SCOTT: Scheduling of Comprehensive Objectives for Tasks with Multitargets in Computing Networks

Local and customized services are realized with new type computing architecture by utilizing the spare resources distributed on the helper nodes (HNs) throughout the network. The heterogeneity of mobile edge and fog computing networks makes them natural to support multitarget tasks, and e ﬃ cient task scheduling is always a fundamental and hot issue in multitask multihelper (MTMH) computing networks. Unlike most of the researches concentrating on the optimization of a single or limited service metrics, this article proposes a service framework for multitarget tasks, which is more universal for future 6G networks supporting customized services. The comprehensive quality of service (CQoS) is constructed to indicate the comprehensive objectives of the task nodes (TNs) with multiple targets. By formulating and transforming the CQoS maximal problem into two one-variable form subproblems, an algorithm named scheduling of comprehensive objectives for tasks with multitargets (SCOTT) is proposed. The SCOTT algorithm achieves the optimal o ﬄ oading service solutions considering service metrics including delay, energy consumption, and economic cost. Extensive numerical simulations are carried out, which indicate that the proposed SCOTT algorithm can e ﬀ ectively achieve the optimal o ﬄ oading solutions including node selection, task division, and transmission power for TNs with various service targets. Moreover, the universal applicability of the SCOTT algorithm is veri ﬁ ed with case studies and numerical results.


Introduction
Benefitted from the development of the technologies including wireless communications and local processing, the world is entering the all-connect era, where the data exchange and computing transfer are ubiquitous [1]. Billions of terminal devices are connected to the network and construct the Internet of Things (IoT) systems, which leads to the exponential growth of the data traffic [2,3]. Fully local processing cannot support applications of all scenes for the reason that local processing capabilities are limited [4]. In the welldeveloped traditional networks, tasks generated at the task nodes (TNs) that exceed the local processing capabilities can be transferred to the central cloud server [4,5]. However, with the explosion of the mobile data generated by the emerging 5G and IoT applications, traditional centralized offloading architecture will bring a heavy burden to the link between the cloud server and the TNs. Besides, the increasing of the network scale and complexity makes the real-time processing and global optimization impractical and challenges the overall service quality [6,7]. To cope with the problems emerged in the upcoming internet of everything, new network architectures that are more flexible and extensible need to be developed; thus, the massive and

Related Works
Real-time performance is an ever-increasing requirement of the network services [20][21][22][23]. Better real-time performance can be achieved through the services provided by the nearby HNs, and this makes the task delay an important scheduling metric of the mobile computing services. Markov decision process approach is adopted to deal with computing task scheduling problem from the cloud to the mobile-edge computing (MEC) server, and delay optimal offloading solution is achieved under a power-constrained condition [20]. In [23], fog computing is integrated with vehicular networks, and a three-layer vehicular fog computing (VFC) mode is constructed to minimize the response time by leveraging moving and parked vehicles as fog nodes. A new hybrid offloading architecture for VFC is proposed in [24], and the node selection is optimized to reduce the offloading delay. In [25], the maximum delay among users in a mobile cloud computing system is minimized by randomization mapping method. In [26], the autonomy of the HNs is taken into consideration when pursing the delay-optimal offloading solution. Based on queueing theory, analytical model is introduced for service delay in [27], and the delayminimized policy is provided when fog computing is introduced as a complement to cloud computing and an essential ingredient of the IoT. Considering the task scheduling problem for multitasks, low processing delay offloading solution for unsplittable tasks is achieved in [13], and the work is extended to splittable tasks in [28].
The decreasing of the distance between the user and server can dramatically reduce the transmission energy consumption [29,30]. Meanwhile, the energy consumption is usually a sensitive metric in computing and IoT networks, for the reason that a large portion of the devices in IoT networks have a limited battery life [31][32][33]. This makes the energy efficiency an influential scheduling metric of the mobile computing services. The energy-efficient task offloading problem in mobile cloud computing networks is considered in [34], in which a distributed energy-efficient dynamic offloading and resource scheduling (eDors) algorithm is proposed. The eDors algorithm achieves the energy-efficient task offloading solution by simultaneously deciding the computation offloading selection, clock frequency control, and transmission power allocation. A task selection and scheduling scheme called CoESMS is introduced in [35], which minimizes the overall energy consumption and makespan through cooperative game theory models. In [33], a wireless powered MEC network architecture is proposed to support task offloading services, and energy-efficient offloading scheme is analyzed to support mobile devices with finite battery life. The authors of [36] proposed a scheduling strategy of the frequency division technique based on machine learning, which achieves good energy consumption minimization performance in mobile edge computation offloading.
In most cases, incentive is essential to get the services from HNs or the mobile service operators. From the view of the HNs, they want to make profit as much as possible based on their own capabilities. From the view of the TNs, they want to minimize their economic cost on condition that the services are satisfactory. Therefore, economic cost of is another important service metric when making scheduling decisions. Game theory is widely adopted in the researches of this area. In [37], a two-stage game in three-layer mobile crowd sensing (MCS) architecture is considered in edge computing networks, and a Markov decision process-(MDP-) based social model is built to achieve the maximal social welfare. A quality-aware traffic offloading (QATO) framework is proposed in [38], incentive schemes are adopted among neighbor nodes to achieve better service quality. Shen et al. [39] proposed an incentive framework for resource sensing based on the Stackelberg game, and the optimal solutions including sensing price and sensing frequency are derived. A trilateral game among service provider, end users, and edge resource owners is modeled in [40], and a two-stage dynamic game is used to evaluate the profit of each participant. In addition, service metrics such as fairness, security, and resilience are widely investigated in mobile computing networks [37,[41][42][43].
Tradeoff between different service metrics is also widely studied in this area. The performance indexes including task delay and energy consumption are abstracted to revenue and cost in the operation process of the fog-enabled computing network [44,45], and game theories are adopted to achieve the balance of payments. In [46], a solution to the helper node location problem is provided, which provides support 2 Wireless Communications and Mobile Computing for mobile users with limited battery while being able to process heavy workloads with low latency constraints. Yang et al. [47] proposed a low complexity algorithm that provides the maximal energy efficiency scheduling decisions under feasible modulation and time allocations. Tradeoff between energy consumption and task delay is achieved by Zhao et al. [48], in which the total energy consumption of multiple mobile devices is minimized subject to bounded-delay requirement. In [49], state-of-the-art studies for the joint wireless power transfer (WPT) and offloading in MEC are compared, and a taxonomy are formulated for the technologies that provide offloading service for smart devices while extending battery lifetime. The user mobility is considered in [50], and a lightweight mobility prediction and offloading (LiMPO) framework using artificial neural networks with less complexity is proposed, which achieves better performances in latency reduction, energy efficiency, and resource utilization. Based on the above literature review, we find that most of the researches on the scheduling of computing services focus on the optimization of a single or very limited kinds of service metrics. However, the applications in future 6G and IoT networks always have various service targets. In addition, mobile computing is always in heterogeneous and MTMH style, which is appropriate for the processing of multitarget tasks. The tasks that are sensitive to different metrics are scheduled together, which have different tendencies of node selection and offloading strategy. To cope with this, it is of great necessary to develop universal task scheduling scheme in computing networks. Thus, the heterogeneous resources distribute on the HNs can be integrated to provide customized services for the comprehensive service objectives of the TNs. Therefore, the main contributions of this paper are summarized as follows: (1) We propose a general service model for multitarget tasks in MTMH computing networks. Heterogeneous service capabilities of the HNs and the various service targets of the TNs are collected at the scheduler. The comprehensive objective of the service is formulated as the comprehensive QoS (CQoS) by weighting the absolute service metrics with service target factors, and scheduling scheme is made aiming to maximize the CQoS (2) Considering the service metrics including task delay, energy consumption, and economic cost, the CQoS maximal problem for the offloading service with three targets is formulated. By transforming the original problem into two one-variable form subproblems, we develop an algorithm named scheduling of comprehensive objectives for tasks with multitargets (SCOTT), which provide the optimal offloading solution including node selection, task division, and transmission power. Case studies are conducted out to further prove the practicability of our proved offloading scheme (3) Extensive simulations in a computing network are carried out to investigate the performance of our proposed scheduling algorithm. Numerical results show that the SCOTT algorithm can effectively obtain the CQoS maximal offloading solution based on multiple available HNs and provide the optimal offloading services for TNs with various targets in different network scenarios The rest of this paper is organized as follows. The general service model for multitarget tasks is introduced in Section 3. In Section 4, we formulate the CQoS and the corresponding optimization problem of the offloading service concerning metrics including delay, energy consumption, and economic cost. In Section 5, the CQoS maximal problem for 3-target tasks is solved, and the SCOTT algorithm is proposed, which provides the optimal offloading solution including node selection, task division, and transmission power. Case studies for the proposed SCOTT algorithm are carried out in Section 6. The numerical estimations are provided in Section 7. Section 8 concludes this paper.

Service Model for Multitarget Tasks
In this section, a general MTMH computing network supporting tasks with N targets is introduced. The service capabilities, service objectives, and service scheme are intergraded to represent the comprehensive satisfactory level of the offloading service, which can guide the direction to achieve the optimal service solutions.
3.1. Task Scheduling in MTMH Computing Networks. As shown in Figure 1, we consider an MTMH mobile computing network consisting of multiple TNs and HNs, which have various service targets and service capabilities. A task scheduler in this network collects these service capabilities from the HNs and the service requests from the TNs and provides the service scheme. The scheduler may be located at the cloud server or a specific HN. In this mobile computing network, the task generated at the TN with size l can be offloaded to the nearby HNs to achieve better task processing quality. The task processing targets of different TNs are always diverse, and the task processing target of a same user can be time-varying. For the service provided by a certain HN, the relationship between the service capabilities and the service targets can be revealed by the goodness of fit between the HN and TN characteristics, which is illustrated in Figure 1. This goodness of fit can reflect the comprehensive satisfactory level of the service, and it depends on the following three elements: (1) The service capabilities of the M HNs, which can be represented by Λ = fΛ 1 , Λ 2 ,⋯Λ M g. The service capabilities of HN i, i.e., Λ i , may consist of the service rate, service energy consumption, service price, and any other elements related to the service process (2) The comprehensive service objective of the TN with multitargets, which can be represented by K = fK 1 , K 2 ,⋯,K N g. The parameter N is the number of the service metrics such as delay and energy 3 Wireless Communications and Mobile Computing consumption. The larger the factor K n is, the more sensitive the TN is to the corresponding service metric (3) The service scheme provided by the scheduler, which can be represented by O = fi, l i , p i g. The parameters i, l i , and p i are the index of the selected HN, the size of the subtask offloaded to the selected HN, and the transmission power of the TN, respectively 3.2. Comprehensive QoS. For a specific task, the service scheme O is provided based on the collected service capability Λ. Then, the absolute service metrics such as service delay and cost can be achieved, which is denoted by S = fS 1 , S 2 ,⋯,S N g. Therefore, we have where ξ is the map function between the service capabilities/scheme and the absolute service metrics. The task has different sensitivities to different service metrics, which are quantized by K n , n = 1, 2, ⋯, N. In order to estimate the service quality in a general way, the absolute service metric S n is weighted by the corresponding service objective factor K n . Then, the summation of the weighted service metrics can be calculated by the scalar product of K and S, i.e., Based on the service scheme O and the service capabilities Λ, we define the weighted summation Q as the CQoS of the service provided for task with service objective K, and this integrated metric Q reveals the goodness of fit between the service provider and service requester.
Taking a look at the expression of CQoS in (2), we find that the only variable is the service scheme S. Therefore, the general optimization problem that achieves the CQoS maximal service scheme O * can be formulated as where F is the set of the available HNs in this computing network.
For any TN with various service objectives in a heterogeneous computing network, the optimization problem P provides the direction to search the CQoS maximal service scheme, no matter what the service capabilities Λ and the service objectives K are. This demonstrates the universal applicability of this service framework.

Offloading Service for 3-Target Tasks
Based on the proposed service framework, the rest of the paper concentrates on the offloading service for 3-target tasks. The service metrics including delay, energy consumption, and economic cost are investigated.

Metric Formulation.
We use K = fK d , K e , K c g to denote the comprehensive service objective of a TN, in which K d , K e , and K c with nonnegative values are the delay factor, energy consumption factor, and the cost factor, respectively. The higher a factor in K is, the more sensitive the task is to the corresponding service metric. In particular, the task with K d ≠ 0 and K e = K c = 0 is completely delay-sensitive, and the delay-minimized offloading scheme achieves the highest service quality for this task.
The service capabilities of an available HN, say HN i, is specified as the explanations of the parameters are summarized in Table 1. The task offloading scheme provided by the task scheduler, i.e., O = fi, l i , p i g, includes the HN selection, task division ðl T , l i Þ, and the task transmission power p i . In other words, the scheduler needs to select a proper HN, determine the offload data size, and provide the optimal transmission power from TN to the selected HN.
Next, we formulate the delay D i , energy consumption E i , and economic cost C i based on Λ i and O. Thus, we can get the absolute service metrics as S = fD i , E i , C i g.
4.1.1. Task Offloading Delay. The overall task offloading delay when HN i is selected includes two parts, i.e., the delay of the local subtask with l T bits and the delay of the offloaded   Wireless Communications and Mobile Computing subtask with l i bits, which are denoted by D Ti and D Oi , respectively. In most applications, the overall delay of the task offloading service is decided by the maximum processing time of the subtasks; thus, we have Following the model in our previous research [41], the time of processing 1 bit data locally is η T /f T , in which f T is the CPU frequency of the TN, and η T is the CPU cycles for processing 1 bit data at the TN. Thus, the local delay D Ti can be expressed as Compared with the local delay, the offloading delay D Oi involves the processing delay in similar form to D Ti , and a transmission delay in addition, i.e., where f i is the CPU frequency of HN i, η i is the CPU cycles for processing 1 bit data at HN i, W is the spectrum bandwidth allocated to the offloading service, and B i is the spectral efficiency of the wireless link from the TN to HN i. Given the terminal transmission power p i , B i is obtained through the Shannon capacity as In the expression of B i , γ i and β i are the path loss and shadowing factors of this wireless link. I i and N 0 are the interference power and the noise power spectral density, respectively.

Task
Offloading Energy Consumption. The overall offloading energy consumption E i includes the computing energy consumption and the transmission energy consumption. In this research, we use θ T and θ i to represent the energy consumption per CPU cycle of the TN and HN i. Then, the computing energy consumptions per bit data for the TN and HN i are represented by η T θ T and η i θ i , respectively. Taking the transmission energy consumption with transmission power p i into consideration, the overall energy consumption is formulated as where E T,i = l T η T θ T + ðl i p i /WB i Þ is the energy consumptions of the TN, and E O,i = l i η i θ i is the offloading energy consumption when HN i is selected.

Task Offloading Cost.
Remunerations are requisite in most computing network applications, regardless of the HNs are individual devices with spare resources or specially deployed by operators. The economic cost of the task offloading service is usually proportional to the offloading data size. We use a parameter π i to denote the remuneration of HN i when one bit data is offloaded to it. Therefore, the economic cost of the offloading service with offloading task size l i is Based on the metrics of the task offloading service including D i , E i , and C i , the CQoS and the optimization problem need to be specified.

CQoS and Optimization
Problem. The satisfaction degree of the TN for the service provided by the computing network depends on both the service target of the task itself which indicates that task offloading schemes with low delay, low energy consumption, and low economic cost can achieve high comprehensive service qualities, and the impact of specific service targets are weighted by the corresponding factors. This is also the reason why there is a reciprocal in (10). Given a selected HN, the CQoS provided above is taken as the utility of the provided service, and it is directly decided by the subtask size l i and the TN transmission power p i . Therefore, we propose the following optimization problem.
where p max is the upper bound of TN transmission power. For each available HN, we need to solve the corresponding optimization problem to find the local optimal offloading solution ð l * i , p * i Þ and the corresponding local maximal CQoS Q * i , i ∈ F. In this way, the global optimal offloading solution O * = ði * , l * i * , p * i * Þ and global maximal CQoS Q * can be obtained by selecting the HN with the highest local maximal CQoS. This scheme is applicable to TNs with differentiated service targets.

SCOTT Algorithm
In this section, we propose the SCOTT algorithm for the scheduling of the 3-target tasks, which solves the CQoS optimization problem by transformed into two one-variable form subproblems. Thus, the global optimal offloading solution O * = ði * , l * i * , p * i * Þ and global maximal CQoS Q * are obtained. 5.1. Problem Transformation. For the original optimization problem P0, the maximization of the local CQoS Q i is equivalent to the minimization of the denominator in (10). Therefore, we can transform P0 into P1 as P1 : min in which Q i1 = Q −1 i . As defined in (4), the overall delay D i of the task offloading service provided by HN i is decided by the larger subtask delay. Then, we have the following proposition. According to Proposition 1, the delay target in P0 and P1 can be represented as K d D Oi , and the subtask size l i should satisfies Therefore, P1 can be transformed into P2 : min Remark 2. The conclusions in Proposition 1 and P2 can be explained as follows. For a certain HN and a subtask size l i , the increase of the transmission power p i cannot continually decrease the overall task offloading delay, for the reason that the local processing capability of the TN is limited. Besides, a larger transmission power will undoubtedly lead to a higher energy consumption and thus a lower CQoS. The correlation between l i and p i in the CQoS maximization problem is revealed by (13).
It is easy to know that problem P2 is not convex. Then, we will further transform P2 into one-variable form to find the optimal offloading solution. For the optimization objective Q i2 , the first derivative with respect to l i is The derivative ∂Q i2 /∂l i is uncorrelated with l i . At the mean time, given the comprehensive service target K = fK d , K e , K c g of the TN and the service capabilities of the HN i, ∂Q i2 /∂l i is directly decided by the TN transmission power p i . As a result, we can divide the value range of p i in P2, i.e., ½0, p max , into two parts, in which ∂Q i2 /∂l i is nonnegative and negative, respectively. As shown below, these two value ranges are denoted as R 1 and R 2 , respectively.
Wireless Communications and Mobile Computing When the subtask size l i increases, the minimization goal Q i2 in P2 is severally monotone increasing in R 1 and monotone decreasing in R 2 . Consequently, the optimal value of l i that minimizes Q i2 in R 1 and R 2 should be lðη T /f T Þ ððη T /f T Þ + ð1/WB i Þ + ðη i /f i ÞÞ −1 and l, respectively.
Based on the above analysis, we can transform the optimization problem P2 into two subproblems as follows: s:t:p i ∈ R 1 : ð20Þ Obviously, P2 − 1 and P2 − 2 are both one-variable form optimization problems. We can solve the original problem P0 by firstly finding the optimal solutions of these two subproblems severally, then achieving optimal CQoS Q * i based on Q * i21 and Q * i22 . The HN with the highest Q * i will be selected as the helper node, and the corresponding task division and transmission power will also be achieved.

Subproblem Solving.
To solve the two subproblems obtained above, the two corresponding value ranges, i.e., R 1 and R 2 , need to be determined first.
The value ranges of P2 − 1 and P2 − 2 are determined by the sign of the gradient ∂Q i2 /∂l i (16). Therefore, the following proposition is provided. Proposition 3. The gradient ∂Q i2 /∂l i is monotone decreasing when p i ∈ ½0,p i and monotone increasing when p i ∈ ðp i ,∞Þ, in whichp i is the only positive solution of the following equation.
Proof. Please refer to Appendix B.
According to the conclusions in Proposition 3, ∂Q i2 /∂l i achieves its minimum value when p i =p i . If ∂Q i2 /∂l i jp i ≥ 0, ∂Q i2 /∂l i is always nonnegative when p i ∈ ½0,∞Þ. Otherwise, ∂Q i2 /∂l i has two zero points in ð0, ∞Þ, which are severally denoted by 'p i and p′ i ('p i < p′ i ). Then, the sign of ∂Q i2 /∂l i can be summarized as: Taking the value range of p i in the original optimization problem P0, i.e., ½0, p max , into consideration (16), a subalgorithm is introduced in Algorithm 1 to achieve R 1 and R 2 .
We need to solve the two subproblems based on the values ranges achieved by Algorithm 1. First, the following proposition are provided for the optimal solutions of P2 − 1.

Proposition 4.
The optimal transmission power p * i1 of the subproblem P2 − 1 and the corresponding optimal subtask size l * i1 are provided as follows: In (25), P i1 = f0, p max ,p i g when the following three conditions are satisfied. Otherwise, P i1 = f0, p max g.

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Proof. Please refer to Appendix C.
When the value range of P2 − 2 is not empty, the following proposition provides the optimal offloading solution for this subproblem, as well as the relationship between Q * i21 and Q * i22 .

Proposition 5.
When R 2 ≠ ∅, the optimal transmission power p * i2 of the subproblem P2 − 2 and the corresponding optimal subtask size l * i2 are provided as follows.
Proof. Please refer to Appendix D.
Remark 6. The conclusions in the above two propositions can be intuitively explained as follows. If the value range of P2 − 2 is not empty, the offloading scheme that achieves the highest CQoS has l * o = l. This means that in the value range R 2 , it is better to offload all the entire task to the HN because of the high cost performance of the offloading service. According to the expression of ∂Q i2 /∂l i in (15), this high cost performance may come from the low processing energy consumption, the low service price, or the high energy consumption factor of the task.
Based on the value ranges achieved by Algorithm 1, Proposition 4 and 5 provide the optimal offloading solution ðl * i1 , p * i1 Þ, ðl * i2 , p * i2 Þ and minimized utilities Q * i21 , Q * i22 of the two subproblems. The local optimal offloading solution ðl * i , p * i Þ and the corresponding local maximal CQoS Q * i are given by This process is introduced in Algorithm 2.

Optimal Offloading Solution.
Given a certain HN, the local optimal offloading solution and the local maximal CQoS are provided by Algorithms 1 and 2. In order to achieve the global CQoS maximal offloading solution O * = ði * , l * i * , p * i * Þ and the corresponding Q * , we propose the SCOTT algorithm in Algorithm 3, in which the HN with the highest local maximal CQoS are selected.

Case Study for SCOTT Algorithm
Now, we investigate the task offloading services of several special cases, which are compared with the existing researches. Thus, the universal applicability of our proposed SCOTT task offloading scheme is further proved. 1: Initialize R 1 = ∅, R 2 = ∅,p i = 'p i = p′ i = 0; 2: According to the system parameters, calculate the value ofp i from K e B i − ðγ i β i /ðI i + WN 0 Þ/ð1 + ðp i γ i β i /ðI i + WN 0 ÞÞÞ ln 2ÞðK d + K e p i Þ = 0 with bisection method; 3: if ∂Q i2 /∂l i jp i ≥ 0 then 4: R 1 = ½0, p max , R 2 = ∅; 5: else 6: Calculate the value of 'p i and p′ i from Algorithm 1: Achieving value ranges. 8 Wireless Communications and Mobile Computing 6.1. Local Processing. The aim of calling for offloading service is to achieve a higher CQoS than local processing. If the cost performance of the offloading service is too low, the TN tends to abandon the offloading service and process the task locally. This happens when the processing efficiency of the corresponding HN is too low, or the economic cost is too high. The lower bound of the CQoS Q is which corresponds to the offloading solution ðl i = 0, p i = 0Þ, i.e., local processing. Substituting this solution into (10), we get Q i = K d lðη T / f T Þ + K e lη T θ T = 1/Q. The SCOTT algorithm minimizes Q i . This guarantees that the offloading solution obtained by our proposed SCOTT algorithms can always achieve the Q * that is no less than Q. Therefore, the SCOTT algorithm is applicable to local processing.

Delay-Sensitive Tasks.
If the comprehensive service objective of a TN is K = fK d > 0, K e = 0, K c = 0g, this task is a delay-sensitive task. This kind of task is not sensitive to the energy consumption or economic cost of the offloading service and focuses on the delay performance.
For this kind of tasks, the optimization goals of P2 and respectively. Besides, the value ranges R 1 and R 2 are obviously ½0, p max and ∅. For delay-sensitive tasks, the SCOTT algorithm achieves the local optimal offloading solution based on the conclusions in Proposition 4. Therefore, the SCOTT algorithm is applicable to delay sensitive tasks. This case corresponds to the problem solved in [26], in which task delay is the minimization goal.
1: Initialize F, Q, L, P as the sets of available HNs, local maximal CQoS, local optimal task division, and the local optimal TN transmission power. 2: while A task is generated do 3: Acquire the TN's service target factor K = fK d , K e , K c g; 4: for each HN i ∈ F do 5: Call Algorithm 1; 6: Call Algorithm 2; 7: Update Q = Q ∪ Q * i ; 8: Update L = L ∪ l * i ; 9: Update P = P ∪ p * i ; 10: end for 11: Get the optimal HN: i * = argmax i∈F Q; 12: Get the optimal offloaded task size: l * i * = argmax l * i ∈L Q; 13: Get the optimal offloading power: p * i * = argmax  Wireless Communications and Mobile Computing 6.3. Economic Cost-Sensitive Tasks. If the comprehensive service objective of a TN is K = fK d = 0, K e = 0, K c > 0g, this task is a economic cost-sensitive task. This kind of task is not sensitive to the processing delay or energy consumption of the offloading service and focuses on the economic cost performance.
For this kind of tasks, local processing is the optimal solution, which can achieve a infinitely high CQoS. The optimization goal of P2 becomes K c l i π i , which is obviously proportional to the offloading task size l i . Besides, the value ranges R 1 and R 2 are obviously ½0, p max and ∅. Based on Proposition 4, the conditions in (27) are not fully satisfied, and Q i 21 is a monotone increasing function of p i . Therefore, the SCOTT algorithms will provide p * i = 0 and l * i = 0 in this case. Therefore, the SCOTT algorithm is applicable to economic cost sensitive tasks. This case can be applied to the case in [39], and the resource sensing frequency corresponds to the offloading task size in this paper.

Economic Cost-Insensitive
Tasks. If the comprehensive service objective of a TN is K = fK d > 0, K e > 0, K c = 0g, this task is not sensitive to the economic cost during the offloading service and tends to achieve low delay and high energy efficiency.
For this kind of tasks, the optimization goal of P2 becomes K d D Oi + K e E i . This will not change the procedure of the SCOTT algorithm, which transforms the original problem into two one-variable form subproblems. Therefore, the SCOTT algorithm is applicable to economic costinsensitive tasks. This case corresponds to the researches seeking the balance between task delay and energy cost, such as the DEBTS algorithm proposed in [51].
We omit the analyses of other cases like energy-sensitive (K = fK d = 0, K e > 0, K c = 0g) tasks, which corresponds to the optimization problems in [41,47]. The above investigations reveal the universal applicability of the SCOTT algorithm for multitarget tasks, and this will be further verified by the numerical simulation results in the next section.

Numerical Results
In this section, plenty of numerical simulations are carried out to investigate the performance of our proposed scheduling scheme. The task offloading solution and the corresponding service performance are evaluated for tasks with various service targets.

Simulation Setting.
A heterogonous computing network is considered, in which HNs with various service capabilities are randomly distributed in the TN-centered computing network. The TN calls for offloading services from the task scheduler, which collect the service objectives of the TN and the service capabilities of the HNs. The offloading subtask is transmitted from the TN to the selected HN through a flat wireless channel with bandwidth of 10 MHz. The interference power I i and the noise power spectral density N 0 are −43 dBm and −173 dBm/Hz, respectively. The path loss factor γ i (in dB) is obtained through 38:46 + 20 log 10 ðd i Þ, where d i (in m) is the distance between the TN and HN i. Besides, a shadowing factor −5 dB is adopted for each HN. The other parameter settings are specified in the corresponding simulation results.

CQoS Maximal Offloading Solution.
Firstly, we investigate the task offloading services through a specific HN. The service objective of a TN is K = f1, 1, 1g, and the task size is 2 Mbits. The capabilities of the TN and HN i are provided in Table 2. Figure 2 shows the local maximal CQoS Q * i and the weighted service metrics including delay metric K d D i , energy consumption metric K e E i , and the economic cost metric K c C i . In Figure 1, we plot the local maximal CQoS of the offloading service provided by HN i, and the distance between the TN and HN i varies from 10 m to 100 m. With the increasing of the upper bound for the terminal transmission power, the local maximal CQoS increases from a lower bound to an upper bound. When p max = 0, the task has to be processed locally at the TN. Therefore, the lower bound in Figure 1 is the CQoS of local processing, i.e., Q, which has been discussed in Section 6. The weighted metrics of local processing are shown in Figure 1 ðp max = 0Þ. A higher p max helps achieve lower task delay and energy consumption metrics, but a higher economic cost metric at the same time, which is revealed by the numerical results in Figure 1. When p max increases continually, the energy consumption of the offloading service can not continually decreases. Because the energy consumption for transforming 1 bit data, i.e., p i /ðWB i Þ, is an increasing function of p i . As a result, an upper bound of Q * i is achieved. The simulations results also show that an HN located close to the TN can achieve a higher CQoS, for the reason that the transmission energy consumption and transmission delay are lower when the distance is small. For an HN that is too far away, the cost performance of the offloading service is too low; thus, the local processing is adopted. For example, the HN that is 100 m away from the TN cannot provide service better than local processing.
In Figure 3, the CQoS maximal task offloading solutions through HNs located at different distances are plotted. As shown in Figure 3(a), the optimal transmission power p * i equals to p max when p max is small. With the increasing of p max , p * i reaches an upper bound, which corresponds to the upper bound of Q * i shown in Figure 2(a). We can also observe that the upper bound of p * i is small when the

Wireless Communications and Mobile
Computing distance is small. It is because that the a small p i can provide a high CQoS in this case. At the same time, the upper bound of p * i is also small when the distance is large. It is because that the increasing of p i cannot provide a small task delay but a high energy consumption in this case. The extreme case in Figure 3(a) is the case when the distance is 100 m, which makes local processing be the optimal offloading solution. Figure 3(b) shows the optimal offloading task size l * i when p max increases. We observe that the larger p max is, the larger the subtask the TN offloads to the HN. For the nearby HNs with high cost performance, offloading the whole task can achieve the maximal CQoS. On the contrary, local processing is preferred when the HN is too far away, and the optimal offloading task size l * i is 0 in this case.

Offloading Service for Multitarget
Tasks. Now, we investigate the task offloading service achieved by our proposed SCOTT algorithm, and three tasks with various service targets are considered. Specifically, the offloading service objectives of the three tasks are f1, 0, 0g, f0, 1, 0g, and f0:1,0:1,1g, respectively. The task size is 2 Mbits, and the upper bound of the transmission power is 4 W. Three HNs with various capabilities are available for the offloading service, and the parameters of the three HNs are provided in Table 3. Besides, the capabilities of the TN are the same with the previous subsection. Figure 4 plots the maximal CQoS Q * i of the three tasks through the three available HNs. It is obvious that HN 1, HN 2, and HN 3 provide the highest CQoS for task 1, task 2, and task 3, respectively. Therefore, the SCOTT algorithm will assign task 1 to HN 1, and so on for the other two tasks.
It is easy to find that the three tasks are sensitive to different service metrics. Task 1 with service objective f1, 0, 0g is a delay-sensitive task; thus, the SCOTT algorithm turns into the DOTS algorithm proposed in [26], which achieves the delay-minimized offloading scheme. Task 2 with service objective f0, 1, 0g is an energy-sensitive task; thus, the SCOTT algorithm turns into the FEMTO algorithm proposed in [41], which achieves the energyminimized offloading scheme. Task 3 with service objective f0:1,0:1,1g is sensitive to service cost. The delay and energy factors of task 3 do not equal to 0 because that the service objective f0, 0, 1g will lead to totally local processing and an infinitely great CQoS. On the other hand, Table 3 reveals that HN 1 has a fast CPU frequency, HN 2 has a low unit processing energy consumption, and HN 3 has a low unit economic cost. The above task and HN characteristics led to the numerical results in Figure 4. In conclusion, the SCOTT algorithm can provide the optimal offloading solution with the maximal CQoS for multitarget tasks, and it can universally cover the task scheduling schemes that concern limited metrics.

CQoS Maximal Offloading in Different Network
Scenarios. Next, the CQoS maximal offloading through SCOTT algorithm in service clusters with different radius and HN amount is evaluated. Figure 5 plots the maximal CQoS of a TN with K = f1, 1, 1g. The HN amount equals to 10, 20, or 30, and the HNs are uniformly distributed in the service cluster with radius ranges from 20 m to 100 m. The parameters f i , θ i , and π i of the HNs follows Gaussian distributions, the mean values of which are 5 GHz, 2 × 10 −10 J/cycle, and 3 × 10 −7 $/bit, respectively.
We can observe from Figure 5 that the CQoS of the offloading service decreases with the increasing of the network radius. The reason is that the transmission delay and transmission energy consumption between the TN and the optimal HN increase with the increasing of the network radius, which lead to higher D i and E i . Besides, a large amount of available HNs can provide a higher CQoS for  Figure 4: Maximal CQoS for 3-target tasks. The service objectives of the three tasks are f1, 0, 0g, f0, 1, 0g, and f0:1,0:1,1g, respectively. Task 1 and Task 2 can be scheduled with DOTS and FEMTO algorithm, respectively.

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Wireless Communications and Mobile Computing the TN. It is because that the probability to find a befitting HN for the TN with specific service objective increases when the HN amount is large.

Conclusions
In order to provide the customized services for the emerging multifarious IoT applications with multiple targets, we propose a general service framework in homogeneous MTMH computing networks, in which the TNs are served according to specific service objectives. The CQoS combining metrics including service delay, energy consumption, and economic cost is formulated to quantify the TN's comprehensive satisfactory level for the provided service. An algorithm named SCOTT is developed, which achieves the CQoS maximal offloading solutions by problem transforming. Numerical results based on extensive simulations in a heterogeneous computing network demonstrate that the proposed algorithm can effectively provide the optimal node selection, task division, and transmission power for the TNs with various service targets. The universal applicability of the task scheduling scheme is also verified by case studies and simulations. Future research directions of this work are the universal scheduling scheme for multitarget tasks of mobile network nodes in a multilayered computing network.
Assume that there is an offloading scheme ðl i , p i Þ for the available HN i, and the corresponding subtask delays satisfy D Ti > D Oi .
Based on this offloading scheme, we can decrease the TN transmission power p i to p i′ = p i − Δ p i , such that D Ti = D Oi . Then, the delay target K d D i = K d max ðD Ti , D Oi Þ and the economic cost target K c C i = K c l i π i remain unchanged.
The energy consumption for the transmission of 1 bit data, i.e., ðA:1Þ is a monotone increasing function of the transmission power p i when p i is nonnegative [41]. So, the decrease of p i leads to a small energy consumption target K e E i = K e ðl T η T θ T + ðl i p i /WB i Þ + l i η i θ i Þ. Therefore, the utility Q i = 1/ðK d D i + K e E i + K c C i Þ can always be increased by this transmission power adjustment, and Q i is not maximized with the given offloading scheme ðl i , p i Þ.
The above proves Proposition 1.

B. Proof of Proposition 3
Take the derivative of ∂Q i2 /∂l i with respect to p i , we get Therefore, G is a monotone increasing function of p i and has a single zero point when p i ∈ ½0,∞Þ. Denote the only zero point of the equation G = 0 asp i . Then, ∂ 2 Q i2 /∂l i ∂p i is positive when p i ∈ ½0,p i and negative when p i ∈ ðp i ,∞Þ. In other words, the gradient ∂Q i2 /∂l i is monotone decreasing when p i ∈ ½0,p i and monotone increasing when p i ∈ ðp i ,∞Þ.