Optimal Cooperative Offloading Scheme for Energy Efficient Multi-Access Edge Computation

The distributed cooperative offloading technique with wireless setting and power transmission provides a possible solution to meet the requirements of next-generation Multi-access Edge Computation (MEC). MEC is a model which avails cloud computing the aptitude to smoothly compute data at the edge of a largely dense network and in nearness to smart communicating devices (SCDs). This paper presents a cooperative offloading technique based on the Lagrangian Suboptimal Convergent Computation Offloading Algorithm (LSCCOA) for multi-access MEC in a distributed Internet of Things (IoT) network. A computational competition of the SCDs for limited resources which tends to obstructs smooth task offloading for MEC in an IoT high demand network is considered. The proposed suboptimal computational algorithm is implemented to perform task offloading which is optimized at the cloud edge server without relocating it to the centralized network. These resulted in a minimized weighted sum of transmit power consumption and outputs as a mixed-integer optimization problem. Also, the derived fast-convergent suboptimal algorithm is implemented to resolve the non-deterministic polynomial-time (NP)-hard problem. In conclusion, simulation results are performed to prove that the proposed algorithm substantially outperforms recent techniques with regards to energy efficiency, energy consumption reduction, throughput, and transmission delay performance.


I. INTRODUCTION
In recent years, the implementation of the internet of things (IoT) network allows smart communicating devices (SCDs) embedded with sensors the capacity to interconnect through internet infrastructures. However, the SCDs are resource-constraint with low processing capacity and limited battery lifetime [1] to fully satisfy the demands of the mobile users. The exponential growth of smart communicating devices requires a high demand for network bandwidth and storage capabilities. In order to overcome the above challenge, multi-access edge computing (MEC) has been initiated.
The associate editor coordinating the review of this manuscript and approving it for publication was Eklas Hossain .
The introduction and recent innovations of MEC have provided SCDs with a systematic network model which avails the usability of cloud computing aptitudes at the radio access network (RAN) edge. MEC is gradually changing cloud computing services to facilitate the high performance of distributed IoT networks [2], [3]. Specifically, MEC offloading can enhance the IoT smart devices by offloading high computation tasks to the proximity of edge servers with the priority to minimize their energy consumption. We can justify the fact that offloading is needed regularly due to limited computational power, low mobile device storage capacity, and high energy consumption. Since the MEC cloud server has a high computation capability, its deployment will significantly boost faster data processing in IoT networks [4], without adding extra processing power. The MEC computation VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ offloading [5] can be performed either locally or the computational task is transfer to the nearest cloud edge server for data processing. Cooperative allocation of the computation task among mobile users can mitigate uneven computation workloads distribution and computation resources. The authors in [6], [7] stated that to achieve a reliable MEC computation offloading in IoT networked devices remains a challenging issue. This has resulted and formed the basis of this research.
In this paper, we propose an energy-efficient suboptimal algorithm for cooperative offloading based on a Lagrangian offloading algorithm for MEC computation in distributed IoT networks. The SCDs compete for limited computation resource that impedes smooth task offloading for multi-access MEC in high demand environments. In the proposed system, task scheduler in each SCD contains dual servers; the local central processor (LCP) which locally executes tasks, and the wireless transmitters (i.e., LTE-A or Wi-Fi) which offloads the task non-locally. Without relocating to the central network, the offloading task will be optimized at the cloud server. The next target will be to minimize the total energy consumed by the SCDs. For this, we mutually optimized the computation speed for data transmission, the transmit power allocation per sub-channel, and the offloading ratio, leading to a mixed-integer optimization problem which is an NP-hard power problem. Using the Lagrangian dual decomposition approach, an algorithm based on suboptimal convergent is proposed to mitigate this problem, and to improve the data transmission throughput which in turn minimizes the energy consumption of computational tasks offloading. Therefore, we summarized our contributions in this paper as follows: • We propose an energy-efficient cooperative offloading algorithm for multi-access edge computing in the distributive IoT network, where the offloading task is optimized at the cloud edge server.
• With the aim of minimizing the total transmission and computational power consumed by the SCDs, our techniques mutually optimized the computation of data transmission speed, offloading ratio, and transmit power allocation per sub-channel and the outcome becomes a problem of mixed-integer optimization. The challenge inner-and inter-coupling that influences each transmitting SCDs is tackled by joint optimization of the computational speed through Dynamic Voltage Scaling (DVS) technique, subchannel distribution, subchannel transmit power, amount of data transmitted per subchannel, and the subchannel offloading ratio.
• We propose a suboptimal convergent algorithm by applying the Lagrangian dual decomposition technique, to improve the NP-hard problem and enhance latency requirements so as to minimize the energy consumed in the computation of SCDs tasks.
• Finally, our proposed technique is validated and the simulation results show a significant out-performance of existing techniques as regards data throughput and energy consumption. The rest of this paper is arranged as follows: Section II contains related works while the system model is contained in Section III. The research problem is formulated in Section IV. Section V describes the Multi-access computation offloading scheme analysis, and the Simulation results for the system performances are presented in Section VI while the Conclusion is stated in Section VII.

II. RELATED WORKS
The advent of MEC has formed a novel computing model to enhance data processing in proximity to SCDs and connected things at the network edge [8]. Many recent works surveyed for cooperative SCDs are aimed to improve the performance of IoT networks, subject resource-intensive constraints such as network bandwidth capacity [9], computation offloading, and energy consumption budgets [10]. In [11], a distribution of computation load for smart mobile devices was studied by employing both computations offloading and radio resource constraints. [12] proposed a clustering algorithm for load balancing in heterogeneous networks to minimize energy consumption while sustaining and satisfying users' demands. The effective computation offloading among the energyconstrained MEC is important to avoid huge computation latency in order to achieve a high QoS in the network.
The overall MEC systems performance solely depends on offloading technique design, which has a close relationship with the type of applications SCDs run. While multiple SCDs simultaneously transmit similar or different highly intensive computation tasks [13], because of parallel local and cloud execution, the ideal system performances do not only assume inner-coupling for each transmitting SCD, but is correspondingly inter-coupled amid SCDs because of the competition for limited transmission resource. The inner-and inter-coupling also affects each other, and therefore complicates multiple SCDs offloading technique and strategy [11].
Recent researches have broadly studied the offloading technique and strategy for multiuser MEC schemes [14]- [16]. Most recent studies have jointly investigated the computation offloading, not just with resource allocation constraints, but coupled with caching techniques [17]. In [18], an energyefficient autonomic offloading (EEAO) technique that jointly applies the physical layer design and latency for application running was designed. The energy consumption was modeled for computation task for identical mobile consumptions in MEC environment. Thus, the computation offloading by mobile SCDs is randomly derived as a partly Markov decision approach to reduce the cost of MEC systems, consisting of the offloading execution time and the energy consumption [19]. In [20], the optimal energy efficiency performance in mobile-edge computing was investigated. The computation offloading technique was observed to have achieved reduced energy consumption for each mobile user in allocated time slot. The authors in [21] studied an energy efficient task offloading (EETO) in 5G MEC based on a two-tier small-cell network setting. By jointly examining the energy cost in offloading task for backhaul communication links, the minimized energy consumption problem was formulated. An algorithm is designed to improve the computation offloading task in order to realize global convergence. Therefore, a joint optimized transmit power, required number of data transmission throughput and the CPU cycles for mobile devices achieved a low energy consumption, however, the systems latency was not greatly improved as expected [22], [23].
Moreover, due to the high demands for SCDs in a computation system, the energy-efficient offloading is critical target in the construction of an effective computation offloading system in MEC networks. In [24], the authors considered some energy-efficient offloading strategies in task computational transcoding for edge-cloud mechanism. An algorithm based on online offloading was proposed with a focus of achieving a minimized energy consumption while reaching low latency. To enhance energy efficiency in MEC, a multiuser-based computation offloading problem was investigated by [25], and [26] used a game theoretic technique to design a distributive algorithm for a wireless network based on multi-channel. Different from these studies, our focus is on improved MEC which does not only minimize energy consumption but also improves throughput and latency between transmitting mobile SCDs. Hence, we propose an optimal cooperative offloading technique to enhance energy efficiency in dynamic IoT networks of the cloud computing system. However, recent works did not give much consideration to the influence terminal execution technique has on multi-access computation which results in highly deteriorated network performance [27]- [31]. This also contributes to the focus of our research.

III. SYSTEM MODEL
The system model consisting of the network, communication and computation models of proposed techniques is analyzed in this section.

A. NETWORK MODEL
As described in Figure 1, a MEC-based cooperative computation offloading setting in IoT Network is considered. In the network, the numbers of SCDs are alternatively enclosed by a base station (BS), a nearby small cell (SC) transmitters, such as Wi-Fi AP or an LTE-A, coupled with a wireless relay (WR). With the aim of availing all transmitting SCDs the MEC services, either a single or multiple MEC servers is linked to both the (BS) and (SC) through the fiber links. Hence, SCDs tasks computations is either offloaded at the (BS) via the connected MEC server, the (SC) connected MEC server, or indirectly to the (BS) through the (WR) and the wireless transmitters (WT ). The fiber links is used in connecting the (SCs) and the (BS) to the central network. With the aim of achieving an efficient spectrum reuse, the same frequency band is shared between the (WR) and the (BS) during computation and task transmission. The rate at which the task arrives at the SCD i's scheduler is given as δ SCD i . The decision of the SCD i task scheduler is implemented according to the offloading probability α i , rate. This represents the probability of offloading an inbound task is to the MEC server. The tasks computed are presumed to be indivisible, therefore it is impossible to further break them down into sub-tasks. The system further assumes a task scheduler is incorporated in all the MEC servers, which either selects to compute an inbound task or to offload the task to the remote cloud. For the SCDs, the inbound task through the MEC server S will either be offloaded remotely to the cloud with a probability β j or can be locally executed with probability (1 − β j ).
In this MEC scenario, assuming SCDs in unit cell will function as [26]. During data processing, the SCDs send SC a request. Using the information gathered the SC fashion out a strategy for computation task offloading and updating independent SCD.
Considering a group of SCDs represented by R = {1, 2, . . . , R} is presented. It is assumed that only one computation task C i is available to be executed on SCD i during the period of computation offloading. Recall that all the computation tasks are indivisible. Therefore, there are two terms that may clearly define the computation task C i i.e., C i = (s i , p i ), where S i represents the size of input data of task C i , while p i represents the amount of LCP sequences required in achieving C i . We assume that there are M uplink channels connected to the BS and represented as M = {1, 2, . . . , M }, and N uplink channels connected to the SC and characterized as N = {1, 2, . . . , N }.
Considering the SCDs features and their tasks, for example the density of workload, the computing capacity, the energy consumption, and the data size of the task, the SCD users are categorized into two. Let λ i ∈ {0, 1} denote the offloading result of task C i , where λ i(0) implies that C i is intended to be accomplished locally at SCD i's LPC, and λ i(1) implies that VOLUME 8, 2020 C i will be offloaded either locally or to the MEC server that is indirectly connected to the k through the WR and the wireless transmitter. This kind of offloading decision is dependent of the quality of communication and the channel.

B. COMMUNICATION MODEL
An identical bandwidth B in the subchannels is solely allocated without channel interference among the SCDs [12], [13]. Assuming P r,m , e r,m and σ 2 indicate the transmit power of SCD r on subchannel m, Gaussian noise, and the coefficient of uplink channel fading from SCD r to subchannel m respectively. Thus, the rate of transmission of SCD r on subchannel m is given by This section describes the computation offloading technique in two scenarios, where U i and V i indicates size of the input data and the latency requirements: • Local computing: Power consumed P by CPU is P = τ S 3 , where τ is the coefficient subject to chip design and S is the computational speed of CPU based on dynamic voltage scaling technique that improves energy management scheme. Assuming the computational speed of SCD is S u i and the task execution time t u i . Therefore, the task execution time is given by And the energy consumed E u i is • Computation Offloading to Central network: Let (1 − γ i )U i denotes the bits offloaded to the MEC cloud server at uplink data ψ(1 − γ i )U i , where ψ is the uplink transmission overhead. Let u r,m represents the size of the data offloaded to subchannel m. Thus, we expressed transmission time as And the energy consumed for transmitting data to the MEC cloud server as where µ denotes the reverse efficiency of power amplifier. It is assumed that cloud task computation capacity is infinite. Thus, we can ignore the cloud computing time. In addition, the downlink transmission cost could be ignored due to less data received compared to the large downlink transmission rate [4], [31]. Table 1 presents a description of all mathematical parameters and their derivations. For the λ i(3) category of SCDs whose task offloading is directed either locally or to the transmitting MEC server which is indirectly connected to base station (k), we set different offloading priorities for them and is defined as where g i,k is set as the systems channel gain. Algorithm 1 illustrates a comprehensive SCD user offloading priority selection.

D. COMPUTATION PROBLEM FORMULATION
The Multi-access computational offloading (MCO) problems P1 . . . P3 are formulated in this section. x r E r (g l r , b r ,m , P r,m , l r,m , λ r ) s.t.D 1 : max{t l r , t a r } ≤ L r , ∀r, 1: for SCD i = 1toR do. 2: for transmission channel j = 1toN do. 3: compute the channel data execution rate t ui of each SCDs as stated in (2), and the energy consumption E ui represented in (3); 4: for transmission channel j = 1toN do 5: if E r ≤ E ui then; 6: i ⇒ λ i(0) ; Selection priority of SCD: where E r (g l r , b r , m , P r,m , l r,m , λ r ) denotes the energy consumption (EC) of SCDs r, and can be represented as E r (g l r , b r ,m , P r,m , l r,m , λ r ) = E l r + E i r . Furthermore, x r , L r, , G l r , and P T r are respectively considered as the weighting measure, computational latency, optimal velocity for computation, and optimal transit power allocation (of SCDs r).
Our objective in P 1 is to lessen the weighted amount of power consumed by communicating devices subject to D 1 − D 9 . In this regard, the weighted sum is considered as the tradeoff of power consumed by the SCDs. The weighting sum value measures relatively in reflection to the importance of SCDs. Technically, SCDs with less residual energy could be assigned greater weighting measures. We therefore explains the constraints as follows; D 1 ensures a guaranteed response time of communicating SCDs; D 2 , D 3 and D 4 represents the maximum computational velocity and the maximum transit power allocation assigned to individual SCD; D 5 and D 6 ensures that all are task offloaded and transmitted over an allocated sub-channel; D 7 and D 8 guarantees the assignment of maximum of one SCD for each sub-channel for uplink communication. Considering that b r,m assumes an integer state, P 1 is a non-deterministic polynomial-time hardness (NP-harder).

IV. MULTI-ACCESS COMPUTATIONAL OFFLOADING SCHEME
In this section, we attempt to derive the multi-access computational offloading, hence, in close forms, transmit power allocation (TPA) and an optimal computation velocity (OCV), is calculated while a suboptimal algorithm based on Lagrangian dual decomposition (LDD) is proposed.

A. OPTIMAL COMPUTATIONAL VELOCITY AND TRANSMIT POWER ALLOCATION
In this subsection, simplifying P 1 by minimizing the variables over g l r and first P r,m we attempt to compute the OCV and TPA. Hence, the optimal power g l r generated for computation is then obtained as While the optimal power auxiliary P r,m derived from (1) is given as Further analyses of the multi-access computational problem in P 1 indicates that at every increase of the optimal power (g l r ), the power consumption of SCDs r also increases in a monotonic form. Hence, t l r ≤ L r is further derived and this further results in g l r ≥ α r λ r J r L r . Therefore, the optimal computational velocity problem (P 2 ) is formulated as; s.t.D 10 : λ r ≤ L r F lr α r J r , ∀r,

B. SUBOPTIMAL LAGRANGIAN DUAL DECOMPOSITION ALGORITHM
This subsection applies the Lagrangian dual decomposition Algorithm (LDDA) to resolve the aforementioned simplified computational problem (P 2 ). Diminishing b r,m to 0 ≤ b r,m ≤ 1, we introduce a fresh variable s r,m = b r,m l r,m , hence, the diminished problem can be stated as P 3 below:

1) OPTIMIZATION VARIABLE UPDATE
The optimized LDD function can be expressed as; as is considered the area consistent with D 9 ,D 10 ,D 14 , and D 16 . Combining D 9 and D 10 will yield 0 ≤ λ r ≤ min 1, L r G lr By denoting the optimal solutions of (13) asb * r,m , s * r,m and λ * r , giving the KKT conditions as: To minimize L(B, S, λ, µ, v, γ ) for given parameters (µ, v, γ ), we solved three subproblems (Q 1 , Q 2 ) and (Q 3 ) as follows:

(Q 2 ): Optimal sub-channel assignment:
Since the OCBs on each sub-channel is achieved, we therefore generate their optimal sub-channel assignment (OSA) as follows: As we substitute (16) into (18) using (13), we obtained the where D r,m is expressed as Beginning from (20), it is expected that the sub-channel will be allocated to the transmitting SCDs with the maximal D r,m , particularly b * r,m = 1, r = arg max 1≤r≤R D r,m 0, else, which rounds b r,m to an integer.

V. SIMULATION RESULTS
Using an LTE-A network coupled with a fiber Wi-Fi network parameter, we performed the following numerical analysis. For our experiment, 80 smart communication devices (SCDs) were randomly deployed within the range of 80m from each network base station (N-BS). Additionally, six SCDs are positioned across the area of network coverage of each access point (AP). Channel gain of the cellular access mode is set as g i,k, = c −σ i,k amid SCD base station k and SCD i, representing c i,k as the spatial separation between base station k and SCD i, while σ = 6 as the factor for network path loss. We also set α i = α(∀i = 1, 2, 3 . . .) and β s = β(∀s = 1, 2, 3 . . .).
Considering | | = 6 MEC servers, each linked to η end-users, which are capable of controlling their task offloading flexibly as their probability of computation offloading change. Figure 2 illustrates the performance of the network average response time against the system offloading probability α of SCDs. From the illustration, the observed SCDs experienced a reduction in their latency by configuring their individual offloading probabilities subsequent to technique we proposed. It is important to note that the latency of local computation severely rely on the competence of computation of each SCDs, however, the reliance system latency on the capabilities of computation is substantially minimized in our proposed cooperative offloading scheme. For example, assuming the clock frequency cf i (LCP processing cycles/second) for SCD i's increases from 200MHz to 300MHz, the local computations average response time will decrease from 14.5 s to 3.2s, as against 1.9s to 1.4s performance in our proposed technique.
We further examine the relevance of the coordination between the remote cloud and MEC servers in Figure 3. Our observation proves that although response time is minimized in the remote cloud-computing when compared to the edgeonly computation, however, our proposed technique significantly outperforms both techniques, as long as the MEC servers' offloading probability α is set accordingly.
Our proposed Lagrangian LSCCOA algorithm is compared against EEAO proposed in [18] and EETO in [21] for energy efficiency for different number of SCDs in Figure 4. Considering EEAO and EETO, their objectives concentrated mainly on minimizing energy consumed in sub-channel assignment and the distribution of power in the system, respectively, However, in our proposed technique, by setting the maximum power for transmission at 40dBm and the system sum-rate coefficient at 0.42.
It is observed that the proposed LSCCOA algorithm outperforms the compared EEAO and EETO in terms of energy efficiency. As the SCDs increases, the EE slightly increase and then stabilizes as computation continues in all the technique. Due to the co-channel interference minimized effect, the transmitting density of all SCDs is minimized as well. However, due to the allocation of more subchannels, the system performance is constrained by the limited system resources as the number of SCDs increases. A decline of EE is also observed with the increasing requirement of minimum data rate in the technique, because, there is need for the base stations to optimize the subchannels transmit power in order VOLUME 8, 2020  to preserve the requirements of the system throughput which negatively affects energy efficiency.
In Figure 5, relative transmission energy consumed by different active SCDs in LSCCOA is observed to be less than that of EEAO and EETO, this is because, our proposed optimal computational transmit power distribution sturdily controls the transmit power existing at the unallocated subchannels necessitated in minimized levels of transmit power. With an increase of the active SCDs, all available spectrums are coordinated at different layers, and thus, significantly improving the interference of the co-channel. Simultaneously, it indicates that the energy efficiency increases alongside the downward minimum targets rate for both LSCCOA, EEAO and EETO, respectively, while the rate of rise declines. This is because when the threshold is high, more active SCDs experience difficulty in attaining the requirements, this in turn exhausts the transmission power required to optimize the systems performance. Therefore, this enhanced performance indicates how the proposed LSCCOA algorithms outperforms the compared techniques. Figure 6 evaluates the average power consumed by the LSCCOA algorithm. In the evaluation, the SCDs power consumption performance with an increase in the number of active SCDs from 60 to 1200 is expressed, and compared against three other techniques. The average power consumption of each SCD in the entire system computation task is approximately 44.206J . As compared with the local system computing technique, although the two compared algorithms save energy to an extent, however, in computation, optimally intended energy conservation is achieved by the proposed LSCCOA through task offloading.
By initiating 60 SCDs in the task computation process, all three techniques manifest an independent power consumption rate of 13.341J , 13.412J , and 14.751J . When the number of SCDs is gradually increased, at 1200 transmitting SCDs, the average power consumed by these SCDs independently increases to 25.002J , 26.521J , and 28.063J , respectively. This is because the same wireless channel resource is accessed concurrently by multiple SCDs for a simultaneous task offloading implementation. Hence, this results in increase of system interference. This interference between each transmitting SCD in the system as described in (13), will result in a minimized quality of communication, and thus, the computational offloading rates. Therefore, as SCDs increase to 1200, several users subscribe to use the local computing technique which results in an increase of the average power consumption of SCDs. Our proposed technique can save at least 58.6% of the power consumption.
Considering system throughput, our proposed algorithm is compared against two other techniques (EEAO and EETO) in the research. Figure 7 indicates that, as 60 SCDs were initiated in the computation process, the techniques all display an average throughput of 5823.52, 6848.51, and 7038.56 (all in bit per seconds), respectively. Although the SCDs throughput in our proposed technique is minimal at the initial stage, but, as the amount of SCDs increased from 60 to 100, further minimization is observed at the throughput rate slope than the compared two techniques. Throughout the entire computation process, it is observed that as the amount of SCDs increases, the throughput of SCDs with respect to our proposed technique grew higher than that in the other techniques. Finally, with 1200 SCDs, the techniques manifest an average throughput of 1166.2, 860.9, and 970.2 (all in bps), respectively. With an increase exponential in the amount of deployed active SCDs, there will be a relative and intensive rise in the joint interference between SCDs.
In addition, uplink data transmission rate will be decreased, which will result in the intensive surge of the power consumed by cloud computing offloading much higher the power consumption of the local MEC computing. Thus, many of the SCDs will implement their computation through the conventional MEC computing, which substitutes for offloading process. Comparing our proposed technique in this regard with the EEAO and EETO algorithms, respectively, it is observed that the throughput tends to go higher while the corresponding decline rate is relatively slowed when measured with our proposed technique.
Comparing the average latency of SCDs task execution in the proposed technique with other two techniques, Figure 8 shows that the average latency of SCDs per task execution is approximately 55.215s within the entire locally SCDs computation technique. Deploying 60 SCDs, the latency of these three techniques are 28.641s, 28.682s, and 32.543s. In comparison with the system overall computation technique, a minimum of 48.90% of this latency is conserved by the proposed technique. When 1200 SCDs are deployed, the respective latency gained by using the four techniques are 39.952s, 40.001s, 44.532s, and 55.215s. When compare with the local computation method, our proposed technique conserves about 45.41% of the computation time. This to some extent higher than what is obtainable in the performance of the compared algorithms. Table 2 below shows a comparison analysis for the performance of all three algorithms with respect to Energy  efficiency, average energy consumption, average throughput performance and Latency performances different numbers of deployed SCDs.

VI. CONCLUSION
This paper has examined and formulated multi-access cooperative computation offloading of SCDs in an IoT network based on the DVS-enabled MEC system. The target is to improve energy efficiency by minimizing the weighted sum of energy consumed by the SCDs. The formulated NP-hard problem was addressed via the application of our proposed LSCCOA Algorithm. Finally, simulation results validate that our proposed technique attains better performance in computation offloading and also optimally performs well at every increase in the amount of SCDs.