A Real-Time Resource Dispatch Approach for Edge Computing Devices in Digital Distribution Networks Considering Burst Tasks

Abstract

Edge computing technology can effectively solve huge challenges posed by the large number of terminal devices accessing and massive data processing in digital distribution networks. Burst tasks, such as faults and data requests from the cloud, can occur at any time for edge computing devices in distribution networks. These tasks are unpredictable and usually hold the highest priority and must be completed as soon as possible. Although resources can be reserved partially at each period in the pre-scheduled operation plan, they may still be insufficient to handle burst tasks adequately. A real-time resource dispatch approach for burst tasks is developed in this study to address the above problems. The concept of flexibility for edge computing devices is presented, determining the real-time dispatch duration. Real-time resource dispatch and task handling processing are analyzed in detail, considered as task real-time dispatch models, computation process real-time dispatch constraints, and resource limitation constraints. The proposed real-time resource dispatch approach takes full advantage of the transferable characteristics for partial original plan tasks to adjust the pre-scheduled operation plan and release flexible resources for immediate processing of the burst task, completing burst tasks quickly and minimizing the impact for previous planned tasks on the edge computing device. The capability of the proposed method to efficiently deal with the burst tasks is also verified by the case study.

1. Introduction

Edge computing configures cloud computing capacity to the edge of the network approaching the user terminal, transferring computation tasks to be processed closer to the data source from the cloud computation center [1]. Nowadays, Edge computing is widely applied to digital distribution networks as an advanced digital technology [2]. Benefiting from the application of edge computing technology, edge computing devices acquire, process and store data from the local area to complete task computation locally [3,4], avoiding large delays, interference and even attacks during data transmission over long distances [5]. However, edge computing devices are equipped with limited computing and storage capacity while computation tasks should be completed quickly and successfully to guarantee the normal operation of digital distribution networks [6,7]. Therefore, it is necessary to allocate resources properly for various tasks by optimal scheduling [8]. By resource scheduling in advance to obtain the pre-scheduled operation plan for guidance, devices make full use of resources and ensure the successful completion of computation tasks.

Edge computing devices in distribution networks should process not only original planned tasks with different characteristics such as measurement acquisition [9], distribution monitoring [10], power flow calculation [11], voltage control [12], and source load forecast [13], but also burst tasks such as fault identification [14], emergency control [15], self-healing control [16], power supply restoration [17] and data requests from the cloud [18]. As for data requests from the cloud, centralized computation and decisions require distributed data as basic support. Therefore, the cloud makes data requests to the edge side, generating the data requests from cloud task. Compared to the original planned computation tasks, burst tasks occur at any time without forecasts during the operation of digital distribution networks and must be immediately processed when they occur. Resources can be reserved partially in the pre-scheduled operation plan for burst tasks. A real-time resource dispatch should be developed to make edge computing devices respond quickly to computational demands of burst task, using limited reserved resources.

There has been some research on resource scheduling methods for tasks under edge computing. Ref. [19] proposed a multiagent task scheduling algorithm based on the dueling double deep recurrent-network method to allocate resources and schedule tasks without global state information, considering associated task generation, communication channel, data queue, and previous computation resource allocation state. Ref. [20] transformed the joint transmission power control and computation resource allocation problem in industrial Internet of Things into a Markov decision process. A deep reinforcement learning-based dynamic resource management algorithm was developed to solve the above problem, reducing the task delay. To solve resource scheduling, task assignment, and transmission scheduling problems in a device-to-device collaboration based multi-access edge computing system, a reverse auction based task assignment and urgency-value based transmission scheduling algorithm were developed in [21], maximizing the platform profit with resource capacity constraint and desired task delay requirements. Ref. [22] developed a two-layer optimization framework with an iterative optimization algorithm based on Deep Q-Network (DQN) and Gradient Descent (GD) to solve task offloading scheduling and resource allocation problems in vehicular edge computing, respectively. The time-varying channel caused by the movement of vehicles was taken into account in detail. Task delay and system energy consumption were reduced with completion time, energy consumption, and computing capability constraints, using the proposed scheduling method. A coalitional game-based cooperative offloading algorithm was proposed in [23], formalizing the task offloading and resource scheduling process into a coalitional game based on the coalitional game theory. The task execution time delay and transmission energy consumption of all devices were minimized by reusing loose coupling tasks between different devices without repeated task data transmission, achieving joint collaboration of devices. For the problem of task offloading and resource allocation in mobile edge computing (MEC), an online joint offloading and resource allocation framework under the long-term MEC energy constraint was proposed to ensure the end-users’ quality of experience in [24]. An online joint offloading and resource allocation method was further developed to achieve the close-to-optimal performance with the long-term MEC energy constraint. Ref. [25] proposed an online unmanned aerial vehicle (UAV)-assisted task offloading algorithm based on Markov approximation optimization to significantly reduce the vehicular task delay constrained by the long-term UAV energy budget under various system parameters.

As shown in the above research, the resource scheduling problem aims to improve the quality of service, user experience and system performance by reducing delay, energy consumption, and costs. There are two types of resource scheduling: static scheduling and dynamic scheduling. Static scheduling is often based on fixed known system information to process known tasks under limited resources. However, dynamic scheduling is always based on actual task requirements and resource limitations of the system to schedule online.

Table 1. The summary of some research with optimization objectives and scheduling approaches.

References	Optimization Objectives			Scheduling Approach
	Delay	Energy Consumption	Costs	Static	Dynamic
[19]			✓		✓
[20]	✓				✓
[23]			✓	✓
[24]	✓	✓			✓
[26]		✓		✓
[27]	✓			✓
[28]	✓	✓			✓
[29]	✓	✓		✓
[30]	✓		✓		✓
[31]	✓			✓
[32]	✓	✓			✓
[33]		✓		✓

summarizes some research with optimization objectives and scheduling approaches.

Although the above resource scheduling methods can develop the system operation performance effectively with various optimization objectives. However, the power dissipation is not concerned with the digital distribution network resource scheduling problem. It is more concerned about the service quality of applications on the edge side of digital distribution networks by reducing the task completion time and improving the task completion percentage. Meanwhile, real-time burst tasks with high priority which should be completed at once are considered rare. Real-time burst tasks need to be processed as quickly as possible while satisfying the requirements for resources, completion deadline and logical correlation of the original computational tasks as much as possible. It is a great challenge to handle burst tasks quickly with the pre-scheduled operation plan, guaranteeing the successful completion of original computation tasks at the same time. The existing resource scheduling method can’t be directly applied in the actual operation scenario for edge computing devices of digital distribution networks. Therefore, it is necessary to research on the real-time processing mechanism for burst tasks of digital distribution networks with a lack of effective resource scheduling methods.

In this study, a real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is proposed. When burst tasks occur at any time during the actual operation of digital distribution networks with resource requirements for the process, the edge computing device receives the burst task parameters and calculates its flexibility next according to the pre-scheduled operation plan. Then the real-time dispatch duration is further determined based on the current flexibility. The proposed real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is applied to address the real-time resource dispatch problem for burst tasks. Finally, the real-time optimal dispatch strategies and computation results are obtained, including real-time resource allocation, core configuration adjustment, and computation status update.

The space-time transfer characteristics of delayable and interruptible tasks and non-delayable tasks are utilized in the real-time resource dispatch approach to release resources at once for burst tasks. State variables such as resource allocation and core configuration are updated, adjusting the pre-scheduled operation plan dynamically.

The main contributions can be summarized as follows.

(1)

Real-time dispatch constraints for burst tasks and the edge computing device are analyzed in detail particularly. Distribution network applications such as fault identification, emergency control, self-healing control, and data requests from the cloud are taken into consideration in the actual operation of digital distribution networks, considered as real-time burst tasks from the point of computation task. Real-time dispatch constraints for burst tasks and the edge computing device consist determination of real-time dispatch duration, task real-time dispatch model, real-time dispatch constraints of task computation process, and resource limitation constraints in real-time dispatch to describe the real-time dispatch processing.

(2)

A real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is proposed. The spatial and temporal transfer capability of transferable tasks in original planned tasks are utilized by scheduling resources and configuring tasks appropriately. The real-time resource dispatch approach enables a quick response to computational demands of burst tasks. Meanwhile, original planned tasks are successfully completed with minimum impact. The normal, efficient, and reliable operation of digital distribution networks is guaranteed by the proposed real-time resource dispatch approach.

The remainder of this paper is organized as follows. Section 2 establishes real-time dispatch constraints for burst tasks and the device to lay the foundation. The objective function and all considered constraints are presented in Section 3 to summarize the overall real-time resource dispatch problem for burst tasks. The case studies and analysis are presented in Section 4. Finally, the conclusions are discussed in Section 5.

2. Real-Time Dispatch Constraints for Burst Tasks and the Device

The real-time resource dispatch in cloud-edge collaborative edge distribution networks is depicted in Figure 1. Original planned tasks consist of delayable and interruptible, non-delayable, periodic, and continuous tasks. In order to process burst tasks quickly, the proposed real-time resource dispatch approach fully utilizes space-time transfer characteristics of delayable and interruptible tasks and non-delayable tasks which are regarded as transferable computation tasks. Based on the pre-scheduled operation plan, real-time dispatch enables transfer of transferable computation tasks to subsequent periods or alternative cores, freeing up resources for burst tasks. The following describes real-time dispatch constraints for burst tasks and the devices in detail.

2.1. Presentation of System Operation Scenarios

Before each optimal scheduling begins, the edge computing device receives parameters of computation tasks, that need to be processed within the current scheduling period. Computation tasks categorized into delayable and interruptible, non-delayable, periodic, and continuous tasks according to different computational characteristics. To ensure quick and successful completion of computation tasks with limited computation and storage resources, the edge computing device optimizes the resource scheduling for computation tasks with the consideration of computation task characteristics, core configuration for tasks, logic correlations between tasks, and resource allocation, obtaining the pre-scheduled operation plan. However, burst tasks are not considered in the pre-scheduled operation plan. In the actual operation stage of the edge computing device, a real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is proposed to complete burst tasks as soon as possible. Therefore, the study in this paper develops based on the pre-scheduled operation plan.

2.2. Determination of Real-Time Dispatch Duration

Flexibility is defined for the edge computing device to quantify its ability to release resources for computation of a burst task, denoted by $F_t$ and expressed as Formulation (1).

$$F_t={\sum }_t^H({\sum }_{k=1}^K{e}_k^{\mathrm{M}}-{\sum }_{i=1}^N{e}_{i,t})$$

(1)

where $H$ denotes the total scheduling cycle. $K$ denotes the total number of edge computing device cores. $e_k^{\mathrm{M}}$ denotes the maximum computing capacity of core $k$. $N$ denotes the total number of tasks. $e_{i,t}$ denotes computation resources allocated to task $i$ in period $t$ according to the pre-scheduled operation plan.

The real-time dispatch duration $T^{\mathrm{D}}$ is the period that can provide sufficient resources for the burst task via real-time dispatch and can be determined according to the flexibility of the edge computing device when the burst task arrives. The real-time dispatch duration $T^{\mathrm{D}}$ is represented as Formulations (2)–(5).

$$F^{\prime }=\left\{\begin{array}{c}0, F_{T^{\mathrm{A},\mathrm{e}}}\ge b_e\\ 1, F_{T^{\mathrm{A},\mathrm{e}}}<b_e\end{array}\right.$$

(2)

$$\left(1-F^{\prime }\right)\left(F_{T^{\mathrm{A},\mathrm{e}}}-F_{T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}}\right)+F^{\prime }\mathrm{M}\ge b_e$$

(3)

$$\left(1-F^{\prime }\right)\left(F_{T^{\mathrm{A},\mathrm{e}}}-F_{T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}-1}\right)<b_e$$

(4)

$$F^{\prime }(T^{\mathrm{D}}-H+T^{\mathrm{A},\mathrm{e}}-1)=0$$

(5)

where $F^{\prime }$ denotes whether the flexibility is sufficient for the burst task in period $t$. $\mathrm{M}$ is a maximum number.

2.3. Task Real-Time Dispatch Model

(1)

Modeling of burst tasks

Parameter set ${\mathit{X}}_B$ is defined to describe the characteristics of burst task $B$ [34], expressed as Formulation (6).

$${\mathit{X}}_B=\{T^{\mathrm{A},\mathrm{e}},b^{\mathrm{e}},d^{\mathrm{e}},L^{\mathrm{e}}\}$$

(6)

where $T^{\mathrm{A},\mathrm{e}}$ denotes the arrival time, $b^{\mathrm{e}}$ denotes the total number of CPU cycles required, $d^{\mathrm{e}}$ denotes the memory occupancy, and $L^{\mathrm{e}}$ denotes the loss factor for task abandonment.

If a burst task is not abandoned, it should be completed within the real-time dispatch duration, shown as Formulations (7) and (8).

$$\left(l^{\mathrm{R}}-1\right)\left({\sum }_{t=T^{\mathrm{A},\mathrm{e}}}^{T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}-1}{e}_t^{\mathrm{R}}-b^{\mathrm{e}}\right)=0$$

(7)

$${\sum }_{t=1}^{T^{\mathrm{A},\mathrm{e}}-1}\left(e_t^{\mathrm{R}}+s_t^{\mathrm{R}}\right)+{\sum }_{t=T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}}^H\left(e_t^{\mathrm{R}}+s_t^{\mathrm{R}}\right)=0$$

(8)

where $e_t^{\mathrm{R}}$ denotes the computation resources allocated to burst task $B$ in period $t$. $l^{\mathrm{R}}$ is a Boolean variable indicating the abandonment state for the burst task. Burst task $B$ is processed only if $l^{\mathrm{R}}=0$. $s_t^{\mathrm{R}}$ denotes the processing status of burst task $B$ in period $t$, $s_t^{\mathrm{R}}=1$ indicates that task $i$ is active in period $t$.

(2)

Modeling of original planned tasks

Periodic tasks need to be completed at intervals throughout the scheduling cycle. The edge computing device should provide dedicated resources to continuous tasks, ensuring continuous processing. It is clear from the above description that transferring periodic tasks and continuous tasks is difficult due to their processing characteristics. Meanwhile, periodic tasks and continuous tasks usually include computation tasks for monitoring and measurement functions in digital distribution networks, such as environment monitoring, distribution monitoring, and measurement acquisition. Thus, the scheduling scheme remains unchanged for these two types of tasks to ensure the normal operation of digital distribution networks. Periodic tasks and continuous tasks are considered as non-transferable tasks in the real-time resource dispatch stage and can be modeled as Formulations (9)–(11).

$$\left(l_i^{\mathrm{R}}-1\right)\left(e_{i,t}^{\mathrm{R}}-e_{i,t}\right)=0$$

(9)

$$\left(l_i^{\mathrm{R}}-1\right)\left(s_{i,t}^{\mathrm{R}}-s_{i,t}\right)=0$$

(10)

$$l_i^{\mathrm{R}}=l_i$$

(11)

where $l_i^{\mathrm{R}}$ is a Boolean variable indicating the abandonment state for task $i$. Computation task $i$ is processed only if $l^{\mathrm{R}}=0$. $s_{i,t}$ denotes the processing status of computation task $i$ in period $t$ according to the pre-scheduled operation plan. ${\mathsf{\Omega }}_3$ and ${\mathsf{\Omega }}_4$ denote the set of periodic tasks and continuous tasks, respectively.

Other types of tasks are treated as transferable computation tasks, for which the following requirements should be satisfied to ensure successful completion. Meanwhile, transferable computation tasks should also maintain their specific processing characteristics during real-time dispatch. Transferable computation tasks can be expressed as Formulations (12)–(15).

$$(l_i^{\mathrm{R}}-1)\left({\sum }_{t=T^{\mathrm{A},\mathrm{e}}}^{T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}-1}{e}_{i,t}^{\mathrm{R}}-{\sum }_{t=T^{\mathrm{A},\mathrm{e}}}^{T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}-1}{e}_{i,t}\right)=0$$

(12)

$$\left(l_i^{\mathrm{R}}-1\right)\left(e_{i,t}^{\mathrm{R}}-e_{i,t}\right)=0,t\not\subset [T^{\mathrm{A},\mathrm{e}},T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}-1]$$

(13)

$$\left(l_i^{\mathrm{R}}-1\right)\left(s_{i,t}^{\mathrm{R}}-s_{i,t}\right)=0,t\not\subset [T^{\mathrm{A},\mathrm{e}},T^{\mathrm{A},\mathrm{e}}+T^{\mathrm{D}}-1]$$

(14)

$$\left(l_i^{\mathrm{R}}-1\right)\left(s_{i,T^{\mathrm{A},\mathrm{e}}}^{\mathrm{R}}-1\right)=0,i\in {\mathsf{\Omega }}_2$$

(15)

where ${\mathsf{\Omega }}_2$ denotes the set of non-delayable tasks.

2.4. Real-Time Dispatch Constraints of Task Computation Process

(1)

Transferable computation task real-time allocation constraints

A transferable computation task abandoned by the edge computing device in the pre-scheduled operation plan is still abandoned in real-time dispatch. The arrival of a burst task may cause further abandonment of transferable computation tasks owing to limited resources, expressed as Formulations (16)–(18).

$$l_i^{\mathrm{R}}({\sum }_{t=1}^H\left(e_{i,t}^{\mathrm{R}}+s_{i,t}^{\mathrm{R}}+r_{i,t}^{\mathrm{R}}\right)+{\sum }_{k=1}^K{c}_{i,k}^{\mathrm{R}})=0$$

(16)

$$l^{\mathrm{R}}({\sum }_{t=1}^H\left(e_t^{\mathrm{R}}+s_t^{\mathrm{R}}\right)+{\sum }_{k=1}^H{c}_k^{\mathrm{R}})=0$$

(17)

$$(1-l_i^{\mathrm{R}})l^{\mathrm{R}}=0$$

(18)

where $c_k^{\mathrm{R}}$ and $c_{i,k}^{\mathrm{R}}$ denotes the occupancy statuses of core $k$ for the burst task and task $i$, respectively. $r_{i,t}^{\mathrm{R}}$ denotes the memory usage state of task $i$ in period $t$, $r_{i,t}^{\mathrm{R}}=1$ indicates that task $i$ requires memory capacity in period $t$.

If the transferable task has already started computing when a burst task arrives, it cannot be assigned to other cores for processing, for which the following constraints (19) and (20) are considered.

$$v_{i,t}=\left\{\begin{array}{c}1, \sum _{t=1}^{T^{\mathrm{A},\mathrm{e}}-1}{s}_{i,t}^{\mathrm{R}}\ge 1\\ 0, \sum _{t=1}^{T^{\mathrm{A},\mathrm{e}}-1}{s}_{i,t}^{\mathrm{R}}<1\end{array}\right.$$

(19)

$$v_{i,t}\left(c_{i,k}^{\mathrm{R}}-c_{i,k}\right)=0$$

(20)

where $v_{i,t}$ denotes the ability of task $i$ to be transferred to other cores.

(2)

Computation status update constraints

Task transfer may change the processing status of transferable computation tasks, which should be updated in the real-time dispatch problem as Formulations (21)–(24) [35].

$$T_i^{\mathrm{S},\mathrm{R}}=H-{\sum }_{t=1}^H{q}_{i,t}^{\prime }+1$$

(21)

$$q_{i,t}^{\prime }=\left\{\begin{array}{c}1, \sum _{t=1}^t{e}_{i,t}^{\mathrm{R}}>0\\ 0, \sum _{t=1}^t{e}_{i,t}^{\mathrm{R}}=0\end{array}\right.$$

(22)

$$T_i^{\mathrm{E},\mathrm{R}}={\sum }_{t=1}^H{p}_{i,t}^{\prime }+1$$

(23)

$$p_{i,t}^{\prime }=\left\{\begin{array}{c}0, \sum _{t=1}^t{e}_{i,t}^{\mathrm{R}}\ge b_i\\ 1, \sum _{t=1}^t{e}_{i,t}^{\mathrm{R}}<b_i\end{array}\right.$$

(24)

where $T_i^{\mathrm{S},\mathrm{R}}$ and $T_i^{\mathrm{E},\mathrm{R}}$ denote the actual start and completion time of task $i$, respectively. $q_{i,t}^{\prime }$ denotes the marks for whether task $i$ starts in period $t$. $p_{i,t}^{\prime }$ denotes the marks for whether task $i$ is completed in period $t$.

(3)

Task computation property constraints

The collaborative relationships between tasks should be satisfied during real-time dispatch. The memory usage properties of computation tasks remain the same during real-time dispatch [36]. For the burst task, computing data should be stored in memory from arrival until completion. Task computation property constraints are shown as Formulations (25) and (26).

$$T_n^{\mathrm{E},\mathrm{R}}\le T_m^{\mathrm{S},\mathrm{R}}-1$$

(25)

$$r_t^{\mathrm{R}}=\left\{\begin{array}{l}1,T^{\mathrm{A},\mathrm{e}}\le t\le T^{\mathrm{E},\mathrm{R}}\\ 0, Others\end{array}\right.$$

(26)

where $n$ and $m$ denote the prior and subsequent numbers for the original planned tasks with collaborative processing relationships. $r_t^{\mathrm{R}}$ denotes the memory usage state of the burst task in period $t$. $r_t^{\mathrm{R}}=1$ indicates that the burst task requires memory capacity in period $t$.

2.5. Resource Limitation Constraints in Real-Time Dispatch

The computing and memory resources allocated to all original planned tasks and burst tasks by the edge computing device are limited in each period $t$ [37], represented as Formulations (27) and (28).

$$0\le {\sum }_{i=1}^N\left(c_{i,k}^{\mathrm{R}}{e}_{i,t}^{\mathrm{R}}\right)+c_k^{\mathrm{R}}{e}_t^{\mathrm{R}}\le e_k^{\mathrm{M}}$$

(27)

$$0\le {\sum }_{i=1}^N\left(r_{i,t}^{\mathrm{R}}{d}_i\right)+r_t^{\mathrm{R}}{d}^{\mathrm{e}}\le d^{\mathrm{M}}$$

(28)

where $d^{\mathrm{M}}$ denotes maximum memory capacity of the edge computing device.

3. Formulation of Real-Time Resource Dispatch Problem for Burst Task

3.1. Objective Function

The objective of real-time dispatch is to ensure early completion of the burst task while minimizing the impact for other tasks on the edge computing device. To address these considerations, a comprehensive objective function is established for the real-time resource dispatch problem, expressed as Formulation (29).

$$min f^{\prime }={\tau }_1{T}^{\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{e}}+{\tau }_2\psi T^{\mathrm{E},\mathrm{R}}+{\tau }_3{E}^{\mathrm{A},\mathrm{r}}+{\tau }_4{E}^{\mathrm{A},\mathrm{e}}$$

(29)

where ${\tau }_1$, ${\tau }_2$, ${\tau }_3$, and ${\tau }_4$ denote the weighting factor selected according to the importance attached to each objective.

The first term in the objective function represents the summation of the completion time delay for each transferable task, and can be expressed as Formulation (30).

$$T^{\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{e}}={\sum }_{i=1}^N(T_i^{\mathrm{E},\mathrm{R}}-T_i^{\mathrm{E}}),i\in \{{\mathit{\Omega }}_1\cup {\mathit{\Omega }}_2\}$$

(30)

where $T^{\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{e}}$ denotes the summation of the completion time delay for each transferable task. ${\mathit{\Omega }}_1$ donates the set of delayable and interruptible tasks.

The second term in the objective function aims to minimize the completion time of the burst task. The actual completion time of the burst task $T^{\mathrm{E},\mathrm{R}}$ has a form similar to $T_i^{\mathrm{E},\mathrm{R}}$. $\psi$ denotes the completion time threshold factor of the burst task, which can be expressed as Formulation (31).

$$\psi =\left\{\begin{array}{c}{m}_1,T^{\mathrm{E},\mathrm{R}}\le T^{\mathrm{E},\mathrm{f}}\\ m_2,T^{\mathrm{E},\mathrm{R}}>T^{\mathrm{E},\mathrm{f}}\end{array}\right.$$

(31)

where $T^{\mathrm{E},\mathrm{f}}$ denotes the threshold for the completion time of the burst task. $m_1$ and $m_2$ denote the penalty factors.

The third and fourth terms in the objective function minimize the total loss incurred due to abandonment of transferable tasks and the burst task, which can be expressed as Formulations (32) and (33).

$$E^{\mathrm{A},\mathrm{r}}={\sum }_{i=1}^N{l}_i^{\mathrm{R}}{L}_i,i\in \{{\mathit{\Omega }}_1\cup {\mathit{\Omega }}_2\}$$

(32)

$$E^{\mathrm{A},\mathrm{e}}=l^{\mathrm{R}}{L}^{\mathrm{e}}$$

(33)

where $E^{\mathrm{A},\mathrm{e}}$ and $E^{\mathrm{A},\mathrm{r}}$ denote the total losses due to abandonment of burst and transferable tasks, respectively. ${\mathit{\Omega }}_1$ and ${\mathit{\Omega }}_2$ are the set of delayable and interruptible tasks and non-delayable tasks, respectively. $L_i$ and $L^{\mathrm{e}}$ denote loss factors for the burst and original planned task abandonment, respectively. Loss factors $L_i$ and $L^{\mathrm{e}}$ are input and received by edge computing devices as the known fixed-value task parameter.

The loss factor is the intrinsic property for the original planned task and burst task, known by the experience of the distribution network operation.

3.2. Constraints

The constraints of task properties, computation processes, and device resources during the real-time dispatch should be considered to address the real-time resource dispatch problem for burst tasks, and are presented as Formulation (34).

$$\left\{\begin{array}{c}min f^{\prime }\hfill \\ \hspace{1em} s.t.\left(1\right)–\left(5\right) (Real\text{-}time dispatch duration determination constraints)\hfill \\ \hspace{1em}\hspace{1em} \left(6\right)–\left(15\right) (Task real\text{-}time dispatch models)\hfill \\ \hspace{1em}\hspace{1em} \left(16\right)–\left(26\right) (Computation process real\text{-}time dispatch constraints)\hfill \\ \hspace{1em}\hspace{1em} \left(27\right)–\left(28\right) (Resource limitation constraints in real\text{-}time dispatch)\hfill \\ \hspace{1em}\hspace{1em} \left(30\right)–\left(33\right) (Intermediate variable constraints for objective function)\hfill \end{array}\right.$$

(34)

3.3. Solving Process for the Real-Time Resource Dispatch Problem

The real-time resource dispatch problem for burst tasks can be effectively solved by CPLEX solver. Figure 2 shows the holistic flowchart of the proposed real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks.

Burst tasks occur at any time during the actual operation of digital distribution networks, requiring resources for the process. After receiving the burst task parameters, the edge computing device calculates its flexibility first according to the pre-scheduled operation plan. Then the real-time dispatch duration is further determined based on the current flexibility. The proposed real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is applied to address the real-time resource dispatch problem for burst tasks. Finally, the real-time optimal dispatch strategies and computation results are obtained, including real-time resource allocation, core configuration adjustment, and computation status update.

4. Case Studies and Analysis

4.1. Scenario Configuration

In this section, the effectiveness of the real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is verified using the following case study. The total scheduling cycle $H$ is set as 15 min. The edge computing device has 3 cores with the maximum computing capacity of 3 × 10¹⁰ CPU cycles/min, 3 × 10¹⁰ CPU cycles/min, and 2 × 10¹⁰ CPU cycles/min. The maximum memory space of the edge computing device is 800 MB. In the pre-scheduled operation plan, the edge computing device has completed optimal resource scheduling for 22 original tasks. The detailed pre-scheduling plan is shown in Figure 3. (A, B) in Figure 3 indicates the task of type A is assigned to core B during the current period. Meanwhile, the color depth indicates the amount of computation resources allocated to tasks. Type 1–4 represent delayable and interruptible, non-delayable, periodic, and continuous tasks, respectively.

In this study, the burst task refers to data requests from the master operation station, noted by Task 23 that unexpectedly occurs in period 10 for the edge computing device. We assume that the burst task requires 4.5 × 10¹⁰ CPU cycles and occupies 10 MB of memory for computation.

To demonstrate the effectiveness of the proposed real-time resource dispatch approach method, the following two schemes are compared.

Scheme 1: The priority-based resource scheduling method is used. The edge computing device core with more adequate reserved resources and shorter completion time has a higher priority to be assigned to burst tasks. The configuration core allocates all reserved resources for the burst task in each period until the burst task completes its computation.

Scheme 2: A real-time resource dispatch approach for edge computing devices in digital distribution networks proposed in this study is used to obtain the handling mechanism for the burst task.

4.2. Result Analysis

Figure 4 shows the occupancy of computation resources for each core in Scheme 1. It can be concluded that cores 1 and 3 cannot process the burst task independently with inadequate reserved resources. Under these circumstances, the burst task has no choice or option but to be configured to core 2 for computation after arriving at the edge computing device. The burst task completes computation in period 15, existing a processing delay of 6 min.

As for Scheme 2, When the burst task occurs in period 10, the first step is to immediately calculate the real-time dispatch duration. According to the current flexibility of the edge computing device, the real-time dispatch duration is determined as periods 10–13 in this case study. The tasks involved in this duration are presented in

Table 2. Real-time dispatch results and comparison with the pre-scheduled operation plan.

Task Number	Core Assignment		Deadline	Completion Time
	Real-Time Dispatch	Pre-Scheduled Plan		Real-Time Dispatch	Pre-Scheduled Plan
1	1	1	15	15	15
2	2	2	15	14	14
8	2	3	12	11	12
9	3	3	14	10	10
12	3	3	15	15	15
14	1	1	15	15	15
18	3	3	15	13	13
21	2	3	12	10	11
22	3	2	14	12	13
23	/	2	/	/	11

. In this duration, the pre-scheduled operation plan for resource allocation strategy is adjusted by real-time dispatch to complete the burst task as quickly as possible.

The first adjustment to free up resources for the burst task is on core assignments of transferable computation tasks. As shown in Table 2, Tasks 8 and 21 are re-assigned from core 2 to core 3 for computation during the real-time dispatch duration; Task 22 is re-assigned from core 3 to core 2. The other tasks remain unchanged. Burst Task 23 is assigned to core 2 for computation.

Figure 5 shows the occupancy of computation resources for each core during periods 10–13 in two stages. As shown in Figure 5a, the computation resources reserved for periods 10–13 in the pre-scheduled operation plan are distributed across different cores, which is not adequate to accommodate the burst task for a single core. However, in Figure 5b, by re-assigning Tasks 8 and 21, sufficient computation resources are freed up on core 2 to process the burst task effectively. Meanwhile, Task 22 is re-assigned to core 2, releasing resources for the successful completion of Task 8 before its completion deadline. Consequently, inter-core transfer of Tasks 8, 21, and 22 allows resource allocation, initially distributed among different cores, to be consolidated and utilized optimally, guaranteeing successful and prompt completion of the burst task. The utilization factor of resource reservation for periods 10–13 is 78%.

The second adjustment made to free up resources for the burst task is related to the time-series resource allocation strategy for different tasks. Figure 6 illustrates the changes in the processing strategy of computation tasks during real-time dispatch. Different colors and their depths represent the allocation of computation resources to tasks. The resources allocated to un-transferable tasks and tasks beyond the real-time dispatch duration remain unchanged. Regarding transferable tasks, the resources allocated to Tasks 8, 12, 21, and 22 in periods 11, 11, 10, and 12 are reduced to accommodate the burst task. Consequently, the device increases resource allocation for Tasks 8, 12, 21, and 22 in periods 12, 12, 11, and 13 to ensure on-time completion. Although the completion times of Tasks 8, 21, and 22 are delayed, Tasks 21 and 22 are still ahead of the deadline and Task 8 is completed successfully on schedule. Moreover, the collaborative relationship between Tasks 8 and 9 remains intact after real-time dispatch. In Scheme 2, All original planned tasks and the burst task are processed successfully.

With the above two adjustments, Task 23 is completed within 2 min without causing any additional task abandonment, demonstrating that the proposed real-time resource dispatch approach is effective in responding to the unexpected burst tasks. The proposed real-time resource dispatch approach transfers transferable tasks to subsequent periods in time and other cores in space for computation, achieving effective utilization of reserved resources and regular, efficient and reliable operation for the edge computing device in digital distribution networks.

5. Conclusions

Edge computing devices with limited resources should respond to burst tasks quickly such as fault identification, emergency control, and data requests from the cloud at any time. A real-time resource dispatch approach for edge computing devices in digital distribution networks considering burst tasks is developed. In the real-time dispatch, the pre-scheduled operation plan is adjusted for quick and successful completion of burst tasks by transferring delayable and interruptible tasks and non-delayable tasks regarded as transferable computation tasks. The case study is set to verify the effectiveness of the proposed real-time resource dispatch approach. When a burst task occurs, the real-time dispatch is triggered, which aggregates the available flexibility in core assignments and task processing to complete the burst task as soon as possible. With the proposed real-time resource dispatch approach, the burst task is completed within 2 min, reducing completion time by 60%. The burst task has been successfully completed without causing any additional failed completions for the remaining tasks. The successful completion percentage for all tasks is 100%. Resource reservation is fully utilized with a utilization factor of 78%.

Based on the research in this paper, we will consider investigating the overall optimal scheduling for resources and collaborative processing for tasks with multiple edge computing devices and the cloud center in our future work.