Received August 25, 2020, accepted August 29, 2020, date of publication September 10, 2020, date of current version September 24, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.3023128

Contract-Based Scheduling of URLLC Packetsin Incumbent EMBB TrafficAUNAS MANZOOR 1, S. M. AHSAN KAZMI 1,2, SHASHI RAJ PANDEY 1,AND CHOONG SEON HONG 1, (Senior Member, IEEE)1Department of Computer Science and Engineering, Kyung Hee University, Yongin-si 17104, South Korea2Networks and Blockchain Laboratory, Institute of Secure and Cyber Physical System, Innopolis University, 420500 Tatarstan, Russia

Corresponding author: Choong Seon Hong (cshong@khu.ac.kr)

This work was partially supported by the Institute of Information communications Technology Planning Evaluation (IITP) grant funded bythe Korean Government Ministry of Science and ICT (MSIT) (No. 2019-0-01287, Evolvable Deep Learning Model Generation Platformfor Edge Computing).

ABSTRACT Recently, the coexistence of ultra-reliable and low-latency communication (URLLC) andenhanced mobile broadband (eMBB) services on the same licensed spectrum has gained a lot of attentionfrom both academia and industry. However, the coexistence of these services is not trivial due to the diversemultiple access protocols, contrasting frame distributions in the existing network, and the distinct qualityof service requirements posed by these services. Therefore, such coexistence drives towards a challengingresource scheduling problem. To address this problem, in this paper, we first investigate the possibilities ofschedulingURLLC packets in incumbent eMBB traffic. In this regard, we formulate an optimization problemfor coexistence by dynamically adopting a superposition or puncturing scheme. In particular, the aim is toprovide spectrum access to the URLLC users while reducing the intervention on incumbent eMBB users.Next, we apply the one-to-one matching game to find stable URLLC-eMBB pairs that can coexist on thesame spectrum. Then, we apply the contract theory framework to design contracts for URLLC users to adoptthe superposition scheme. Simulation results reveal that the proposed contract-based scheduling schemeachieves up to 63% of the eMBB rate for the ‘‘No URLLC’’ case compared to the ‘‘Puncturing’’ scheme.

INDEX TERMS Contract theory, enhance mobile broadband (eMBB), fifth-generation new radio, matchingtheory, scheduling, ultra-reliable and low-latency communication (URLLC).

I. INTRODUCTIONAs a result of rapid technological developments in therecent years, there has been a growing interest in tac-tile internet applications such as industrial automation,autonomous vehicles, massive IoT connectivity, and digitalentertainment expansion. These novel applications have verystringent and diverse communication requirements such ascoverage, data rate, latency and reliability. To meet thesediverse communication requirements of diverse applications,the International Telecommunication Union (ITU) has clas-sified fifth-generation new-radio (5G NR) services into threecategories: ultra-reliable and low-latency communication(URLLC), enhanced mobile broadband (eMBB), and massivemachine type communication (mMTC) [1]. Among theseservices, URLLC is designed for the event-driven, mission-critical, and industrial scenarios, in which it can contribute

The associate editor coordinating the review of this manuscript and

approving it for publication was Asad Waqar Malik .

to meet the quality-of-service (QoS) requirements such asultra-low latency and ultra-high reliability. Furthermore,the standard URLLC imposes strict latency and reliabilityrequirements, typically of 1 ms/packet and up to 99.999%successful packet delivery, respectively [2], [3].

Since both the eMBB and URLLC are essential com-ponents of communication traffic in 5G cellular networks,various studies have addressed the coexistence issue of theseservices [4]. From the perspective of network throughput,the eMBB generates an enormous amount of data commu-nication traffic over cellular networks. Unlike the eMBB,URLLC produces less data as it has stringent latency andreliability requirements. Therefore, the coexistence of thesetwo services involves the challenge of achieving sufficienteMBB throughput while satisfying URLLC requirements [5].Due to the time-sensitivity of mission-critical applications,such as UAV automation, autonomous vehicular control,and critical medical apparatus management, URLLC isprioritized over eMBB for scheduling. In general, eMBB

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scheduling involves the enhancement of network throughputto improve spectral efficiency while the reliability of packetdelivery is ensured through re-transmissions. However,eMBB scheduling approaches may not ensure the reliabilityand latency thresholds required for URLLC, and thus cannotbe applied in URLLC scheduling. On the contrary, URLLCinvolves the transmission of short packets within certainlatency and reliability bounds.

One well-thought way to handle the aforementionedconstraints is using re-transmissions approach. However,it is impractical to simultaneously satisfy the contradictingrequirements of latency and reliability in URLLC onlythrough re-transmissions approach. For instance, a greaternumber of transmissions ensures reliability while compro-mising latency, and vice versa. To address this challenge,small-packet communication has been proposed for URLLC,as it can meet the reliability requirements at the costof reduced spectrum efficiency due to additional controloverhead. However, it does not suffice as an efficientscheduling scheme is further required for the coexistence ofURLLC and eMBB services such that the penalization of theeMBB traffic is minimized [6].

In this regard, conventional scheduling schemes based onorthogonal channel allocation are proven to be inefficient andunderutilized when applied to the coexistence scenarios ofURLLC and eMBB networks. In fact, the third generationpartnership project (3GPP) suggested a short and longtransmission time interval (TTI)-based frame distributionfor these coexistence scenarios. In this frame distribution,eMBB traffic is scheduled for a long TTI and URLLC isopportunistically scheduled for a short TTI over the existingeMBB traffic by adopting a puncturing or superpositionscheme [7]. The puncturing scheme involves the schedulingof URLLC packets by halting the eMBB communicationduring the URLLC transmission for the duration of a shortTTI. Note that the puncturing scheme can significantly reducethe throughput of eMBB users. Thus, to compensate forthis loss, the superposition scheme is proposed that involvesthe non-orthogonal scheduling of both eMBB and URLLCtraffic on the single channel simultaneously. This is achievedby exploiting the non-orthogonal multiple access (NOMA)scheme, in which the difference between the channel gains ofthe cellular users is exploited to pack the coexisting users ona single channel resource [8], [9].

A. CONTRIBUTIONIn this study, we propose an efficient scheduling schemefor the coexistence of eMBB and URLLC by dynamicallyadopting puncturing or superposition schemes. For thispurpose, we consider a cellular network in which manyURLLC and eMBB users are associated with a base-station(BS). The BS performs eMBB scheduling at the start of along TTI, and URLLC scheduling is performed for a shortTTI using the puncturing or superposition scheme. To meetthe latency requirements of URLLC users, their scheduling isperformed in the same or next URLLC TTI of the scheduling

request. Moreover, the reliability requirement is met by eitherusing the puncturing or the superposition scheme to ensurecertain channel quality. To perform the pairing betweenURLLC and eMBB users, we apply a one-to-one matchingscheme that is based on the preference profiles of the eMBBand URLLC users. The BS attempts to enhance the eMBBthroughput by reducing the effects of URLLC scheduling,which is achieved by selecting the superposition scheme.To encourage URLLC users to opt for the superpositionscheme, we propose a contract-based incentive mechanismthat involves sharing the payoff received by the BS forapplying the superposition scheme with the contributingURLLC users. In addition, the URLLC users prefer optingfor the superposition scheme unless their QoS requirementsare satisfied; otherwise, they select the puncturing scheme.

In the case of the proposed contract-based incentivemechanism, superposition is well-suited for both URLLC andeMBB users. However, in some cases, both type of the usersexperience similar channel gains that makes the adoptionof the superposition scheme infeasible. In these cases,the puncturing scheme is essential. Therefore, we proposeapplying the puncturing or superposition scheme based onnetwork and channel conditions. For this purpose, we usethe contract theory framework [10] to design a bundle ofcontracts by the BS for URLLC users. Contract theory isuseful because the BS cannot reveal complete information(i.e., channel gain, willingness for superposition, and thematching with a particular eMBB user) fromURLLC users ina timely manner due to the strict latency requirements. As aresult, an asymmetric information problem arises due to thelack of complete information that is solved by using contracttheory [11]. Note that the pairing of eMBB and URLLC usersbefore designing the contracts using the one-to-one matchingis essential for better spectrum efficiency. In case of not usingthe matching pairs, it is possible to select the pairs which maynot coexist on a single channel.

The main contributions of this paper are summarized asfollows:• We model the problem of URLLC and eMBB coex-istence, in which eMBB users are modeled using theShannon rate, and finite block length codes are used tomodel the rates for URLLC users. In addition, we modelthe superposition and puncturing framework for thecoexistence of URLLC and eMBB users on the samechannels.

• For URLLC scheduling, we formulate the optimizationproblem to maximize the eMBB rate under the URLLCQoS requirements of latency and reliability to optimizethe puncturing or superposition scheme and URLLCpower allocation.

• To solve the formulated problem, we first pair eachURLLC user with a suitable eMBB user. This pairingis performed by applying the one-to-one matchingconsidering the preference profiles of both participants.

• Based on the pairing, appropriate contracts are designedfor each URLLC type. The URLLC type refers to

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the classification of URLLC users for the adoption ofsuperposition scheme. After verifying the feasibilityand optimality of the contracts, power allocation tothe URLLC users is performed according to theirutility constraints. Furthermore, we formulate a convexproblem that maximizes the BS profit by optimizing thepower allocation.

• Numerical results validate the performance of theproposed contract-based scheme. The results demon-strate that the proposed contract-based superpositionscheme achieves up to 63% of the eMBB rate for thenon-URLLC case compared to the puncturing scheme.

The remainder of this paper is organized as follows. Therelated work is summarized in Section II. The system modelis presented in Section III. Subsequently, in Section III-B,the problem is formulated to maximize the eMBB rate subjectto URLLC requirements. In Section IV, after performing theone-to-one matching, a contract design for URLLC users ispresented which is used for the resource allocation to theURLLC users. Finally, numerical results and conclusions areprovided in Sections V and VI, respectively.

II. RELATED WORKSIn this section, we discuss some of the significant relatedworks and challenges, which are grouped into three cate-gories: (a) 5G-NR, (b) contract theory, and (c) matchingtheory.

A. 5G-NRRecently, numerous puncturing-based scheduling schemeshave been proposed in the literature. For instance, the authorsin [12] utilized puncturing and superposition schemes toschedule URLLC traffic over pre-scheduled eMBB commu-nication. However, the authors did not consider the reliabilityconstraints of URLLC communication. A statistical analysisof URLLC communication over a wireless channel wasperformed in [13]. The authors proposed a method ofselecting a transmission rate according to the channelconditions and reliability requirements.

In [14], the authors considered a CRAN environmentwhere the decoding of eMBB traffic was performed onthe cloud while URLLC decoding was performed by edgenodes to meet the latency requirements. In [15], the authorssolved the URLLC resource allocation problem in the shortblocklength regime. However, the global optimal solutionwas identified in the subset of the feasible region only. Theauthors demonstrated the insignificance of power control forsmall URLLC packets. In [16], the authors proposed URLLCpacket transmission among device-to-device (D2D) users,in which the D2D pairs communicated opportunistically forshort packets. However, the authors did not consider thereliability requirements in their formulation. In [17], machinelearning based adaptive TTI interval is proposed for thescheduling in eMBB and URLLC coexistence networks.

The problem of ensuring ultra-low latency and ultra-reliability has been addressed in the literature. For instance,

backbone network latency can be improved using a dedi-cated link for URLLC communication. Similarly, fronthaullatency reduction is possible by reducing the transmissionoverhead. Furthermore, the control signaling mechanism canbe improved to eliminate the signaling latency in the LTEsystems [18]. In [19], the authors proposed a risk-sensitivebased formulation for the coexistence problem of eMBB andURLLC traffics that aims at maximizing the eMBB data ratewhile considering the URLLC reliability. In [20], the authorsproposed a scheduling scheme for the URLLC downlinktraffic.

The main cause of reliability losses in current LTEsystems is erroneous channel estimation. Therefore, URLLCreliability can be increased by the improving channelestimation, which can be achieved by improving the controlsignaling mechanism. As mentioned earlier, one solution tothe problem of simultaneously meeting reliability and latencyrequirements involves reducing the packet size in URLLC,which results in meeting the reliability constraints for a givenlatency at the cost of low achievable rates. Furthermore,spatial diversity can be used to achieve an improved URLLCreliability i.e., using multiple transmitters for sending dupli-cate URLLC packets. In this way, the required reliability canbe achieved at the cost of spectrum efficiency [21].

B. CONTRACT THEORYContract theory has been widely used in various wirelesscommunication schemes for situations involving informationasymmetry, as well as to encourage agents to contribute totasks assigned by the principal [22]. For instance, the studyconducted in [23] proposed an incentive mechanism toencourage D2D users to share content. Similarly, in a cloudradio access network, contract theory was used to motivatethe content providers to rent the cache to the networkoperator [24]. In addition, the use of contract theory for thecase of incomplete information was exploited in [25]. In [26],the authors addressed the problem of secure data sharing inthe Internet of Vehicles by leveraging blockchain. Moreover,to address the problem of minor selection, the authors appliedcontract theory. In [27], the authors proposed task offloadingfrom the BS to nearby underutilized vehicular fog nodes.They proposed a contract-matching based incentive and taskassignment scheme. In [28], the contract theory was used tomodel communication among D2D users. A multi-principalmulti-agent problem was mapped to the D2D communicationproblem. The aforementioned works thus indicate the utilityof using contract theory in real-world problems.

C. MATCHING THEORYIn economics, a Nobel prize-winning mathematical frame-work called matching theory has been developed that isapplied in the formation of collectively valuable groupsamong participants. Recently matching theory has beenextensively used for efficient resource management inwireless networks [29]. For instance, the authors of [30]used matching theory to associate users for task offloading

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in mobile edge computing (MEC). Similarly, the problem ofuser association and resource allocation in a fog network wassolved using matching theory for the two-way associationbetween fog nodes and (IoT) users [4]. Furthermore,a matching-based D2D resource allocation with interferencemanagement was proposed in [31]. The aforementionedresearch that demonstrates the significance and contributionof matching-based approaches in wireless networks.

To the best of our knowledge, the present study is the first toemploy contract theory to address the problem of coexistenceof URLLC and eMBB users in cellular networks.

FIGURE 1. System model for the coexisting URLLC and eMBB networks.

III. SYSTEM MODEL AND PROBLEM FORMULATIONIn the system model, we consider a downlink radio accessnetwork (RAN) consisting of a set of BSs denoted by J ={1, 2, · · · , J}, each connected to the core network throughbackhaul links. Each BS j ∈ J is associated with thecorresponding sets of URLLC and eMBB users denoted byU = {1, 2, · · · ,U} and E = {1, 2, · · · ,E}, respectivelyas shown in Figure 1. The eMBB users are scheduledaccording to the standard LTE scheduling while URLLCcommunication is overlaid on the pre-scheduled eMBBtraffic. Specifically, both eMBB and URLLC networkscoexist to share the same spectral resources consisting of a setof resource blocks (RBs) denoted by K = {1, 2, · · · ,K }. Inorder to enable coexistence, either the puncturing scheme orthe superposition scheme can be used. Figure 2 demonstratesthe frame structure for eMBB and URLLC schedulingthrough both the aforementioned schemes. Each eMBB usere ∈ E is assigned a timeslot of duration 1 ms and bandwidthW of an RB k . We assume eMBB users are pre-scheduled andeach eMBBuser experiences a level of signal-to-interference-plus-noise ratio (SINR) that is known to the BS. In eachmini-slot of duration 0.125 ms, there is a random arrival ofURLLC users that are scheduled over the incumbent eMBBallocation using the puncturing or superposition scheme.

A. WIRELESS MODELIn our model, we assume a saturated network scenario inwhich eMBB users always have packets to transmit and

FIGURE 2. Resource block frame structure for eMBB and URLLCscheduling.

the number of eMBB users are more than the available BSresources. Then, the BS assigns its resources to a set ofoptimal eMBB users for downlink communication. On theother hand, with respect to the URLLC traffic, we model thearrival of a URLLC request using Poisson distribution [32].

1) eMBB TRAFFICIn wireless networks, we have orthogonal and non-orthogonalchannel access schemes. In the scenarios of URLLC andeMBB coexistence, the orthogonal channel access schemecorresponds to the puncturing scheme and non-orthogonalchannel access scheme corresponds to superposition scheme,respectively. Upon the arrival of URLLC requests, appro-priate mini-slots are allocated to URLLC users accordingto two schemes: 1) puncturing scheme, in which eMBBtransmission is stopped to schedule a URLLC user, and2) superposition scheme, in which both eMBB and URLLCcan operate in the same mini-slot while utilizing thesuccessive interference cancellation (SIC) technique. Underthe superposition scheme, the SINR at the eMBB user e ∈ Efrom the BS j is defined as:

γsupej =

PejgejIurllc + N0

, (1)

where Pej and gej are the transmit power and channel gain,respectively, from the BS j to the eMBB user e ∈ E . Iurllc =Pujgej denote the received interference from the coexistingURLLC users and N0 denote the noise level. Similarly,the SINR for the puncturing scheme denoted by γ punej fromthe BS to the eMBB user is expressed as follows:

γpunej =

PejgejN0

. (2)

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Using (1) and (2), the corresponding eMBB rate iscalculated as follows:

Rej(γ(·)ej

)= W log

(1+ γ (·)

ej

), (3)

where W denotes the bandwidth of RB, and γ (·)ej denotes

the corresponding SINR for the superposition or puncturingcase. The total eMBB rate using superposition and puncturingscheme is expressed as Rej = Rej

(γ(sup)ej

)+ Rej

(γ(pun)ej

).

2) URLLC TRAFFICThe traditional Shannon capacity rates cannot be used due tosmall packet size in URLLC traffic [15]. Therefore, we usethe finite blocklength to define the URLLC rate to deliver thenumber of bits using RB k with a certain error probability εu.The SINR for the puncturing and superposition cases

denoted by γ (·)uj is given below:

γsupuj =

PujgujIembb + N0

, (4)

γpunuj =

PujgujN0

, (5)

wherePuj and guj denote the transmit power and channel gain,respectively, from the BS j to the URLLC user u ∈ U . Iembb =Pejguj denotes the received interference from the coexistingeMBB users.

Using (4) and (5), the corresponding URLLC rate based onfinite block length codes is given as follows [33]:

Ruj(γ(·)uj

)= W log(1+ γ (·)

uj )

−

√√√√ 1mu

(1−

1

(γ (·)uj + 1)2

)Q−1(ε)ln 2

, (6)

where mu denotes the packet size of URLLC user u, Q−1(·)denotes the inverse Q-function and ε denotes the reliabilitythreshold of URLLC, respectively.

The adoption of superposition or puncturing scheme by theURLLC user u is represented by xkuj and z

kuj, respectively and

defined as follows:

xkuj =

{1, if URLLC user u users superposition,0, otherwise.

zkuj =

{1, if URLLC user u uses puncturing,0, otherwise.

For the coexistence of eMBB and URLLC, we denote theeMBB TTI with T which is set it to 1 ms and we denotethe URLLC TTI (also called mini-slot) with t which is setto 0.125 ms. For each eMBB TTI, we consider a set oforthogonal resource blocks denoted by K = {1, 2, · · · ,K },where each RB k ∈ K has spectrum bandwidth W . At thestart of each eMBB TTI, eMBB users are scheduled for aneMBB TTI of 1 ms and spectrum bandwidth ofW .Fig. 2 indicates that eMBB users are scheduled for eMBB

TTI and URLLC users are scheduled in the mini-slot.

Note that an appropriate selection of mini-slots for URLLCtraffic is required for spectrum efficiency and to achievehigh eMBB rate. Each eMBB user experiences a differentSINR level, depending on the distance from the BS andthe corresponding channel gain. Therefore, suitable eMBBusers can operate on the same channel with an appropriateURLLC user. In a traditional superposition scheme, URLLCusers receive interference from coexisting eMBB users,as given in (4), which can compromise reliability. Therefore,we propose a superposition scheme in which URLLCreliability is not affected.

For the case of superposition in which xkuj = 1, botheMBB and URLLC transmit on the same channel k . TheBS j transmits the superposed signal xj = Pejxe + Pujxu toboth eMBB and URLLC users, where xe and xu denote themessages for eMBB and URLLC users, respectively [34].The superimposed signal is received by both eMBB andURLLC users, and only the eMBB user performs SIC. TheeMBB user decodes the interference signal from the URLLCuser and cancels it to get its own message. Conversely,the URLLC user can receive the message without any SIC.The corresponding rates for the eMBB and URLLC users aregiven as follows:

yej = Rej

(PejgejN0

), (7)

yuj = Ruj

(Pujguj

Pejgej + N0

). (8)

B. PROBLEM FORMULATIONThe objective of this work is to maximize the eMBB ratewhile satisfying the latency and reliability constraints for theURLLC users. Therefore, the goal is to select the optimalmini-slots from the pre-scheduled eMBB traffic such thatthe latency constraints are not violated. Moreover, it is alsorequired to choose the optimal channel and power to satisfythe reliability constraints for the URLLC traffic. Hence,we formulate our optimization problem as follows:

maxx,z,p

∑j∈J

∑k∈K

∑e∈E

(T − t

∑u∈U

zkuj

)Rej, (9)

s.t.∑k∈K

∑u∈U

(xkuj + z

kuj

)= λ, ∀j ∈ J , (9a)

∑j∈J

∑k∈K

Pr[(xkuj + z

kuj

)Ruj

(γ(·)uj

)≥ R̃

]≥ εu, ∀u ∈ U, (9b)

xkuj, zkuj ∈ {0, 1}, ∀u ∈ U,∀j ∈ J , k ∈ K, (9c)

puj ≥ 0, ∀u ∈ U, j ∈ J . (9d)

The objective to maximize the network rate of eMBB usersis dependent on the superposition and puncturing schemesrepresented by xkuj and z

kuj, respectively. The constraint in (9a)

ensures that URLLC packets are strictly scheduled just afterthe arrival of λ number of transmission requests which isassumed to be fixed while solving (9). (9b) ensures ultra

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reliability εu of each URLLC user u by guaranteeing theirrate above the threshold R̃. Equations (9c) and (9d) containthe bounds for the decision variables.

The aforementioned problem optimizes the use of superpo-sition/puncturing scheme for URLLC traffic scheduling. Theproblem is a large mixed integer linear programming (MILP)problem with very high complexity and is difficult to solve.To solve this problem, we use the contract theory frameworkto determine the willingness of the URLLC users to adoptthe superposition scheme. In order to reduce the number ofcontracts for each URLLC user and to make the contractdesign scalable, we use one-to-one matching between theeMBB and URLLC users. After the optimal contract designfor the superposition, the power allocation is performed forthe URLLC users to meet the reliability constraint.

IV. SOLUTION APPROACHA. CONTRACT THEORY FOR SUPERPOSITIONThe wireless spectrum and number of RBs at each BSare limited. In the coexistence environment of URLLCand eMBB, the aim of the BS is to meet the URLLCQoS requirements and maximize the served number ofeMBB users. This can be achieved by efficiently packingthe URLLC users on the ongoing eMBB communicationusing the superposition. Therefore, each BS requires anincentive mechanism to encourage URLLC users to opt forsuperposition. Moreover, the URLLC users must also meettheir QoS requirements. However, the BS does not knowthe willingness of URLLC users in the network to opt forsuperposition. Therefore, the problem of optimal resourceallocation becomes difficult for each BS, which results ininformation asymmetry between the BS and URLLC users.We use the contract theory framework to motivate URLLCusers for superposition, and each BS designs a bundle ofcontracts for the URLLC users.

FIGURE 3. URLLC user tiers of willingness to opt for superposition.

First, we define the types of URLLC users based on theirpreference to opt for superposition based on the geographicallocation of theURLLCuser, as illustrated in Fig. 3. AURLLCuser with a higher type is more willing to opt for thesuperposition than a URLLC user with a lower type.

Definition 1: We define the willingness of URLLC usersto opt for superposition by considering N number of tiers ina geographical cell. The URLLC users closer to the BS aremore willing to opt for superposition. Therefore, the URLLCusers are classified into a set Θ = {θ1, θ2, . . . , θN } withtheir corresponding willingness for superposition provided indescending order θ1 > · · · > θn > · · · > θN .

1) UTILITY OF URLLC USERSThe utility of URLLC user u is defined as follows:

Uu =

{θnyuj−βu + ςβe, if θn ≥ υ(µ(u)), xkuj = 1,

θnyuj−βu, if θn < υ(µ(u)), zkuj = 1,(10)

where υ(µ(u)) = duj denotes the parameter of choosingbetween superposition or puncturing scheme by the URLLCuser which is function of the distance duj between theURLLC user and BS. Depending on the utility obtainedfrom the matched pair, each URLLC user selects the optimalsuperposition or puncturing scheme xkuj

∗or zkuj

∗, respectively.

βu and βe denote the price per mega bytes (MB) paid bythe URLLC and eMBB users to the BS, respectively, and ςdenotes the proportion of the incentive paid to the URLLCuser on choosing the superposition scheme.

2) BS UTILITYThe utility of the BS j is the difference between the profitobtained from URLLC and eMBB users, and the resourcesallocated to them and is defined as:

Uj = ξ

(∑u∈U

βu +∑e∈E

βe

)

− ζ

(∑u∈U

πu

(Ruj

(γ(·)uj

))+

∑e∈E

πe(Rej)

), (11)

where ξ and ζ denote the normalizing constants. We considerβu � βe, which signifies that the price βu paid by URLLCusers is significantly greater than the price βe paid by eMBBusers. Therefore, the BS preferes scheduling URLLC usersover eMBB users. πu(·) and πe(·) denote the expenses of theBS in terms of channel and power allocation to URLLC andeMBB users, respectively.

Next, we present the one-to-one matching scheme betweenthe URLLC and eMBB users which is essential for thescalability of the designed number of contracts.

B. MATCHING URLLC AND eMBB USERSIn the coexistence scenario of eMBB and URLLC, eachURLLC user can be paired with at most one eMBB user andvice versa. Therefore, we formulate a one-to-one matchinggame between URLLC and eMBB networks. The matchingis defined as follows:Definition 2: A matching µ is defined by a function from

the set {E ∪ U} into the set of elements of {E ∪ U} such that:1) |µ(e)| ≤ 1 and µ(e) ∈ U ,2) |µ(u)| ≤ 1 and µ(u) ∈ E ∪ φ,

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3) µ(e) = u if and only if u is in µ(e),where µ(e) = {u} ⇔ µ(u) = {e} for ∀e ∈ E,∀u ∈ U and|µ(·)| represents the cardinality of thematching outcomeµ(·).The first two properties ensure that the matching between theeMBB and URLLC networks has a one-to-one relation in thatan eMBB user e can be paired with only one URLLC user u.Additionally, when a matching pair cannot be paired for anyreason, we have µ(n) = φ.

Algorithm 1 URLLC-eMBB Matching Algorithm1: Phase 1: Initialization:2: input: Pu, Pe, ∀u, e3: initialize: t = 0, µ(t) , {µ(u)(t), µ(e)(t)}u∈U ,e∈E = ∅,

Re(t)= ∅, Pu(0) = Pu, Pe(0) = Pe, ∀u, e

4: Phase 2: Matching:5: repeat6: t ← t + 17: for e ∈ E , propose u according to Pe(t) do8: if e �u µ(u)(t) then9: µ(u)(t)← µ(u)(t) \ e′

10: µ(u)(t)← e11: P ′(t)u = {e′ ∈ µ(u)(t)|e �u e′}12: else13: P ′′(t)u = {e ∈ E |µ(u)(t) �u e}14: end if15: Ru

(t)= {P ′(t)u } ∪ {P ′′

(t)u }

16: for l ∈ Ru(t) do

17: Pl (t)← Pl (t) \ {l}18: end for19: end for20: until µ(t)

= µ(t−1)

1) PREFERENCE PROFILES OF PLAYERSIn this subsection, we first formulate pair selection as atwo-sided matching game. In our model, there are two typesof cellular users. The first type is eMBB users E , whilethe second type is URLLC usersU . In the two-sidedmatchinggame, each player of one side must rank the players ofthe other side in descending order of priority, which isrepresented by a preference profile.

The willingness of URLLC users to adopt the superposi-tion scheme is determined by the BS through the geographicallocations of URLLC users. Each eMBB user e ranks thepotential URLLC users on the basis of their willingnessto adopt the superposition scheme. For a URLLC user,the preference of the eMBB user is high that possesses highchannel gain so that it can help adopt the superpositionscheme according to (7) and (8) by using SIC. The URLLCuser u creates a preference profile based on the followingpreference function:

Pu = gej, ∀u ∈ U . (12)

Similarly, the preference of the eMBB user is to select aURLLC user whose willingness to adopt the superposition

scheme is the highest. Then, in such case, the superpositionscheme is selected for the URLLC transmission. Thepreference profile for the eMBB user e is based on theclassification of the superposition according to Definition 1expressed as follows:

Pe = θn, ∀e ∈ E . (13)

Note that once both sides build their respective preferenceprofiles, then, the all eMBB users propose to find theirbest suited URLLC user based on their preference profiles.We can adopt the deferred acceptance algorithm to executethis process.

Next, we present our URLLC-eMBB matching algorithmwhich is based on the deferred acceptance algorithm. In theinitialization phase (lines 1-3), all variables are initialized.Then, each eMBB user will send proposals to their mostpreferred URLLC user based on their preference profilesPe(t) (line 7). The URLLC users on receiving the proposalscompare them with existing proposals and choose theone which is the highest ranked in its preference profile(lines 8-11). However there is the possibility of getting theblocking pairs which refer to the case when the eMBB orURLLC user prefers any other user more than its currentlymatched pair. Therefore, if the received proposal is rankedlower in the URLLC profile it is immediately rejected whichprevents blocking pairs in our scheme (lines 13 and 14). Theserejected proposals are then removed from both preferencelists of emBB and URLLC users (lines 15-19). Note that thisprocess of removal ensures the stability of the matching gameand prevents blocking pairs to occur. Finally, we receive astable matching after a number of iterations once the set ofmatching pairs to do not change (lines 21).

Note that the pairing of eMBB and URLLC users beforedesigning the contracts using the one-to-one matching isessential for scalability. Moreover, matching theory allowsus to achieve eMBB optimal solution which is the goal ofthe problem in (9) [31]. Therefore, one-to-one matching isused to select the suitable eMBB and URLLC pairs for thesuperposition. However, in some cases superposition schemeis not possible to adopt due to the channel gains of matchedpairs. In such cases, the puncturing scheme is adopted by theURLLC users.

C. CONTRACT FEASIBILITY AND OPTIMALITYUsing matching theory, which is discussed in previoussection, the suitable contracts for URLLC users are designed.To provide the conditions for the feasibility of the designedcontracts, the following conditions apply:Definition 3 (Individual Rationality (I.R)): For any u ∈

U , Uu > 0.IR condition ensures that to encourage the URLLC user forthe superposition scheme, its individual utility should bepositive.Definition 4 (Incentive Compatibility (I.C)): For any u ∈

U , Uu(θn) ≥ Uu(θn′ ).

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IC condition ensures that the URLLC user will choose thecontract designed for its own type θn instead of other types θn′ .The IR and IC conditions guarantee the feasibility of thecontract.

In addition to the above conditions, there are sufficient andnecessary conditions for the feasibility of the contracts givenas follows:Definition 5 (Necessary Condition): For any u, u′ ∈ U ,

Uu > Uu′ if and only if yuj > yu′j.A similar proof of the Definition 5 is provided in [25]. This

definition states that a URLLC user u who is more willing toopt for superposition has higher utility than a user u′, who isless willing to select superposition.

D. CONTRACT-BASED PROBLEM FORMULATIONAfter solving the adoption of superposition or puncturingscheme xkuj

∗and zkuj

∗for the URLLC users in (10), the rest

of the problem is the power allocation to the URLLC users.In this section, we formulate a contract-based optimizationproblem which is equivalent to (9). The proof of equivalenceis given in Appendix A.

maxp

∑j∈J

Uj, (14)

s.t. Uu ≥ 0, ∀u ∈ U, (I.R), (14a)

Uu(θn) ≥ Uu(θn′ ), ∀u ∈ U, (I.C), (14b)

puj ≥ 0, ∀u ∈ U , j ∈ J . (14c)

The objective (14) is to maximize the profit of BS j. Theconstraints (14a) and (14b) are individual rationality (IR)and incentive compatibility (IC) constraints, respectively.Problem (14) is a constrained maximization problem forPuj and the solution can be found at the boundary ofconstraint (14b). Therefore, optimal power allocation, P∗uj,is performed such that the conditions in (10) are satisfied.Note that, the power allocated to the URLLC user is samefor both puncturing and superposition schemes; however,the URLLC user utility is less in the puncturing case ascompared to the superposition case because the user is notgiven the contribution incentive ςβe.Contract-based resource association is performed as

described in Algorithm 2. The inputs are the total numberof BSs J , total number of URLLC users U , total numberof eMBB users E , set of classification Θ of the URLLCusers’ willingness to opt for superposition, γ , which is theset of SINR levels for the URLLC and eMBB users, and µ(t),which is set of matching pairs. In Algorithm 2, the contractis first designed for every URLLC user u after identifying theclass θn. Next, the feasibility and optimality of the contractare verified such that the URLLC QoS requirements aresatisfied. Then, power allocation is performed by selectingthe superposition or puncturing scheme based on the designedcontract.

V. NUMERICAL RESULTSWe perform extensive simulations to evaluate the proposedcontract-based scheduling scheme in the URLLC and eMBB

Algorithm 2Contract-Based Resource Allocation Algorithm

1: Input: J , U , E , Θ , γ , µ(t)

2: for u = 1 to U do3: Step1: Contract Design4: Identify class θn of each URLLC user u5: Design contract for URLLC user u to superpose with

eMBB user e using the pairing µ(t)

6: Check the contract feasibility and optimality for thematching pair µ(t)

7: Step2:8: if Contract is feasible then9: Compute utility Uu according to (10) for θn ≥ θ

10: else11: Compute utility Uu according to (10) for θn < θ

12: end if13: end for14: Output: P∗jk

coexistence network. Firstly, we model a system havinga single macro BS (MBS) located at the center of ageographical area of 1000 m × 1000 m, with two coexistingeMBB and URLLC networks. We uniformly deploy URLLCand eMBB users in the area, as illustrated in Figure 4.The arrival of a URLLC transmission request is modeledas a Poisson distribution with an arrival rate of λ. Then,we simulate the network for multiple runs to obtain theaverage results with a different number of URLLC users.Figure 4 presents a snapshot of the network topology.Other simulation parameters are summarized in Table 1.We compare the proposed contract-based scheduling schemewith the following two baseline schemes: 1) The ‘‘NoURLLC’’ scheme refers that there are no URLLC users inthe network. This scheme is used to determine the impactof URLLC users and compare the loss in eMBB rate.2) The ‘‘Puncturing’’ scheme refers to the traditional URLLCscheduling scheme in which eMBB traffic is paused duringURLLC transmission.

FIGURE 4. Network topology consisting of a single macro basestatoin (MBS) deployed at the center of the network and a number ofURLLC and eMBB users uniformly deployed in the area.

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TABLE 1. Simulation parameters.

FIGURE 5. Snapshot of the matching pairs of URLLC and eMBB users.

Figure 5 displays the snapshot of the matching pairsof URLLC and eMBB users in the network, where thedots and triangles represent the eMBB and URLLC users,respectively while the same colors are assigned to matchedusers. To construct this topology, the URLLC and eMBBusers are uniformly deployed in the geographical area. Afterthat matching scheme is applied to pair the best suitable usersfor the coexistence scenarios.

Figure 6 shows the dependence of the URLLC utility onthe contract type. It can be observed that the user with certaincontract type gets the maximum utility as compared to theother users. For instance, the user with type θ2 will getmaximum utility on choosing the contract type 2. Thereforeeach URLLC user chooses the contract according to its typemaximize its utility.

Figure 7 displays the eMBB rate against an increasingnumber of URLLC users in the network. It can be observedthat as the number of URLLC users increases, the eMBBrate decreases due to scheduling of the URLLC users. It canalso be seen that the eMBB rate in the contract-based schemeapproaches 63% for the non-URLLC case compared to thepuncturing scheme. This is due to the use of superposition,in which both URLLC and eMBB users operate on the samechannel.

Figure 8 illustrates the BS profit against an increasingnumber of URLLC users in the network. Because the pricepaid by URLLC users is significantly higher than that paid

FIGURE 6. Utility of URLLC users vs. the contract type.

FIGURE 7. eMBB rate vs. the number of URLLC users in the network.

FIGURE 8. BS profit vs. the number of URLLC users in the network.

by eMBB users, the BS profit is increased by serving alarger number of URLLC users. It can be observed that theproposed contract-based scheme provides up to 100.25% ofthe puncturing scheme’s profit. This is due to the fact thatin the contract-based scheme, the BS offers a portion ofthe eMBB profit to the participating URLLC users as anincentive.

Figure 9 illustrates the URLLC network utility againstan increasing number of URLLC users in the network.Because the proposed contract-based scheme use an incentive

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FIGURE 9. URLLC network profit vs. number of URLLC users in thenetwork.

mechanism to encourage the URLLC users for the adoptionof superposition scheme, the URLLC profit using theproposed scheme is greater than the puncturing scheme. Forinstance, when there are 30 number of URLLC users in thenetwork, the proposed contract-based scheme provides up to106% of the NoURLLC scheme’s profit while the puncturingscheme provides only 103% of the profit. The contract-basedscheme also offers a portion of the profit to the participatingURLLC users as an incentive.

FIGURE 10. eMBB rate vs. number of URLLC users in the network fordifferent reliability constraints.

Figure 10 illustrates the effect of various reliability valueson the eMBB rate against an increasing number of URLLCusers in the network. We tested the proposed contract-basedapproach for different values of reliability parameters ε. It canbe observed that the eMBB rate is reduced for high reliabilityvalues. This is due to the fact that the high reliabilityconstraint causes higher SINR requirement for the URLLCusers. As a result of this high SINR requirement of SINRrequirement, the eMBB users are penalized by choosing thepuncturing scheme by the URLLC users to meet the highreliability constraints. Moreover the trends of reduction ineMBB rates with the increase in the number of URLLC usersin the network are observed same as shown in Figure. 7.

VI. CONCLUSIONIn this paper, we have addressed the resource allocationproblem in URLLC and eMBB coexistence networks.We have formulated an optimization problem to maximizethe eMBB network rate with respect to the QoS requirementsimposed by the URLLC traffics in the cellular network. Usingthe puncturing scheme, URLLC users significantly affectthe performance of an eMBB network, therefore, we usedthe contract theory framework to encourage URLLC usersto opt for the superposition scheme such that eMBB losswas minimized. This has been achieved by classifying theURLLC users according to their willingness to opt for thesuperposition scheme, which is favorable for the eMBBnetwork. By using such contracts, resource allocation hasbeen performed to the URLLC users. The numerical resultshave revealed that the contract-based scheme outperformedthe puncturing scheme.

APPENDIX APROOF OF EQUIVALENCE OF PROBLEM (9)AND PROBLEM (14)The utility of the BS Uj in (14) is a function of theachievable rates of eMBB and URLLC users as givenin (11). Therefore maximizing βu and βe is equivalent tomaximizing the corresponding URLLC and eMBB rate.Moreover, the high prices paid by the URLLC users prioritizetheir scheduling over eMBB scheduling. From this pricingmodel, the constraint (9a) is ensured. Further, the individualrationality constraint (14a) ensures the individual utilityof each URLLC user to satisfy the reliability requirementgiven in (9b). Therefore the problem (9) is equivalent toproblem (14).

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AUNAS MANZOOR received the M.S. degreein electrical engineering with a specializationin telecommunication from the National Uni-versity of Science and Technology, Pakistan,in 2015. He is currently pursuing the Ph.D.degree with the Department of Computer Scienceand Engineering, Kyung Hee University, SouthKorea. His research interests are applying ana-lytical techniques for resource management inmobile-cellular networks.

S. M. AHSAN KAZMI received the master’sdegree in communication system engineering fromthe National University of Sciences and Technol-ogy, Pakistan, in 2012, and the Ph.D. degree incomputer science and engineering from KyungHee University, South Korea, in 2017. Since2018, he has been with the Network, Cyber, andInformation Security Laboratory, Secure Systemand Network Engineering, Innopolis University,Russia, where he is currently an Assistant Pro-

fessor. His research interests include applying analytical techniques ofoptimization and game theory to radio resource management for futurecellular networks. He received the Best KHU Thesis Award in engineering,in 2017, and several best paper awards from prestigious conferences.

SHASHI RAJ PANDEY received the B.E. degreein electrical and electronics with a specializationin communication from Kathmandu University,Nepal, in 2013. He is currently pursuing thePh.D. degree in computer science and engineeringwith Kyung Hee University, South Korea. Aftergraduation, he served as a Network Engineerat Huawei Technologies Nepal Co., Pvt., Ltd.,Nepal, from 2013 to 2016. His research interestsinclude network economics, game theory, wireless

communications and networking, and distributed machine learning.

CHOONG SEON HONG (Senior Member, IEEE)received the B.S. and M.S. degrees in electronicengineering from Kyung Hee University, Seoul,South Korea, in 1983 and 1985, respectively, andthe Ph.D. degree from Keio University, Minato,Japan, in 1997. In 1988, he joined Korea TelecomCo., Ltd., where he was involved in broadbandnetworks as a member of the Technical Staff.In 1993, he joined Keio University. He waswith the Telecommunications Network Labora-

tory, Korea Telecom, as a Senior Member of Technical Staff and the Directorof the Networking Research Team until 1999. Since 1999, he has beena Professor with the Department of Computer Science and Engineering,Kyung Hee University. His research interests include future Internet, ad hocnetworks, network management, and network security. He is a member ofthe ACM, IEICE, IPSJ, KIISE, KICS, KIPS, and OSIA. He has servedas the General Chair, a TPC Chair/Member, or an Organizing CommitteeMember for international conferences, such as NOMS, IM, AP-NOMS,E2EMON, CCNC, ADSN, ICPP, DIM, WISA, BcN, TINA, SAINT, andICOIN. In addition, he was an Associate Editor of the IEEE TRANSACTIONS ON

NETWORK AND SERVICE MANAGEMENT and the Journal of Communications andNetworks, and an Associate Technical Editor of the IEEE CommunicationsMagazine. He is currently an Associate Editor of the International Journalof Network Management and Future Internet Journal.

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