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

Authors: Guowei Zhang; Zening Liu; Kunlun Wang; Xiaodong Zang; Yong Zuo; Yang Yang
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

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 efficient 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 offloading 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 effectively achieve the optimal offloading solutions including node selection, task division, and transmission power for TNs with various service targets. Moreover, the universal applicability of the SCOTT algorithm is verified with case studies and numerical results.


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## Body

## 1. 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 well-developed 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 diverse TNs can be efficiently supported, which are more universal for future 6G networks providing customized services.Assisted by technologies including the network function virtualization (NFV) and the software defined network (SDN) [8], the concept of mobile computing has emerged. Mobile computing combines the cloud computing, edge computing [9], and fog computing [10] and provides computing for user services anywhere anytime. In a network supported by mobile computing technology, the networks resources including relaying, caching, and computing are subsided from the central server and extended to the whole network space [11, 12]. The resources are carried by the helper nodes (HNs) distributed throughout the network, which construct the multitask multihelper (MTMH) computing network together with the numerous TNs [13]. This architecture provides a rich collection of the ubiquitous network resources, and it has characteristics such as location awareness, widespread geographical distribution, huge number of nodes, and heterogeneity [14, 15]. For the tasks generated at anywhere of the network, their particular service targets can be satisfied by offloading all the data, or partially, to the proper HNs rather than the only choice, i.e., the central cloud server. Therefore, through jointly scheduling the HNs with various capabilities and TNs with various service targets, mobile computing can achieve better quality of service (QoS) for metrics such as delay, energy consumption, and security [16–18]. The heterogeneities and massiveness of the TNs and HNs make the optimal radio and computing resource management in computing networks challenging [19], which leads to extensive researches on the task scheduling in computing networks.


## 2. Related Works

Real-time performance is an ever-increasing requirement of the network services [20–23]. 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 delay-minimized 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 [31–33]. 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, 41–43].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 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 scenariosThe rest of this paper is organized as follows. The general service model for multitarget tasks is introduced in Section3. 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.


## 3. Service Model for Multitarget Tasks

In this section, a general MTMH computing network supporting tasks withN 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 Figure1, 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 theM HNs, which can be represented by Λ=Λ1,Λ2,⋯ΛM. The service capabilities of HN i, i.e., Λi, 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 byK=K1,K2,⋯,KN. The parameter N is the number of the service metrics such as delay and energy consumption. The larger the factor Kn is, the more sensitive the TN is to the corresponding service metric(3)
The service scheme provided by the scheduler, which can be represented byO=i,li,pi. The parameters i, li, and pi are the index of the selected HN, the size of the subtask offloaded to the selected HN, and the transmission power of the TN, respectivelyFigure 1
Service framework for multitarget tasks in an MTMH computing network. The service capabilities of the HNs and the service requests of the TNs are collected at the task scheduler, which makes the service scheme for the tasks with multitarget.


### 3.2. Comprehensive QoS

For a specific task, the service schemeO 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=S1,S2,⋯,SN. Therefore, we have
(1)S=ξΛ,O,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 byKn,n=1,2,⋯,N. In order to estimate the service quality in a general way, the absolute service metric Sn is weighted by the corresponding service objective factor Kn. Then, the summation of the weighted service metrics can be calculated by the scalar product of K and S, i.e.,
(2)Q=K•S=K•ξΛ,O.Based on the service schemeO 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
(3)P:maxOQ=K•ξΛ,O,s.t.i∈F,0≤li≤l,0≤pi≤pmax,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 problemP 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.


## 3.1. Task Scheduling in MTMH Computing Networks

As shown in Figure1, 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 theM HNs, which can be represented by Λ=Λ1,Λ2,⋯ΛM. The service capabilities of HN i, i.e., Λi, 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 byK=K1,K2,⋯,KN. The parameter N is the number of the service metrics such as delay and energy consumption. The larger the factor Kn is, the more sensitive the TN is to the corresponding service metric(3)
The service scheme provided by the scheduler, which can be represented byO=i,li,pi. The parameters i, li, and pi are the index of the selected HN, the size of the subtask offloaded to the selected HN, and the transmission power of the TN, respectivelyFigure 1
Service framework for multitarget tasks in an MTMH computing network. The service capabilities of the HNs and the service requests of the TNs are collected at the task scheduler, which makes the service scheme for the tasks with multitarget.


## 3.2. Comprehensive QoS

For a specific task, the service schemeO 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=S1,S2,⋯,SN. Therefore, we have
(1)S=ξΛ,O,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 byKn,n=1,2,⋯,N. In order to estimate the service quality in a general way, the absolute service metric Sn is weighted by the corresponding service objective factor Kn. Then, the summation of the weighted service metrics can be calculated by the scalar product of K and S, i.e.,
(2)Q=K•S=K•ξΛ,O.Based on the service schemeO 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
(3)P:maxOQ=K•ξΛ,O,s.t.i∈F,0≤li≤l,0≤pi≤pmax,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 problemP 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.


## 4. 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.


### 4.1. Metric Formulation

We useK=Kd,Ke,Kc to denote the comprehensive service objective of a TN, in which Kd, Ke, and Kc 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 Kd≠0 and Ke=Kc=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 HNi, is specified as Λi=fi,ηi,θi,πi; the explanations of the parameters are summarized in Table 1. The task offloading scheme provided by the task scheduler, i.e., O=i,li,pi, includes the HN selection, task division lT,li, and the task transmission power pi. 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.Table 1
Summary of key notations.
Nota.UnitDescriptionlBitOverall task size of the TN.lTBitSubtask size processed locally at the TN.liBitSubtask size offloaded to HNi.ηTCycle/bitCPU cycles for processing1 bit data at the TN.ηiCycle/bitCPU cycles for processing1 bit data at HN i.fTCycle/sCPU frequency of the TN.fiCycle/sCPU frequency of HNi.θTJ/cycleEnergy consumption per CPU cycle of the TN.θiJ/cycleEnergy consumption per CPU cycle of HNi.πi$/bitThe service price of HNi.WHzSpectrum bandwidth for task offloading.piJ/sTransmission power of the TN to HNi.pmaxJ/sUpper bound of the transmission power of the TN.γi−Path loss factor between the TN and HNi.βi−Shadowing factor between the TN and HNi.IiJ/sInterference power between the TN and HNi.N0J/(s·Hz)Noise power spectral density.Kd/sDelay factor of the comprehensive service objective.Ke/JEnergy consumption factor of the comprehensive service objective.Kc/$Cost factor of the comprehensive service objective.K−Comprehensive service objective.DisTask offloading delay through HNi.EiJTask offloading energy consumption through HNi.Ci$Task offloading economic cost through HNi.Qi−Local CQoS of the offloading service through HNi.Next, we formulate the delayDi, energy consumption Ei, and economic cost Ci based on Λi and O. Thus, we can get the absolute service metrics as S=Di,Ei,Ci.


#### 4.1.1. Task Offloading Delay

The overall task offloading delay when HNi is selected includes two parts, i.e., the delay of the local subtask with lT bits and the delay of the offloaded subtask with li bits, which are denoted by DTi and DOi, 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
(4)Di=maxDTi,DOi.Following the model in our previous research [41], the time of processing 1 bit data locally is ηT/fT, in which fT is the CPU frequency of the TN, and ηT is the CPU cycles for processing 1 bit data at the TN. Thus, the local delay DTi can be expressed as
(5)DTi=lTηTfT.Compared with the local delay, the offloading delayDOi involves the processing delay in similar form to DTi, and a transmission delay in addition, i.e.,
(6)DOi=liηifi+liWBi=li1WBi+ηifi,where fi is the CPU frequency of HN i, ηi is the CPU cycles for processing 1 bit data at HN i, W is the spectrum bandwidth allocated to the offloading service, and Bi is the spectral efficiency of the wireless link from the TN to HN i. Given the terminal transmission power pi, Bi is obtained through the Shannon capacity as
(7)Bi=log21+piγiβiIi+WN0.In the expression ofBi, γi and βi are the path loss and shadowing factors of this wireless link. Ii and N0 are the interference power and the noise power spectral density, respectively.


#### 4.1.2. Task Offloading Energy Consumption

The overall offloading energy consumptionEi includes the computing energy consumption and the transmission energy consumption. In this research, we use θT and θi 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 ηTθT and ηiθi, respectively. Taking the transmission energy consumption with transmission power pi into consideration, the overall energy consumption is formulated as
(8)Ei=ET,i+EOi=lTηTθT+lipiWBi+liηiθi,where ET,i=lTηTθT+lipi/WBi is the energy consumptions of the TN, and EO,i=liηiθi is the offloading energy consumption when HN i is selected.


#### 4.1.3. 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 parameterπi 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 li is
(9)Ci=liπi.Based on the metrics of the task offloading service includingDi, Ei, and Ci, the CQoS and the optimization problem need to be specified.


### 4.2. 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 and the service capabilities of the HNs. For a TN with comprehensive service objectiveK=Kd,Ke,Kc, the weighted offloading service metrics are KdDi, KeEi, and KcCi. Then, we construct the CQoS of the offloading service provided by HN i as
(10)Qi=1KdDi+KeEi+KcCi,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 sizeli and the TN transmission power pi. Therefore, we propose the following optimization problem.
(11)P0:maxli,piQis.t.0≤li≤l0≤pi≤pmax,where pmax 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 li∗,pi∗ and the corresponding local maximal CQoS Qi∗,i∈F. In this way, the global optimal offloading solution O∗=i∗,li∗∗,pi∗∗ 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.


## 4.1. Metric Formulation

We useK=Kd,Ke,Kc to denote the comprehensive service objective of a TN, in which Kd, Ke, and Kc 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 Kd≠0 and Ke=Kc=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 HNi, is specified as Λi=fi,ηi,θi,πi; the explanations of the parameters are summarized in Table 1. The task offloading scheme provided by the task scheduler, i.e., O=i,li,pi, includes the HN selection, task division lT,li, and the task transmission power pi. 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.Table 1
Summary of key notations.
Nota.UnitDescriptionlBitOverall task size of the TN.lTBitSubtask size processed locally at the TN.liBitSubtask size offloaded to HNi.ηTCycle/bitCPU cycles for processing1 bit data at the TN.ηiCycle/bitCPU cycles for processing1 bit data at HN i.fTCycle/sCPU frequency of the TN.fiCycle/sCPU frequency of HNi.θTJ/cycleEnergy consumption per CPU cycle of the TN.θiJ/cycleEnergy consumption per CPU cycle of HNi.πi$/bitThe service price of HNi.WHzSpectrum bandwidth for task offloading.piJ/sTransmission power of the TN to HNi.pmaxJ/sUpper bound of the transmission power of the TN.γi−Path loss factor between the TN and HNi.βi−Shadowing factor between the TN and HNi.IiJ/sInterference power between the TN and HNi.N0J/(s·Hz)Noise power spectral density.Kd/sDelay factor of the comprehensive service objective.Ke/JEnergy consumption factor of the comprehensive service objective.Kc/$Cost factor of the comprehensive service objective.K−Comprehensive service objective.DisTask offloading delay through HNi.EiJTask offloading energy consumption through HNi.Ci$Task offloading economic cost through HNi.Qi−Local CQoS of the offloading service through HNi.Next, we formulate the delayDi, energy consumption Ei, and economic cost Ci based on Λi and O. Thus, we can get the absolute service metrics as S=Di,Ei,Ci.


### 4.1.1. Task Offloading Delay

The overall task offloading delay when HNi is selected includes two parts, i.e., the delay of the local subtask with lT bits and the delay of the offloaded subtask with li bits, which are denoted by DTi and DOi, 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
(4)Di=maxDTi,DOi.Following the model in our previous research [41], the time of processing 1 bit data locally is ηT/fT, in which fT is the CPU frequency of the TN, and ηT is the CPU cycles for processing 1 bit data at the TN. Thus, the local delay DTi can be expressed as
(5)DTi=lTηTfT.Compared with the local delay, the offloading delayDOi involves the processing delay in similar form to DTi, and a transmission delay in addition, i.e.,
(6)DOi=liηifi+liWBi=li1WBi+ηifi,where fi is the CPU frequency of HN i, ηi is the CPU cycles for processing 1 bit data at HN i, W is the spectrum bandwidth allocated to the offloading service, and Bi is the spectral efficiency of the wireless link from the TN to HN i. Given the terminal transmission power pi, Bi is obtained through the Shannon capacity as
(7)Bi=log21+piγiβiIi+WN0.In the expression ofBi, γi and βi are the path loss and shadowing factors of this wireless link. Ii and N0 are the interference power and the noise power spectral density, respectively.


### 4.1.2. Task Offloading Energy Consumption

The overall offloading energy consumptionEi includes the computing energy consumption and the transmission energy consumption. In this research, we use θT and θi 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 ηTθT and ηiθi, respectively. Taking the transmission energy consumption with transmission power pi into consideration, the overall energy consumption is formulated as
(8)Ei=ET,i+EOi=lTηTθT+lipiWBi+liηiθi,where ET,i=lTηTθT+lipi/WBi is the energy consumptions of the TN, and EO,i=liηiθi is the offloading energy consumption when HN i is selected.


### 4.1.3. 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 parameterπi 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 li is
(9)Ci=liπi.Based on the metrics of the task offloading service includingDi, Ei, and Ci, the CQoS and the optimization problem need to be specified.


## 4.1.1. Task Offloading Delay

The overall task offloading delay when HNi is selected includes two parts, i.e., the delay of the local subtask with lT bits and the delay of the offloaded subtask with li bits, which are denoted by DTi and DOi, 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
(4)Di=maxDTi,DOi.Following the model in our previous research [41], the time of processing 1 bit data locally is ηT/fT, in which fT is the CPU frequency of the TN, and ηT is the CPU cycles for processing 1 bit data at the TN. Thus, the local delay DTi can be expressed as
(5)DTi=lTηTfT.Compared with the local delay, the offloading delayDOi involves the processing delay in similar form to DTi, and a transmission delay in addition, i.e.,
(6)DOi=liηifi+liWBi=li1WBi+ηifi,where fi is the CPU frequency of HN i, ηi is the CPU cycles for processing 1 bit data at HN i, W is the spectrum bandwidth allocated to the offloading service, and Bi is the spectral efficiency of the wireless link from the TN to HN i. Given the terminal transmission power pi, Bi is obtained through the Shannon capacity as
(7)Bi=log21+piγiβiIi+WN0.In the expression ofBi, γi and βi are the path loss and shadowing factors of this wireless link. Ii and N0 are the interference power and the noise power spectral density, respectively.


## 4.1.2. Task Offloading Energy Consumption

The overall offloading energy consumptionEi includes the computing energy consumption and the transmission energy consumption. In this research, we use θT and θi 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 ηTθT and ηiθi, respectively. Taking the transmission energy consumption with transmission power pi into consideration, the overall energy consumption is formulated as
(8)Ei=ET,i+EOi=lTηTθT+lipiWBi+liηiθi,where ET,i=lTηTθT+lipi/WBi is the energy consumptions of the TN, and EO,i=liηiθi is the offloading energy consumption when HN i is selected.


## 4.1.3. 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 parameterπi 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 li is
(9)Ci=liπi.Based on the metrics of the task offloading service includingDi, Ei, and Ci, the CQoS and the optimization problem need to be specified.


## 4.2. 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 and the service capabilities of the HNs. For a TN with comprehensive service objectiveK=Kd,Ke,Kc, the weighted offloading service metrics are KdDi, KeEi, and KcCi. Then, we construct the CQoS of the offloading service provided by HN i as
(10)Qi=1KdDi+KeEi+KcCi,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 sizeli and the TN transmission power pi. Therefore, we propose the following optimization problem.
(11)P0:maxli,piQis.t.0≤li≤l0≤pi≤pmax,where pmax 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 li∗,pi∗ and the corresponding local maximal CQoS Qi∗,i∈F. In this way, the global optimal offloading solution O∗=i∗,li∗∗,pi∗∗ 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.


## 5. 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 solutionO∗=i∗,li∗∗,pi∗∗ and global maximal CQoS Q∗ are obtained.


### 5.1. Problem Transformation

For the original optimization problemP0, the maximization of the local CQoS Qi is equivalent to the minimization of the denominator in (10). Therefore, we can transform P0 into P1 as
(12)P1:minli,piQi1=KdDi+KeEi+KcCis.t.0≤li≤l0≤pi≤pmax,in which Qi1=Qi−1.As defined in (4), the overall delay Di of the task offloading service provided by HN i is decided by the larger subtask delay. Then, we have the following proposition.Proposition 1.
When the CQoSQi is maximized under the condition that Di=maxDT,i,DOi, the offloading delay DOi is no less than the local delay DT,i.Proof.
Please refer to AppendixA.According to Proposition1, the delay target in P0 and P1 can be represented as KdDOi, and the subtask size li should satisfies
(13)DTi≤DOi⟹l−liηTfT≤li1WBi+ηifi⟹lηTfTηTfT+1WBi+ηifi−1≤li<l.Therefore,P1 can be transformed into
(14)P2:minli,piQi2=KdDOi+KeEi+KcCi=Kdli1WBi+ηifi+Kcliπi+KelηTθT+lipiWBi+ηiθi−ηTθTs.t.lηTfTηTfT+1WBi+ηifi−1≤li≤l0≤pi≤pmax.Remark 2.
The conclusions in Proposition1 and P2 can be explained as follows. For a certain HN and a subtask size li, the increase of the transmission power pi 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 li and pi in the CQoS maximization problem is revealed by (13).It is easy to know that problemP2 is not convex. Then, we will further transform P2 into one-variable form to find the optimal offloading solution. For the optimization objective Qi2, the first derivative with respect to li is
(15)∂Qi2∂li=Kd1WBi+ηifi+KepiWBi+ηiθi−ηTθT+Kcπi.The derivative∂Qi2/∂li is uncorrelated with li. At the mean time, given the comprehensive service target K=Kd,Ke,Kc of the TN and the service capabilities of the HN i, ∂Qi2/∂li is directly decided by the TN transmission power pi. As a result, we can divide the value range of pi in P2, i.e., 0,pmax, into two parts, in which ∂Qi2/∂li is nonnegative and negative, respectively. As shown below, these two value ranges are denoted as R1 and R2, respectively.
(16)R1=0,pmax∩pi∂Qi2∂li≥0,(17)R2=0,pmax∩pi∂Qi2∂li<0.When the subtask sizeli increases, the minimization goal Qi2 in P2 is severally monotone increasing in R1 and monotone decreasing in R2. Consequently, the optimal value of li that minimizes Qi2 in R1 and R2 should be lηT/fTηT/fT+1/WBi+ηi/fi−1 and l, respectively.Based on the above analysis, we can transform the optimization problemP2 into two subproblems as follows:
(18)P2−1:(19)minpiQi21=KdDOi+KeEi+KcCili=lηT/fTηT/fT+1/WBi+ηi/fi−1(20)s.t.pi∈R1.(21)P2−2:(22)minpiQi22=KdDOi+KeEi+KcCili=l(23)s.t.pi∈R2.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 Qi∗ based on Qi21∗ and Qi22∗. The HN with the highest Qi∗ will be selected as the helper node, and the corresponding task division and transmission power will also be achieved.


### 5.2. Subproblem Solving

To solve the two subproblems obtained above, the two corresponding value ranges, i.e.,R1 and R2, need to be determined first.The value ranges ofP2−1 and P2−2 are determined by the sign of the gradient ∂Qi2/∂li (16). Therefore, the following proposition is provided.Proposition 3.
The gradient∂Qi2/∂li is monotone decreasing when pi∈0,p^i and monotone increasing when pi∈p^i,∞, in which p^i is the only positive solution of the following equation.
(24)KeBi−γiβi/Ii+WN01+piγiβi/Ii+WN0Ii+WN0ln2Kd+Kepi=0.Proof.
Please refer to AppendixB.According to the conclusions in Proposition3, ∂Qi2/∂li achieves its minimum value when pi=p^i. If ∂Qi2/∂lip^i≥0, ∂Qi2/∂li is always nonnegative when pi∈0,∞. Otherwise, ∂Qi2/∂li has two zero points in 0,∞, which are severally denoted by `pi and p′i (`pi<p′i). Then, the sign of ∂Qi2/∂li can be summarized as:When∂Qi2/∂lip^i≥0, ∂Qi2/∂li≥0 in 0,∞.When∂Qi2/∂lip^i<0, ∂Qi2/∂li≥0 in 0,`pi and p′i,∞ and ∂Qi2/∂li<0 in `pi,p′i.Taking the value range ofpi in the original optimization problem P0, i.e., 0,pmax, into consideration (16), a subalgorithm is introduced in Algorithm 1 to achieve R1 and R2.Algorithm 1: Achieving value ranges.
1: InitializeR1=∅, R2=∅, p^i=`pi=p′i=0;2: According to the system parameters, calculate the value ofp^i fromKeBi−γiβi/Ii+WN0/1+piγiβi/Ii+WN0ln2Kd+Kepi=0with bisection method;3:if∂Qi2/∂lip^i≥0then4:R1=0,pmax, R2=∅;5:else6: Calculate the value of`pi and p′i fromKd1/WBi+ηi/fi+Kepi/WBi+ηiθi−ηTθT+Kcπi=0with bisection method;7:ifpmax≤`pithen8:R1=0,pmax, R2=∅;9:end if10:if`pi<pmax<p′ithen11:R1=0,`pi, R2=p′i,pmax;12:end if13:ifpmax≥p′ithen14:R1=0,`pi∩p′i,pmax, R2=`pi,p′i;15:end if16:end if17:returnR1, R2, p^i, `pi, p′i;We need to solve the two subproblems based on the values ranges achieved by Algorithm1. First, the following proposition are provided for the optimal solutions of P2−1.Proposition 4.
The optimal transmission powerpi1∗ of the subproblem P2−1 and the corresponding optimal subtask size li1∗ are provided as follows:
(25)pi1∗=`pi,R1≠0,pmax,argminpi1∈Pi1Qi21,R1=0,pmax,(26)li1∗=lηTfTηTfT+1WBi+ηifi−1pi=pi1∗,
In (25), Pi1=0,pmax,p˘i when the following three conditions are satisfied. Otherwise, Pi1=0,pmax.
(27)α2ln2α3<1,f1<0,f1+pmaxγiβiIi+WN0>0.
The functionfx is
(28)fx=α1+α2x+α3log2x,in which the three parameters, i.e., α1, α2, and α3, are
(29)α1=−KeηTfT+ηifiWln2+Ke,α2=KeηTfT+ηifi−KdηTfT−Keηiθi−ηTθT−KcπiγiβiIi+WN0Wln2,α3=KeηTfT+ηifiW>0.
WhenPi1 is 0,pmax,p˘i, p˘i is the only solution of f1+piγiβi/Ii+WN0=0 valued in 0,pmax.Proof.
Please refer to AppendixC.When the value range ofP2−2 is not empty, the following proposition provides the optimal offloading solution for this subproblem, as well as the relationship between Qi21∗ and Qi22∗.Proposition 5.
WhenR2≠∅, the optimal transmission power pi2∗ of the subproblem P2−2 and the corresponding optimal subtask size li2∗ are provided as follows.
(30)pi2∗=pmax,pmax≤p^i,p^i,pmax>p^i,(31)li2∗=l.
In addition, there isQi21∗≥Qi22∗ when R2≠∅.Proof.
Please refer to AppendixD.Remark 6.
The conclusions in the above two propositions can be intuitively explained as follows. If the value range ofP2−2 is not empty, the offloading scheme that achieves the highest CQoS has lo∗=l. This means that in the value range R2, 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 ∂Qi2/∂li 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 Algorithm1, Proposition 4 and 5 provide the optimal offloading solution li1∗,pi1∗,li2∗,pi2∗ and minimized utilities Qi21∗, Qi22∗ of the two subproblems. The local optimal offloading solution li∗,pi∗ and the corresponding local maximal CQoS Qi∗ are given by
(32)Qi∗=1Qi21∗,R2=∅,1Qi22∗,R2≠∅,li∗,pi∗=li1∗,pi1∗,R2=∅,li2∗,pi2∗,R2≠∅.This process is introduced in Algorithm2.Algorithm 2: Local CQoS maximal algorithm.
1:InputR1, R2, p^i, `pi, p′i;2:ifR2=∅then3:  Calculate the optimal offloading solutions ofP2−1, i.e., li1∗, pi1∗, with (25) and (26);4:  Calculate the minimized utilities ofP2−1 byQi21∗=KdDOi+KeEi+KcCili=li1∗,pi=pi1∗;5:  Setli∗=li1∗, pi∗=pi1∗, Qi∗=Qi21∗−1;6:else7:  Calculate the optimal offloading solutions ofP2−2, i.e., li2∗, pi2∗, with (30) and (31);8:  Calculate the minimized utilities ofP2−2 byQi22∗=KdDOi+KeEi+KcCili=li2∗,pi=pi2∗;9:  Setli∗=li2∗, pi∗=pi2∗, Qi∗=Qi22∗−1;10:end if11:returnli∗,pi∗, Qi∗;


### 5.3. Optimal Offloading Solution

Given a certain HN, the local optimal offloading solution and the local maximal CQoS are provided by Algorithms1 and 2. In order to achieve the global CQoS maximal offloading solution O∗=i∗,li∗∗,pi∗∗ and the corresponding Q∗, we propose the SCOTT algorithm in Algorithm 3, in which the HN with the highest local maximal CQoS are selected.Algorithm 3: SCOTT algorithm.
1: InitializeF, Q, L, P as the sets of available HNs, local maximal CQoS, local optimal task division, and the local optimal TN transmission power.2:whileA task is generated do3: Acquire the TN’s service target factorK=Kd,Ke,Kc;4:for each HN i∈Fdo5:  Call Algorithm1;6:  Call Algorithm2;7:  UpdateQ=Q∪Qi∗;8:  UpdateL=L∪li∗;9:  UpdateP=P∪pi∗;10:end for11: Get the optimal HN:i∗=argmaxi∈FQ;12: Get the optimal offloaded task size:li∗∗=argmaxli∗∈LQ;13: Get the optimal offloading power:pi∗∗=argmaxpi∗∈PQ;14: Get the maximal CQoS:Q∗=maxQ;15:returnO∗=i∗,li∗∗,pi∗∗,Q∗;16:end while


## 5.1. Problem Transformation

For the original optimization problemP0, the maximization of the local CQoS Qi is equivalent to the minimization of the denominator in (10). Therefore, we can transform P0 into P1 as
(12)P1:minli,piQi1=KdDi+KeEi+KcCis.t.0≤li≤l0≤pi≤pmax,in which Qi1=Qi−1.As defined in (4), the overall delay Di of the task offloading service provided by HN i is decided by the larger subtask delay. Then, we have the following proposition.Proposition 1.
When the CQoSQi is maximized under the condition that Di=maxDT,i,DOi, the offloading delay DOi is no less than the local delay DT,i.Proof.
Please refer to AppendixA.According to Proposition1, the delay target in P0 and P1 can be represented as KdDOi, and the subtask size li should satisfies
(13)DTi≤DOi⟹l−liηTfT≤li1WBi+ηifi⟹lηTfTηTfT+1WBi+ηifi−1≤li<l.Therefore,P1 can be transformed into
(14)P2:minli,piQi2=KdDOi+KeEi+KcCi=Kdli1WBi+ηifi+Kcliπi+KelηTθT+lipiWBi+ηiθi−ηTθTs.t.lηTfTηTfT+1WBi+ηifi−1≤li≤l0≤pi≤pmax.Remark 2.
The conclusions in Proposition1 and P2 can be explained as follows. For a certain HN and a subtask size li, the increase of the transmission power pi 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 li and pi in the CQoS maximization problem is revealed by (13).It is easy to know that problemP2 is not convex. Then, we will further transform P2 into one-variable form to find the optimal offloading solution. For the optimization objective Qi2, the first derivative with respect to li is
(15)∂Qi2∂li=Kd1WBi+ηifi+KepiWBi+ηiθi−ηTθT+Kcπi.The derivative∂Qi2/∂li is uncorrelated with li. At the mean time, given the comprehensive service target K=Kd,Ke,Kc of the TN and the service capabilities of the HN i, ∂Qi2/∂li is directly decided by the TN transmission power pi. As a result, we can divide the value range of pi in P2, i.e., 0,pmax, into two parts, in which ∂Qi2/∂li is nonnegative and negative, respectively. As shown below, these two value ranges are denoted as R1 and R2, respectively.
(16)R1=0,pmax∩pi∂Qi2∂li≥0,(17)R2=0,pmax∩pi∂Qi2∂li<0.When the subtask sizeli increases, the minimization goal Qi2 in P2 is severally monotone increasing in R1 and monotone decreasing in R2. Consequently, the optimal value of li that minimizes Qi2 in R1 and R2 should be lηT/fTηT/fT+1/WBi+ηi/fi−1 and l, respectively.Based on the above analysis, we can transform the optimization problemP2 into two subproblems as follows:
(18)P2−1:(19)minpiQi21=KdDOi+KeEi+KcCili=lηT/fTηT/fT+1/WBi+ηi/fi−1(20)s.t.pi∈R1.(21)P2−2:(22)minpiQi22=KdDOi+KeEi+KcCili=l(23)s.t.pi∈R2.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 Qi∗ based on Qi21∗ and Qi22∗. The HN with the highest Qi∗ will be selected as the helper node, and the corresponding task division and transmission power will also be achieved.


## 5.2. Subproblem Solving

To solve the two subproblems obtained above, the two corresponding value ranges, i.e.,R1 and R2, need to be determined first.The value ranges ofP2−1 and P2−2 are determined by the sign of the gradient ∂Qi2/∂li (16). Therefore, the following proposition is provided.Proposition 3.
The gradient∂Qi2/∂li is monotone decreasing when pi∈0,p^i and monotone increasing when pi∈p^i,∞, in which p^i is the only positive solution of the following equation.
(24)KeBi−γiβi/Ii+WN01+piγiβi/Ii+WN0Ii+WN0ln2Kd+Kepi=0.Proof.
Please refer to AppendixB.According to the conclusions in Proposition3, ∂Qi2/∂li achieves its minimum value when pi=p^i. If ∂Qi2/∂lip^i≥0, ∂Qi2/∂li is always nonnegative when pi∈0,∞. Otherwise, ∂Qi2/∂li has two zero points in 0,∞, which are severally denoted by `pi and p′i (`pi<p′i). Then, the sign of ∂Qi2/∂li can be summarized as:When∂Qi2/∂lip^i≥0, ∂Qi2/∂li≥0 in 0,∞.When∂Qi2/∂lip^i<0, ∂Qi2/∂li≥0 in 0,`pi and p′i,∞ and ∂Qi2/∂li<0 in `pi,p′i.Taking the value range ofpi in the original optimization problem P0, i.e., 0,pmax, into consideration (16), a subalgorithm is introduced in Algorithm 1 to achieve R1 and R2.Algorithm 1: Achieving value ranges.
1: InitializeR1=∅, R2=∅, p^i=`pi=p′i=0;2: According to the system parameters, calculate the value ofp^i fromKeBi−γiβi/Ii+WN0/1+piγiβi/Ii+WN0ln2Kd+Kepi=0with bisection method;3:if∂Qi2/∂lip^i≥0then4:R1=0,pmax, R2=∅;5:else6: Calculate the value of`pi and p′i fromKd1/WBi+ηi/fi+Kepi/WBi+ηiθi−ηTθT+Kcπi=0with bisection method;7:ifpmax≤`pithen8:R1=0,pmax, R2=∅;9:end if10:if`pi<pmax<p′ithen11:R1=0,`pi, R2=p′i,pmax;12:end if13:ifpmax≥p′ithen14:R1=0,`pi∩p′i,pmax, R2=`pi,p′i;15:end if16:end if17:returnR1, R2, p^i, `pi, p′i;We need to solve the two subproblems based on the values ranges achieved by Algorithm1. First, the following proposition are provided for the optimal solutions of P2−1.Proposition 4.
The optimal transmission powerpi1∗ of the subproblem P2−1 and the corresponding optimal subtask size li1∗ are provided as follows:
(25)pi1∗=`pi,R1≠0,pmax,argminpi1∈Pi1Qi21,R1=0,pmax,(26)li1∗=lηTfTηTfT+1WBi+ηifi−1pi=pi1∗,
In (25), Pi1=0,pmax,p˘i when the following three conditions are satisfied. Otherwise, Pi1=0,pmax.
(27)α2ln2α3<1,f1<0,f1+pmaxγiβiIi+WN0>0.
The functionfx is
(28)fx=α1+α2x+α3log2x,in which the three parameters, i.e., α1, α2, and α3, are
(29)α1=−KeηTfT+ηifiWln2+Ke,α2=KeηTfT+ηifi−KdηTfT−Keηiθi−ηTθT−KcπiγiβiIi+WN0Wln2,α3=KeηTfT+ηifiW>0.
WhenPi1 is 0,pmax,p˘i, p˘i is the only solution of f1+piγiβi/Ii+WN0=0 valued in 0,pmax.Proof.
Please refer to AppendixC.When the value range ofP2−2 is not empty, the following proposition provides the optimal offloading solution for this subproblem, as well as the relationship between Qi21∗ and Qi22∗.Proposition 5.
WhenR2≠∅, the optimal transmission power pi2∗ of the subproblem P2−2 and the corresponding optimal subtask size li2∗ are provided as follows.
(30)pi2∗=pmax,pmax≤p^i,p^i,pmax>p^i,(31)li2∗=l.
In addition, there isQi21∗≥Qi22∗ when R2≠∅.Proof.
Please refer to AppendixD.Remark 6.
The conclusions in the above two propositions can be intuitively explained as follows. If the value range ofP2−2 is not empty, the offloading scheme that achieves the highest CQoS has lo∗=l. This means that in the value range R2, 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 ∂Qi2/∂li 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 Algorithm1, Proposition 4 and 5 provide the optimal offloading solution li1∗,pi1∗,li2∗,pi2∗ and minimized utilities Qi21∗, Qi22∗ of the two subproblems. The local optimal offloading solution li∗,pi∗ and the corresponding local maximal CQoS Qi∗ are given by
(32)Qi∗=1Qi21∗,R2=∅,1Qi22∗,R2≠∅,li∗,pi∗=li1∗,pi1∗,R2=∅,li2∗,pi2∗,R2≠∅.This process is introduced in Algorithm2.Algorithm 2: Local CQoS maximal algorithm.
1:InputR1, R2, p^i, `pi, p′i;2:ifR2=∅then3:  Calculate the optimal offloading solutions ofP2−1, i.e., li1∗, pi1∗, with (25) and (26);4:  Calculate the minimized utilities ofP2−1 byQi21∗=KdDOi+KeEi+KcCili=li1∗,pi=pi1∗;5:  Setli∗=li1∗, pi∗=pi1∗, Qi∗=Qi21∗−1;6:else7:  Calculate the optimal offloading solutions ofP2−2, i.e., li2∗, pi2∗, with (30) and (31);8:  Calculate the minimized utilities ofP2−2 byQi22∗=KdDOi+KeEi+KcCili=li2∗,pi=pi2∗;9:  Setli∗=li2∗, pi∗=pi2∗, Qi∗=Qi22∗−1;10:end if11:returnli∗,pi∗, Qi∗;


## 5.3. Optimal Offloading Solution

Given a certain HN, the local optimal offloading solution and the local maximal CQoS are provided by Algorithms1 and 2. In order to achieve the global CQoS maximal offloading solution O∗=i∗,li∗∗,pi∗∗ and the corresponding Q∗, we propose the SCOTT algorithm in Algorithm 3, in which the HN with the highest local maximal CQoS are selected.Algorithm 3: SCOTT algorithm.
1: InitializeF, Q, L, P as the sets of available HNs, local maximal CQoS, local optimal task division, and the local optimal TN transmission power.2:whileA task is generated do3: Acquire the TN’s service target factorK=Kd,Ke,Kc;4:for each HN i∈Fdo5:  Call Algorithm1;6:  Call Algorithm2;7:  UpdateQ=Q∪Qi∗;8:  UpdateL=L∪li∗;9:  UpdateP=P∪pi∗;10:end for11: Get the optimal HN:i∗=argmaxi∈FQ;12: Get the optimal offloaded task size:li∗∗=argmaxli∗∈LQ;13: Get the optimal offloading power:pi∗∗=argmaxpi∗∈PQ;14: Get the maximal CQoS:Q∗=maxQ;15:returnO∗=i∗,li∗∗,pi∗∗,Q∗;16:end while


## 6. 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.


### 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 CQoSQ is
(33)Q¯=1KdDi+KeEi+KcCi=1KdlηT/fT+KelηTθT,which corresponds to the offloading solution li=0,pi=0, i.e., local processing.Substituting this solution into (10), we get Qi=KdlηT/fT+KelηTθT=1/Q¯. The SCOTT algorithm minimizes Qi. 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.


### 6.2. Delay-Sensitive Tasks

If the comprehensive service objective of a TN isK=Kd>0,Ke=0,Kc=0, 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 ofP2 and P2−1 become Kdli1/WBi+ηi/fi and KdlηT/fTηT/fT1/WBi1/WBi+ηi/fiηi/fi/ηT/fT+1/WBi+ηi/fi, respectively. Besides, the value ranges R1 and R2 are obviously 0,pmax 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.


### 6.3. Economic Cost-Sensitive Tasks

If the comprehensive service objective of a TN isK=Kd=0,Ke=0,Kc>0, 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 ofP2 becomes Kcliπi, which is obviously proportional to the offloading task size li. Besides, the value ranges R1 and R2 are obviously 0,pmax and ∅. Based on Proposition 4, the conditions in (27) are not fully satisfied, and Qi21 is a monotone increasing function of pi. Therefore, the SCOTT algorithms will provide pi∗=0 and li∗=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.


### 6.4. Economic Cost-Insensitive Tasks

If the comprehensive service objective of a TN isK=Kd>0,Ke>0,Kc=0, 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 ofP2 becomes KdDOi+KeEi. 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 cost-insensitive 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=Kd=0,Ke>0,Kc=0) 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.


## 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 CQoSQ is
(33)Q¯=1KdDi+KeEi+KcCi=1KdlηT/fT+KelηTθT,which corresponds to the offloading solution li=0,pi=0, i.e., local processing.Substituting this solution into (10), we get Qi=KdlηT/fT+KelηTθT=1/Q¯. The SCOTT algorithm minimizes Qi. 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.


## 6.2. Delay-Sensitive Tasks

If the comprehensive service objective of a TN isK=Kd>0,Ke=0,Kc=0, 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 ofP2 and P2−1 become Kdli1/WBi+ηi/fi and KdlηT/fTηT/fT1/WBi1/WBi+ηi/fiηi/fi/ηT/fT+1/WBi+ηi/fi, respectively. Besides, the value ranges R1 and R2 are obviously 0,pmax 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.


## 6.3. Economic Cost-Sensitive Tasks

If the comprehensive service objective of a TN isK=Kd=0,Ke=0,Kc>0, 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 ofP2 becomes Kcliπi, which is obviously proportional to the offloading task size li. Besides, the value ranges R1 and R2 are obviously 0,pmax and ∅. Based on Proposition 4, the conditions in (27) are not fully satisfied, and Qi21 is a monotone increasing function of pi. Therefore, the SCOTT algorithms will provide pi∗=0 and li∗=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.


## 6.4. Economic Cost-Insensitive Tasks

If the comprehensive service objective of a TN isK=Kd>0,Ke>0,Kc=0, 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 ofP2 becomes KdDOi+KeEi. 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 cost-insensitive 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=Kd=0,Ke>0,Kc=0) 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.


## 7. 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.


### 7.1. 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 powerIi and the noise power spectral density N0 are −43 dBm and −173 dBm/Hz, respectively. The path loss factor γi (in dB) is obtained through 38.46+20log10di, where di (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.


### 7.2. CQoS Maximal Offloading Solution

Firstly, we investigate the task offloading services through a specific HN. The service objective of a TN isK=1,1,1, and the task size is 2 Mbits. The capabilities of the TN and HN i are provided in Table 2.Table 2
Capabilities of the TN and HNi.
NodeParameterValueTNηT1000 cycle/bitfT1 GHzθT2×10−9 J/cycleHNiηi1000 cycle/bitfi10 GHzθi1×10−9 J/cycleπi5×10−7 $/bitFigure2 shows the local maximal CQoS Qi∗ and the weighted service metrics including delay metric KdDi, energy consumption metric KeEi, and the economic cost metric KcCi. 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 pmax=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 1pmax=0. A higher pmax 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 pmax increases continually, the energy consumption of the offloading service can not continually decreases. Because the energy consumption for transforming 1 bit data, i.e., pi/WBi, is an increasing function of pi. As a result, an upper bound of Qi∗ 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.Figure 2
The maximal CQoS and the service metrics. (a) The maximal CQoS versuspmax. (b) The optimal service metrics versus pmax, di=40 m.
(a)(b)In Figure3, the CQoS maximal task offloading solutions through HNs located at different distances are plotted. As shown in Figure 3(a), the optimal transmission power pi∗ equals to pmax when pmax is small. With the increasing of pmax, pi∗ reaches an upper bound, which corresponds to the upper bound of Qi∗ shown in Figure 2(a). We can also observe that the upper bound of pi∗ is small when the distance is small. It is because that the a small pi can provide a high CQoS in this case. At the same time, the upper bound of pi∗ is also small when the distance is large. It is because that the increasing of pi 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 li∗ when pmax increases. We observe that the larger pmax 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 li∗ is 0 in this case.Figure 3
The CQoS maximal task offloading solutions through HNs located at different distances. (a) The optimal transmission powerpi∗ versus pmax. (b) The optimal offloading task size li∗ versus pmax.
(a)(b)


### 7.3. 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 are1,0,0, 0,1,0, and 0.1,0.1,1, 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.Table 3
Capabilities of the available HNs.
NodeCapabilityηifiθiπidiHN11000 cycle/bit10 GHz3×10−10 J/cycle5×10−7 $/bit10 mHN21000 cycle/bit5 GHz1×10−10 J/cycle5×10−7 $/bit20 mHN31000 cycle/bit5 GHz3×10−10 J/cycle1.5×10−7 $/bit30 mFigure4 plots the maximal CQoS Qi∗ 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.Figure 4
Maximal CQoS for 3-target tasks. The service objectives of the three tasks are1,0,0, 0,1,0, and 0.1,0.1,1, respectively. Task 1 and Task 2 can be scheduled with DOTS and FEMTO algorithm, respectively.It is easy to find that the three tasks are sensitive to different service metrics. Task 1 with service objective1,0,0 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 0,1,0 is an energy-sensitive task; thus, the SCOTT algorithm turns into the FEMTO algorithm proposed in [41], which achieves the energy-minimized offloading scheme. Task 3 with service objective 0.1,0.1,1 is sensitive to service cost. The delay and energy factors of task 3 do not equal to 0 because that the service objective 0,0,1 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.


### 7.4. 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. Figure5 plots the maximal CQoS of a TN with K=1,1,1. 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 fi, θi, and πi 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.Figure 5
Maximal CQoS in service clusters with different radii and HN amount.We can observe from Figure5 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 Di and Ei. Besides, a large amount of available HNs can provide a higher CQoS for 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.


## 7.1. 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 powerIi and the noise power spectral density N0 are −43 dBm and −173 dBm/Hz, respectively. The path loss factor γi (in dB) is obtained through 38.46+20log10di, where di (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.


## 7.2. CQoS Maximal Offloading Solution

Firstly, we investigate the task offloading services through a specific HN. The service objective of a TN isK=1,1,1, and the task size is 2 Mbits. The capabilities of the TN and HN i are provided in Table 2.Table 2
Capabilities of the TN and HNi.
NodeParameterValueTNηT1000 cycle/bitfT1 GHzθT2×10−9 J/cycleHNiηi1000 cycle/bitfi10 GHzθi1×10−9 J/cycleπi5×10−7 $/bitFigure2 shows the local maximal CQoS Qi∗ and the weighted service metrics including delay metric KdDi, energy consumption metric KeEi, and the economic cost metric KcCi. 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 pmax=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 1pmax=0. A higher pmax 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 pmax increases continually, the energy consumption of the offloading service can not continually decreases. Because the energy consumption for transforming 1 bit data, i.e., pi/WBi, is an increasing function of pi. As a result, an upper bound of Qi∗ 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.Figure 2
The maximal CQoS and the service metrics. (a) The maximal CQoS versuspmax. (b) The optimal service metrics versus pmax, di=40 m.
(a)(b)In Figure3, the CQoS maximal task offloading solutions through HNs located at different distances are plotted. As shown in Figure 3(a), the optimal transmission power pi∗ equals to pmax when pmax is small. With the increasing of pmax, pi∗ reaches an upper bound, which corresponds to the upper bound of Qi∗ shown in Figure 2(a). We can also observe that the upper bound of pi∗ is small when the distance is small. It is because that the a small pi can provide a high CQoS in this case. At the same time, the upper bound of pi∗ is also small when the distance is large. It is because that the increasing of pi 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 li∗ when pmax increases. We observe that the larger pmax 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 li∗ is 0 in this case.Figure 3
The CQoS maximal task offloading solutions through HNs located at different distances. (a) The optimal transmission powerpi∗ versus pmax. (b) The optimal offloading task size li∗ versus pmax.
(a)(b)


## 7.3. 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 are1,0,0, 0,1,0, and 0.1,0.1,1, 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.Table 3
Capabilities of the available HNs.
NodeCapabilityηifiθiπidiHN11000 cycle/bit10 GHz3×10−10 J/cycle5×10−7 $/bit10 mHN21000 cycle/bit5 GHz1×10−10 J/cycle5×10−7 $/bit20 mHN31000 cycle/bit5 GHz3×10−10 J/cycle1.5×10−7 $/bit30 mFigure4 plots the maximal CQoS Qi∗ 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.Figure 4
Maximal CQoS for 3-target tasks. The service objectives of the three tasks are1,0,0, 0,1,0, and 0.1,0.1,1, respectively. Task 1 and Task 2 can be scheduled with DOTS and FEMTO algorithm, respectively.It is easy to find that the three tasks are sensitive to different service metrics. Task 1 with service objective1,0,0 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 0,1,0 is an energy-sensitive task; thus, the SCOTT algorithm turns into the FEMTO algorithm proposed in [41], which achieves the energy-minimized offloading scheme. Task 3 with service objective 0.1,0.1,1 is sensitive to service cost. The delay and energy factors of task 3 do not equal to 0 because that the service objective 0,0,1 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.


## 7.4. 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. Figure5 plots the maximal CQoS of a TN with K=1,1,1. 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 fi, θi, and πi 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.Figure 5
Maximal CQoS in service clusters with different radii and HN amount.We can observe from Figure5 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 Di and Ei. Besides, a large amount of available HNs can provide a higher CQoS for 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.


## 8. 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.



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*Source: 4553317-2022-09-27.xml*