G(d1, q1) +

n∑

k=1�k − cqn)

= G(d1, q1)N∑

n=1γn − G(d2, q1)

N∑

n=2γn

+G(d2, q2)N∑

n=2γn − G(d3, q2)

N∑

n=3γn + ...

+G(dN−1, qN−1)N∑

n=N−1γn − G(dN, qN−1)γN

+G(dN, qN)γN + cN∑

n=1γnqn

.

(14)

Then Eq. 12 can be rewritten as follows, where the value of theobjective function is only determined by the variable set {qn}.

max{qn} U ′SP =

N∑

n=1{G(dn, qn)

N∑

i=n

γi

−G(dn+1, qn)N∑

j=n+1γj − cγnqn}

s.t . C1 : 0 ≤ q1 ≤ q2 ≤ ... ≤ qN

C2 : 0 ≤ qi ≤ di, i ∈ N

. (15)

Let Sn =G(dn, qn)N∑

i=n

γi−G(dn+1, qn)N∑

j=n+1γj −cγnqn.

The objective function of Eq. 15 can be presented as U ′SP =

∑Nn=1 Sn. As Sn is independent from Si , n �= i, and Sn is

only related to the amount of computation resources qn, theoptimal {q∗

n} that maximizesU ′SP can be obtained separately

by letting q∗n = argmaxqnSn.

Lemma 5 If (dn+1 − dn)/dn > γn/∑N

i=n+1 γi , Sn is aconcave function in terms of qn, n ∈ N .

Proof We have ∂2Sn/∂q2n = ((dn+1 −

dn)∑N

i=n+1 γi − dnγn)α2λ/(αqn + β)2d0. If (dn+1 −

dn)/dn > γn/∑N

i=n+1 γi , we can get ∂2Sn/∂q2n > 0, which

indicates that Sn is a concave function.

According to Fermat’s theorem, q∗n can be derived by

solving ∂Sn/∂qn|qn=q∗n

= 0. Considering constraint C2 inEq. 15, if the obtained q∗

n is a negative number or exceedsdn, q∗

n should be set as 0 or dn. Here q∗n = 0 means that the

contract is set to {0,Na}. According to this contract, there isno computation offloading between type n vehicles and theVEC servers.

Besides constraint C2, the obtained optimal q∗n should

satisfy constraint C1 of Eq. 15. As each q∗n is derived

separately from the corresponding Sn, there may exist some

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sub-sequences not following the increasing order, whichis described in constraint C1. Noting that when{Sn, n ∈N } are concave functions, the problem of these infeasiblesub-sequences can be solved by an iterative substitutionalgorithm, which is presented as Algorithm 1 [30].

Algorithm 1 The substitution algorithm for the infeasible

sub-sequences.

Initialization: Let argmax

1: while The set is not in the increasing order, do

2: In the set , search for the infeasible sub-sequence

, where

1

3: Set argmax

1

4: end while

5: return The feasible set .

Based on the derived feasible optimal computationresources {q∗

n}, we can get the corresponding payments{p∗

n} through Eq. 13. Thus, we can obtain the optimalcontract set {q∗

n, p∗n} under the condition that {Sn} are

concave functions. If the concave condition is not satisfied,we can first solve the optimization problem (12) withoutconstraint C3 by using Lagrange multiplier. Then, we cancheck whether the solution to this relaxed problem satisfiesconstraint C3.

5 Computing resourcemanagement for taskoffloading

Considering the different delay tolerances of the vehicu-lar computation tasks and the mobilities of the vehicles,there may exist different set of optional VEC servers,which can be chosen as the offloading target by eachtype of vehicles. Furthermore, various locations and com-puting capabilities of the VEC servers make them het-erogeneous available cloud resources to different typesof vehicles. To ensure efficient utilization of the VECresources, in this section, based on the obtained optimaloffloading contracts, we further propose efficient VECoffloading schemes that decide which VEC servers arechosen by each type of vehicles and how much com-puting resources are allocated to execute the vehicularapplications.

5.1 Characteristics of various offloading types

In a practical scenario, the sum of the task offloadingdemands from the arriving vehicles is a variable. The

resource requirement of the demands may exceed the totalcomputation resource of the MEC servers. Thus, a practicalimplementation of the contract-based offloading scheme isrequired.

Theorem 1 According to the optimal contracts {q∗n, p∗

n},the revenue gained by the service provider from offering aunit resource to serve a lower type vehicle is more thanutility gained from a higher type vehicle.

Proof Let u(n) denote the revenue of the service provider,which is gained from offering a unit resource to offloadthe task of a type n vehicle. Here, we have u(n) = (p∗

n −cq∗

n)/q∗n . Thus, we get the difference between u(n + 1) and

u(n) as

D = u(n + 1) − u(n) = p∗n+1/q

∗n+1 − p∗

n/q∗n . (16)

Using Eq. 13, we have q∗np∗

n+1−q∗n+1p

∗n = q∗

n(G(d1, q∗1 )+

∑n+1k=1 �k) − q∗

n+1(G(d1, q∗1 ) + ∑n

k=1 �k) = (q∗n −

q∗n+1)(G(d1, q

∗1 ) + ∑n

k=1 �k) − q∗n�n+1. Due to the

monotonicity proved in Lemma 1, we have q∗n < q∗

n+1.Thus, we get �k = G(dk, q

∗k ) − G(dk, q

∗k−1) =

λdk

d0ln(

αq∗k +β

αq∗k−1+β

) + (1 − λ)e0(q∗k − q∗

k−1) > 0, k ={1, 2, ..., n, n + 1}. Then, we can find q∗

np∗n+1 < q∗

n+1p∗n,

and come to the conclusion that u(n + 1) < u(n).

Theorem 1 indicates that the vehicles of lower typeshould be served with a higher priority, so as to make thelimited resource more profitable.

Due to their mobility, the vehicles may reach differentRSUs at different times as they move along the road. Sinceboth the vehicles’ traveling and the computing executioncost time, there exits a VEC server for each type of vehicles,which is the last server on the road that the vehicles canoffload tasks to under the delay constraints of the vehicularapplications. We denote the id of the last VEC server fortype n vehicles as mmax

n . The definition of mmaxn is given

as

mmaxn = argmax

k

(k∑

m=1

Rm/h + dn/q∗n ≤ tmax

n

)

, n ∈ N .

(17)

Theorem 2 For the vehicles traveling in the same direction,under the concave condition stated in Lemma 5, the lastVEC server of the higher type vehicles is farther than thatof the lower type ones.

Proof According to Lemma 5, Sn is a concave function,and the optimal amount of the computation resources

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provided for a type n vehicle can be obtained by solvingequation ∂Sn/∂qn|qn=q∗

n= 0. Substituting G(dn, qn), we

have αλ(dnγn + ∑Nj=n+1 γj (dn − dn+1))/d0γn(c + (1 −

λ)e0) = αq∗n + β. Let Q = βd0(c + (1 − λ)e0)/α.

Thus, we get q∗n = β(λ(dn +∑N

j=n+1 γj (dn − dn+1)/γn)−Q)/αQ. Given the optimal VEC computation resourcesfor each type of vehicles, the difference between the VECexecution time of a type n task and a type n + 1 taskcan be written as �t = dn/q

∗n − dn+1/q

∗n+1. Here,

we have �′t = q∗

n/dn − q∗n+1/dn+1 = β

αQ{λγn+1(1 −

dn+1/dn)/γn − λ∑N

j=n+2 γj (1 − dn+2/dn+1)/γn+1 +λ

∑Nj=n+2 γj (1 − dn+1/dn)/γn + Q/dn+1 − Q/dn}. Since

dn+1 > dn, we have λγn+1(1 − dn+1/dn)/γn < 0 andQ/dn+1 − Q/dn < 0. Then, we focus on the remain partof �t , which is given as λ

∑Nj=n+2 γj ((1 − dn+1/dn)/γn −

(1−dn+2/dn+1)/γn+1). According to the concave conditionstated in Lemma 5, we find (dn+1 − dn)/dn > (dn+2 −dn+1)γn/dn+1γn+1. Thus, the remain part is negative. Sinceβ

αQ> 0, we get �′

t < 0 and �t > 0, which meansthat the VEC execution time of the higher type vehiclesis less than that of the lower type ones. Thus, under thedelay constraints of vehicular applications, the maximumavailable travel time for lower type vehicles is shorter thanthat of the higher type ones. Thereafter, the last VECserver of the lower type vehicles is closer to their startingpoint.

5.2 VEC server selection and computing resourceallocation schemes

The delay in the VEC offloading process is the sumof two components: the vehicle travel time and thecomputation execution time. Under the offloading delaytolerance of each type of applications, the tolerance in theacceptable delay due to the travel can be higher becauseof the savings in computation time. Thus, the range ofthe available VEC servers for vehicles can be extendedby providing the vehicles with additional computingresources.

Lemma 6 For type n vehicles (n ∈ N ), with the additionalcomputing resource �r,n apart from the optimal contractresource q∗

n , they can choose to offload to a VEC server withindex no more than mmax′

n .

Proof Due to the rationality of the VEC service provider,the provider’s revenue should be nonnegative with theextra resource allocation, i.e., p∗

n − c(q∗n + �r,n) ≥ 0.

Considering the total time cost of the VEC offloadingprocess with the additional resource, we have dn/(q

∗n +

�r,n) + ∑mmax′n

j=1 Rj/h ≤ tmaxn , and here mmax′

n is theextended last VEC server that type n vehicles can offload

to. Combining the above two inequalities, we get mmax′n =

argmaxk

(∑km=1 Rm/h + dnc/p

∗n ≤ tmax

n

).

Although a lower type vehicle brings more revenue to theprovider than a higher type one, which is stated in Theorem1, a unit computing resource allocated to lower type vehiclesmay not always generate more revenue than being allocatedto higher ones with the providing of additional resources.However, there exists relationships of the revenues gainedfrom the vehicles of different types under a givencondition.

Lemma 7 Given the allocated additional computingresources �r,n, if the revenue p∗

n/(q∗n + �r,n) gained from

providing a unit resource to type n vehicles is higher thanthat gained from a unit resource providing to typem vehicles(m > n, m, n ∈ N ), serving type n vehicles is moreprofitable than serving type m vehicles with additionalresources.

Proof Given p∗n/(q

∗n + �r,n) > p∗

m/q∗m, since �r,m >

0, we have p∗m/q∗

m > p∗m/(q∗

m + �r,m). Thus, there hasp∗

n/(q∗n + �r,n) > p∗

m/(q∗m + �r,m).

With the additional allocated computing resources, thevehicles can offload their tasks to more distant VECservers as long as the delay constraints of their tasks canbe satisfied. As a result, more cloud resources can beutilized. Considering the limited computing capacity ofeach VEC server, to raise the VEC provider’s revenue,the computing resources should be allocated to moreprofitable vehicle. When several types of vehicles wantto offload their tasks to the same VEC server, a collisionoccurs. Thus, a VEC computing resource management isrequired.

Here we propose a contract-based efficient VEC serverselection and cloud computing resource allocation schemefor the vehicles. According to Theorems 1 and 2, the lowertype vehicles are more profitable and their available VECservers are nearer to the starting point of the travelingvehicles. Therefore, in the proposed scheme, the computingresource management begins from the VEC servers locatednearest to the starting point, and the computing resourcesare first allocated to the lowest type vehicles. In the systemmodel, the road is bidirectional, and there are vehiclestraveling in opposite directions. Thus, the starting pointsof the road from both sides need to be considered. Whenthere is a competition for the same VEC resources betweendifferent types of vehicles, a revenue comparison is adoptedto decide the resource subscribers. The details of theproposed VEC resource management scheme are describedin Algorithm 2.

Mobile Netw Appl

Algorithm 2 The contract-based VEC resource manage-

ment algorithm.

Initialization: The arriving vehicles 1 and 2; The

computation task ; The

available computation resource for MEC server ,

.

1: Derive the optimal contract set

following the steps described in Section 4;

2: Obtain the maximum id ( ) with

the additional allocated VEC resources according to

Lemma 6;

3: For 1 1 2 do

4: Loop

5: Based on ( ), obtain the set of

candidate vehicle types for offloading tasks to server

(server 1), which is denoted as

( ).

6: Compute the revenues gained from providing a

unit VEC resource to the types of vehicles belonging to

the sets ( 1).

7: Searching from the lowest type vehicles in set

( 1), find type 1 ( 2), which brings the

highest revenues to server (server 1).

8: Allocate VEC resource to type 1 ( 2) vehicles

from server (server 1).

9: Update the remain computation resources of

server ( 1 of server 1).

10: Remove the type of vehicles, whose offloading

requirements have been fully satisfied, from

( 1).

11: If ( 1

1 ) then

12: End loop;

13: end If

14: end Loop

15: end For

6 Numerical Results

In this section, we evaluate the proposed contract-based VEC computing resource management schemes. Weconsider a scenario where M = 6 RSUs randomly locatedin a bidirectional road. The computing resources of theseVEC servers are randomly distributed within the rangeof (100, 500) units [45]. For each RSU, the cost forcomputing for a unit resource is set c = 0.3. There are100 arriving vehicles on the road, and they run at the speed100 km/hr. The vehicles choose the directions of travelwith equal probabilities. The arriving vehicles are classifiedinto N = 5 types in terms of their computation taskswith the probabilities γ = {0.17, 0.23, 0.28, 0.18, 0.16}.

Fig. 2 The revenues of the service provider with different schemes

For each type of vehicular computation tasks, the resourcerequirement is d = {12, 13, 15, 18, 21}, respectively.

Figure 2 evaluates the performance of the proposedcontract-based computing resource management scheme.In the resource allocation process of this scheme, boththe delay tolerance and the priorities of different typesof vehicles are considered. In addition, the additionalVEC resources providing strategies are adopted to furtherimprove cloud utilization. We compare the performanceof our proposed scheme with two other schemes. Oneis the contract-based scheme without additional resourceallocation. The other is the non-contract scheme adoptingfixed offloading payment of the vehicles. It can be seenthat both the contract-based schemes yield higher revenuesto the VEC service provider than the fixed payment one.The reason is that in the contract theoretic approach, eachcontract is designed for the corresponding computation tasktype. Thus, the revenues gained from providing offloadingservice to the vehicles can be improved by making theLDICs binding as described in Lemma 4. Furthermore, wecan find that the revenues obtained by our proposed schemeis higher compared to the contract-based scheme withoutadditional resource. This can be explained as follows. Dueto the vehicles’ travel time cost, the computing resources ofthe VEC servers far away from the road starting points cannot be used by the vehicles within the delay tolerance of thevehicular applications. However, through the adoption ofour proposed additional resource allocation, the range of theavailable VEC servers for the vehicles has been extended.Thus, more VEC resources can be utilized, which bringshigher revenue to the service provider.

Figure 3 shows the computing resource utilizationrates of different VEC servers adopting various resourceallocation schemes. Here, the vehicles traveling from server1 to server 6 is denoted as set Q1 with the vehicle numberQ1 = 50. Due to its proximity to the starting point ofvehicles Q1, server 1 can be chosen as the available server

Mobile Netw Appl

Fig. 3 The resource utilization rate of the VEC servers with differentschemes

by all types of vehicles. Thus, the resource utilization ofserver 1 is always close to 1. In contrast, server 6 isthe farthest one from Q1, but the nearest to the startingpoint of vehicles Q2, which travel in the opposite directionof Q1. When the number of vehicles Q2 is small, theresource utilization of server 6 is low, since the long traveldelay obstructs vehicles Q1 to offload tasks to server 6under delay constraints. In this case, by implementing ourproposed Additional Computing Resource (ACR) scheme,server 6 is turned to be an available offloading target of Q1

with the extended traveling delay tolerance. As a result, theresource utilization of server 6 improves. Server 3 is locatedin the middle of the road. Thus, a large part of the low typevehicles can not offload tasks to this server by adopting thescheme without ACR. However, as can be seen from Fig. 3,our proposed ACR scheme greatly increases the utilizationrate of server 3 with an average rate of 24.9%.

Figure 4 indicates the revenues of the VEC serviceprovider gained from executing an offloading task to a unit

Fig. 4 The revenues of the service provider gained from an unitcomputation resource

Fig. 5 The successful rate of the offloading service in terms of thevehicles’ travel speed

resource. We can see that by utilizing a unit computingresource, the provider gains higher profit from offloadingtasks of the lower type vehicles. This result corroboratesTheorem 1. In addition, the revenue gained from each typeof vehicles first increases and then decreases. This can beexplained as follows. According to Theorem 1, the revenuesgained from running a task Ti on a unit resource is defined asu(i) = pi/qi − c. In the contract-based offloading scheme,the provider raises price pi to gain higher profit with thegrowth of cost c. To cope with the increasing price, vehicleswill reduce the offloading resource consumption qi . Therate of the demand reduction is higher at lower c.

Figure 5 shows successful rate of computation offloadingservice for vehicular applications in the cases with differentnumbers of vehicles traveling in the opposite directions.It can be seen that the rates improve with increase in thespeed of the vehicles, in all cases, until the rates reach theirmaximum thresholds. In addition, we can see that in thecase where the distribution of the vehicles’ travel directionsis more dispersed, the maximum threshold is reached at aslower speed. With a higher speed, vehicles can access moreVEC servers within their task delay constraints. Thus, theyhave more chances to offloading their computation task.When the speed is higher than the threshold, which enablesthe vehicles to offload tasks to the farthest servers, thesuccessful rate will not increase with the speed acceleration.In the case where the vehicles are more dispersed, theaverage distance between the farthest VEC server and thestarting points of the traveling vehicles is shorter. Thus, thespeed threshold is lower in this case.

7 Conclusion

In this paper, we have presented a vehicular edge computingframework for studying computation offloading process.

Mobile Netw Appl

By implementing contract-theoretic approach, we designoptimal computation offloading strategies for the cloudservice provider in terms of computing resource allocationand service pricing. To further improve the utilization ofthe edge cloud servers while maximizing the revenuesof the service provider, we propose an efficient cloudresource management scheme with offloading prioritydistinction and additional resource allocation. Numericalresults demonstrate that our proposed schemes greatlyimprove the performance of the vehicular applicationoffloading process.

Acknowledgments This work is in part supported by the NationalNatural Science Foundation of China under Grant No.61374189, thejoint fund of the Ministry of Education of P.R. China and China Mobileunder Grant MCM20160304.

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