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.
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 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.
3. Service Model for Multitarget Tasks
In this section, a general MTMH computing network supporting tasks with 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 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 HNs, which can be represented by . The service capabilities of HN , i.e., , 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 . The parameter is the number of the service metrics such as delay and energy consumption. The larger the factor 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 . The parameters , , and 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 is provided based on the collected service capability . Then, the absolute service metrics such as service delay and cost can be achieved, which is denoted by . Therefore, we have where 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 . In order to estimate the service quality in a general way, the absolute service metric is weighted by the corresponding service objective factor . Then, the summation of the weighted service metrics can be calculated by the scalar product of and , i.e.,
Based on the service scheme and the service capabilities , we define the weighted summation as the CQoS of the service provided for task with service objective , and this integrated metric 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 . Therefore, the general optimization problem that achieves the CQoS maximal service scheme can be formulated as where 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 provides the direction to search the CQoS maximal service scheme, no matter what the service capabilities and the service objectives 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 use to denote the comprehensive service objective of a TN, in which , , and with nonnegative values are the delay factor, energy consumption factor, and the cost factor, respectively. The higher a factor in is, the more sensitive the task is to the corresponding service metric. In particular, the task with and 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 , is specified as ; the explanations of the parameters are summarized in Table 1. The task offloading scheme provided by the task scheduler, i.e., , includes the HN selection, task division , and the task transmission power . 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 , energy consumption , and economic cost based on and . Thus, we can get the absolute service metrics as .
4.1.1. Task Offloading Delay
The overall task offloading delay when HN is selected includes two parts, i.e., the delay of the local subtask with bits and the delay of the offloaded subtask with bits, which are denoted by and , 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 , in which is the CPU frequency of the TN, and is the CPU cycles for processing bit data at the TN. Thus, the local delay can be expressed as
Compared with the local delay, the offloading delay involves the processing delay in similar form to , and a transmission delay in addition, i.e., where is the CPU frequency of HN , is the CPU cycles for processing bit data at HN , is the spectrum bandwidth allocated to the offloading service, and is the spectral efficiency of the wireless link from the TN to HN . Given the terminal transmission power , is obtained through the Shannon capacity as
In the expression of , and are the path loss and shadowing factors of this wireless link. and are the interference power and the noise power spectral density, respectively.
4.1.2. Task Offloading Energy Consumption
The overall offloading energy consumption includes the computing energy consumption and the transmission energy consumption. In this research, we use and to represent the energy consumption per CPU cycle of the TN and HN . Then, the computing energy consumptions per bit data for the TN and HN are represented by and , respectively. Taking the transmission energy consumption with transmission power into consideration, the overall energy consumption is formulated as where is the energy consumptions of the TN, and is the offloading energy consumption when HN 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 parameter to denote the remuneration of HN when one bit data is offloaded to it. Therefore, the economic cost of the offloading service with offloading task size is
Based on the metrics of the task offloading service including , , and , 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 objective , the weighted offloading service metrics are , , and . Then, we construct the CQoS of the offloading service provided by HN as 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 and the TN transmission power . Therefore, we propose the following optimization problem. where 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 and the corresponding local maximal CQoS . In this way, the global optimal offloading solution and global maximal CQoS 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 solution and global maximal CQoS are obtained.
5.1. Problem Transformation
For the original optimization problem , the maximization of the local CQoS is equivalent to the minimization of the denominator in (10). Therefore, we can transform into as in which .
As defined in (4), the overall delay of the task offloading service provided by HN is decided by the larger subtask delay. Then, we have the following proposition.
Proposition 1. When the CQoS is maximized under the condition that , the offloading delay is no less than the local delay .
Proof. Please refer to Appendix A.
According to Proposition 1, the delay target in and can be represented as , and the subtask size should satisfies
Therefore, can be transformed into
Remark 2. The conclusions in Proposition 1 and can be explained as follows. For a certain HN and a subtask size , the increase of the transmission power 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 and in the CQoS maximization problem is revealed by (13).
It is easy to know that problem is not convex. Then, we will further transform into one-variable form to find the optimal offloading solution. For the optimization objective , the first derivative with respect to is
The derivative is uncorrelated with . At the mean time, given the comprehensive service target of the TN and the service capabilities of the HN , is directly decided by the TN transmission power . As a result, we can divide the value range of in , i.e., , into two parts, in which is nonnegative and negative, respectively. As shown below, these two value ranges are denoted as and , respectively.
When the subtask size increases, the minimization goal in is severally monotone increasing in and monotone decreasing in . Consequently, the optimal value of that minimizes in and should be and , respectively.
Based on the above analysis, we can transform the optimization problem into two subproblems as follows:
Obviously, and are both one-variable form optimization problems. We can solve the original problem by firstly finding the optimal solutions of these two subproblems severally, then achieving optimal CQoS based on and . The HN with the highest 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., and , need to be determined first.
The value ranges of and are determined by the sign of the gradient (16). Therefore, the following proposition is provided.
Proposition 3. The gradient is monotone decreasing when and monotone increasing when , in which is the only positive solution of the following equation.
Proof. Please refer to Appendix B.
According to the conclusions in Proposition 3, achieves its minimum value when . If , is always nonnegative when . Otherwise, has two zero points in , which are severally denoted by and (). Then, the sign of can be summarized as:
When , in .
When , in and and in .
Taking the value range of in the original optimization problem , i.e., , into consideration (16), a subalgorithm is introduced in Algorithm 1 to achieve and .
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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 .
Proposition 4. The optimal transmission power of the subproblem and the corresponding optimal subtask size are provided as follows: In (25), when the following three conditions are satisfied. Otherwise, . The function is in which the three parameters, i.e., , , and , are When is , is the only solution of valued in .
Proof. Please refer to Appendix C.
When the value range of is not empty, the following proposition provides the optimal offloading solution for this subproblem, as well as the relationship between and .
Proposition 5. When , the optimal transmission power of the subproblem and the corresponding optimal subtask size are provided as follows. In addition, there is when .
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 is not empty, the offloading scheme that achieves the highest CQoS has . This means that in the value range , 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 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 and minimized utilities , of the two subproblems. The local optimal offloading solution and the corresponding local maximal CQoS are given by
This process is introduced in Algorithm 2.
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5.3. 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 and the corresponding , we propose the SCOTT algorithm in Algorithm 3, in which the HN with the highest local maximal CQoS are selected.
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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 CQoS is which corresponds to the offloading solution , i.e., local processing.
Substituting this solution into (10), we get . The SCOTT algorithm minimizes . This guarantees that the offloading solution obtained by our proposed SCOTT algorithms can always achieve the that is no less than . Therefore, the SCOTT algorithm is applicable to local processing.
6.2. Delay-Sensitive Tasks
If the comprehensive service objective of a TN is , 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 and become and , respectively. Besides, the value ranges and are obviously 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 is , 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 becomes , which is obviously proportional to the offloading task size . Besides, the value ranges and are obviously and . Based on Proposition 4, the conditions in (27) are not fully satisfied, and is a monotone increasing function of . Therefore, the SCOTT algorithms will provide and 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 is , 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 becomes . 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 () 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 power and the noise power spectral density are dBm and dBm/Hz, respectively. The path loss factor (in dB) is obtained through , where (in m) is the distance between the TN and HN . Besides, a shadowing factor 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 is , and the task size is Mbits. The capabilities of the TN and HN are provided in Table 2.
Figure 2 shows the local maximal CQoS and the weighted service metrics including delay metric , energy consumption metric , and the economic cost metric . In Figure 1, we plot the local maximal CQoS of the offloading service provided by HN , and the distance between the TN and HN varies from m to 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 , 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., , which has been discussed in Section 6. The weighted metrics of local processing are shown in Figure 1. A higher 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 increases continually, the energy consumption of the offloading service can not continually decreases. Because the energy consumption for transforming bit data, i.e., , is an increasing function of . As a result, an upper bound of 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.
(a)
(b)
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 equals to when is small. With the increasing of , reaches an upper bound, which corresponds to the upper bound of shown in Figure 2(a). We can also observe that the upper bound of is small when the distance is small. It is because that the a small can provide a high CQoS in this case. At the same time, the upper bound of is also small when the distance is large. It is because that the increasing of 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 when increases. We observe that the larger 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 is in this case.
(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 are , , and , respectively. The task size is 2 Mbits, and the upper bound of the transmission power is 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 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 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 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 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 is sensitive to service cost. The delay and energy factors of task 3 do not equal to because that the service objective will lead to totally local processing and an infinitely great CQoS. On the other hand, Table 3 reveals that HN has a fast CPU frequency, HN has a low unit processing energy consumption, and HN 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. Figure 5 plots the maximal CQoS of a TN with . 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 , , and of the HNs follows Gaussian distributions, the mean values of which are 5 GHz, J/cycle, and $/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 and . 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.
Appendix
A. Proof of Proposition 1
We prove Proposition 1 with contradiction. In other words, if the condition that is not satisfied, the optimization goal in is not maximized.
Assume that there is an offloading scheme for the available HN , and the corresponding subtask delays satisfy .
Based on this offloading scheme, we can decrease the TN transmission power to , such that . Then, the delay target and the economic cost target remain unchanged.
The energy consumption for the transmission of bit data, i.e., is a monotone increasing function of the transmission power when is nonnegative [41]. So, the decrease of leads to a small energy consumption target .
Therefore, the utility can always be increased by this transmission power adjustment, and is not maximized with the given offloading scheme .
The above proves Proposition 1.
B. Proof of Proposition 3
Take the derivative of with respect to , we get
Denote by . For nonnegative transmission power , we have
Therefore, is a monotone increasing function of and has a single zero point when . Denote the only zero point of the equation as . Then, is positive when and negative when . In other words, the gradient is monotone decreasing when and monotone increasing when .
The above proves Proposition 3.
C. Proof of Proposition 4
According to the expression of in (15), we can expand the objective function of , i.e., in (18), as
The inequation in the last line of the above formula comes from the fact that .
According to Algorithm 1, there is when , and is one of the zero points of . Therefore, the optimal transmission power that minimizes is when , and the minimum value of is in this case.
When , we can get the poles of by searching the solutions of in the value range with bisection method. By comparing the values of at the poles and , we can get the optimal offloading solution in this case. Next, we can prove that the function has at most one solution in , which is denoted by .
The first derivative of with respect to is in which can be expanded as
Therefore, the function is equivalent to
By introducing the variable substitution , can be further equivalent to in which the three parameters, i.e., , , and , are
Now, we need to prove that the equation in (C.5) has at most one solution in .
The first derivative of with respect to is
Then, the solution of in is .
If , we have when , and is monotone increasing in . Therefore, has a single zero point in iff and are satisfied. The only zero point can be obtained with bisection method.
If , is the only pole of , and is monotone decreasing in and monotone increasing in . Besides, we have in which and . Thus, the minimum value of is larger than , and has no solution in this case.
In conclusion, when . When , we get by comparing the values of when , and the set includes the only pole of , i.e, iff the three conditions in (22) are satisfied.
The above proves Proposition 4.
D. Proof of Proposition 5
The first derivative of with respect to is
Compare (D.1) with (B.1), we get
Therefore, the variation trend of is the same with . Based on the conclusions in Proposition 3 and Algorithm 1, we can conclude that is monotone decreasing when and monotone increasing when .
For the cases that or , . Otherwise, we have the following conditions:
If , , and is monotone decreasing in , thus .
If , , and is monotone decreasing in and monotone increasing in , thus .
If , , and is monotone decreasing in and monotone increasing in , thus .
The corresponding optimal subtask size equals to for the reason that is a monotone decreasing function of when .
We have proved the optimal solution of so far. Then, we need to prove that when .
In the proof of Proposition 4, we express as
Besides, can be expressed as in which the in inequality in the last line of the above formula comes from the fact that .
Therefore, is always larger than , and there is when .
The above proves Proposition 5.
Data Availability
No data were used to support this study.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was partially supported by the Natural Science Foundation of Shandong Province, China, under grant ZR2021QF090, partially by the National Key Research and Development Program of China under grant 2020YFB2104300, and partially by the National Natural Science Foundation of China (NSFC) Key Project Program under grant 61932014.