A Cloud-Edge Communication Resource Slicing Allocation Method for Data Monitoring in Integrated Energy Systems

Abstract

With the continuous growth in both volume and variety of monitoring services in integrated energy systems, the disparities between time scales and tasks of heterogeneous energy flow data monitoring pose significant challenges to rational resource allocation and efficient data transmission. To address these challenges, a monitoring resource slicing allocation method with low-cost optimization is presented for energy flow monitoring services in integrated energy systems. Firstly, a dynamic network slicing method for heterogeneous energy flow is proposed, which realizes rational resource allocation for diverse monitoring tasks and time scales through an integrate-then-slice approach. Secondly, a data transmission strategy with a cost representation method for network slicing is proposed. By establishing precise modeling of the complete data monitoring process within each slice, it solves the quantitative problem of data monitoring costs. Thirdly, an adaptive monitoring resource slice allocation algorithm is proposed, which addresses the cost optimization problem in data monitoring under slicing modes through optimized allocation of both intra-slice and inter-slice resources. Finally, tests are conducted on an integrated energy system in China. The results demonstrate that the proposed method successfully achieves data monitoring of heterogeneous energy flows across multiple time scales, while significantly reducing the data monitoring costs.

1. Introduction

The integrated energy system is a modern energy supply model that couples and converts multiple originally independently operated energy sources through coordinated planning, operation, and interaction, utilizing advanced intelligent technologies for unified dispatch and management [1]. With the continuous advancement of monitoring machines, data monitoring equipment has been widely implemented in integrated energy systems [2,3]. The volume of monitoring data uploaded by sensors to monitoring equipment for processing has progressively increased to generate accurate control signals that properly guide the actuation of physical energy network actuators [4]. However, the continuous growth of sensor-generated monitoring data inevitably leads to a dramatic increase in energy consumption of monitoring equipment [5,6]. Nevertheless, the significant disparities in temporal scales for monitoring different energy-flow types result in inefficient utilization of monitoring resources, thereby imposing more stringent requirements on the data monitoring equipment used in integrated energy systems [7,8].

To address critical issues, including excessive workload on cloud control centers and inefficient allocation of data monitoring resources, scholars have proposed mobile edge computing (MEC) technology and network slicing technology as potential solutions. On one hand, MEC technology reduces both the processing burden and bandwidth requirements of cloud control centers by deploying monitoring equipment at the sensor edge to perform data processing operations [9,10]. In [11], a two-level algorithm was proposed, which considers fairness among all tasks and can generate resource allocation schemes that fully utilize server resources. In [12], an efficient relay-assisted joint cooperative computation and communication algorithm was proposed, which minimizes the system’s energy consumption cost while satisfying relay power and computational latency constraints. In [13], a dual-timescale problem of computation offloading and resource allocation was proposed, followed by the application of game theory to discuss the rational attributes of users and edges, enabling each decision-maker to pursue their interests in a socialized and rational manner. In [14], a deep reinforcement learning-based framework was proposed to determine offloading decisions, and an optimization algorithm for the energy allocation problem was designed to achieve bidirectional information. In [15], a unified framework was proposed to provide efficiency through coded distributed computing, minimizing resource consumption while achieving information-theoretic security. In [16], a novel three-level collaborative optimization model was proposed, which comprehensively considers the relationships among various agents to maximize the social welfare of the multilateral system. In [17], a novel computational architecture was proposed, which integrates energy trading and cloud computing-based demand response for managing virtual power plants in smart grids. In [18], a cost-effective and fault-tolerant task offloading strategy was proposed. By decomposing the optimization problem into subproblems for each time slot, the strategy minimizes the average response delay for all tasks. Monitoring data for heterogeneous energy flows contributes to enhancing the operational efficiency and economic performance of integrated energy systems, ensures system security and controllability, and provides a foundation for long-term system planning. This introduces a critical challenge when applying MEC to integrated energy systems: improper allocation of communication resources across different energy-flow monitoring services.

On the other hand, the existing literature demonstrates that network slicing technology abstracts network services from underlying hardware devices, enabling software-defined controllers to isolate and reallocate network resources, which has become one of the most prevalent network virtualization technologies [19,20]. In [21], an end-to-end network slicing scheme for heterogeneous networks was proposed, which enhances the capabilities of next-generation networks by considering control signaling in the control plane and traffic in the core network user plane. In [22], a blockchain-based network slicing management framework was proposed, which enables collaborative slice management among multiple operators with service-level agreement guarantees. In [23], an intelligent dual-timescale network slicing strategy was proposed to maximize sensory information satisfaction while minimizing the costs of slice reconfiguration and synchronization. In [24], a knowledge-driven cross-domain collaborative anomaly detection scheme for end-to-end network slicing was proposed to demonstrate superior performance in anomaly detection metrics such as accuracy. In [25], a multi-leader-disjoint-follower bi-level game approach was proposed to satisfy diverse quality-of-service requirements for various computational tasks. In [26], a collaborative intelligent resource trading framework based on federated deep reinforcement learning was proposed for multiple infrastructure providers and mobile virtual network operators. In [27], a service-customized virtual network function deployment framework was proposed. By leveraging the interplay between the characteristics of the slicing tasks and the features of different servers in beyond-5G networks, it achieves precise control over service quality and cost. In [28], a blockchain-based hierarchical inter-slice computational resource trading scheme was proposed for peer-to-peer computational resource allocation in 5G networks based on autonomous multi-slice edge computing. However, with the exponential growth of energy-flow monitoring data within integrated energy systems, cloud processors face overwhelming data processing demands, while the energy consumption for both data transmission and processing continues to escalate. Moreover, economic considerations necessitate the continued utilization of legacy equipment in existing communication networks while adopting new technologies.

To address these challenges, this paper proposes a communication resource slicing allocation framework for a cloud-edge data monitoring networks in integrated energy systems. Building upon this framework, a monitoring resource slice allocation (MRSA) algorithm is proposed to achieve energy-optimal monitoring in sliced networks, minimizing data monitoring costs while satisfying all communication requirements. The main contributions of this work are as follows:

(1) A heterogeneous energy flow monitoring resource slicing allocation framework is proposed for cloud-edge data monitoring network in integrated energy systems. By adopting an integrate-then-slice approach for diverse energy flow monitoring equipment, the method maximizes utilization of existing communication resources to accommodate data transmission and processing requirements across varying monitoring tasks and time scales.

(2) An edge computing-incorporated network slicing data transmission strategy with cost representation methodology is proposed. Through refined full-process modeling of energy terminal monitoring data under multiple transmission and processing modes within individual slices, this work resolves the cost quantification challenge in sliced communication paradigms.

(3) A dynamic slice resource allocation algorithm is proposed, which optimizes both bandwidth distribution across slices and processing task allocation for energy terminal monitoring data. This approach simultaneously resolves cloud control center overload under throughput constraints and achieves asymptotic optimization of slice data monitoring costs.

The remainder of this paper is organized as follows. Section 2 of this paper introduces the monitoring network resource slicing allocation framework and the slice resource allocation optimal problem. Section 3 presents the proposed MRSA algorithm, followed by simulation case studies in Section 4. The conclusion is provided in Section 5.

2. Monitoring Resource Slice Allocation Framework

2.1. Monitoring Resource Slice Allocation Strategy

Currently, data monitoring for different energy flows in integrated energy systems is typically conducted on independent edge monitoring networks. As illustrated in Figure 1a, the integrated energy system comprises four energy flow types—electricity, gas, cooling, and heating—each with an independent data monitoring network. The data monitoring devices consist of an edge monitoring station ($S_i$), an edge relay server ($R_i$), and a cloud control center (CC), with no interconnection between the edge monitoring stations of different energy flow monitoring services. It is worth noting that the main functions of edge relay servers include assisting in processing terminal monitoring data and aiding edge communication stations in transmitting data to the cloud control center. However, the differing task loads and monitoring time scales among energy flows inevitably compromise the rationality of monitoring resource allocation. To address these challenges, this section presents a monitoring resource slice allocation strategy for integrated energy systems.

(1) Data monitoring equipment integration: as shown in Figure 1b, the monitoring equipment for different energy flow services is integrated into a single network based on their physical adjacency relationships. This integration approach enables efficient utilization and sharing of existing monitoring resources.

(2) Terminal energy equipment access: when terminal energy equipment connects to the edge monitoring station, the station uploads the equipment’s basic information—including monitored energy flow type and monitoring task volume—to the cloud control center.

(3) Energy flow slice dynamic division: as depicted in Figure 1c, after $S_i$ uploads the terminal energy equipment information to the CC, CC performs dynamic energy flow slicing on the integrated data monitoring network based on both device connectivity status and service demand requirements.

(4) Monitoring resource dynamic allocation: following network slicing by CC, each energy flow slice dynamically allocates monitoring data processing tasks among edge monitoring equipment and the cloud control center based on terminal task magnitudes within the slice.

(5) Slice resource dynamic adjustment: based on real-time access status of terminal energy equipment, the framework dynamically adjusts service scope between slices, bandwidth allocation, and intra-slice resource distribution, achieving plug-and-play functionality for terminal devices.

In summary, the proposed method adapts conventional data monitoring equipment to accommodate the presented network slicing scheme by transforming the traditional data monitoring equipment. Through dynamic slicing and resource allocation of the integrated data monitoring network, the on-demand allocation of data processing resources of different energy flow types has been achieved. Compared to traditional isolated data monitoring networks for different energy flows, the network slicing method proposed in this paper reallocates data monitoring resources according to data monitoring requirements.

2.2. Monitoring Resource Slice Allocation Model

Based on the proposed monitoring resource slicing allocation method, this section models the dynamic slicing process of the data monitoring communication network. From a topological perspective, the overall data monitoring network can be represented as an undirected graph $\mathrm{G}=(N,L)$. N denotes the total number of edge data monitoring platforms and terminal energy devices, $N^T$ represents the terminal energy devices, $N^E$ stands for the edge monitoring equipment, and L indicates the data monitoring transmission links. The issue of potential mismatches between the security levels of different monitoring equipment and the security requirements of various energy flow detection services is considered. Moreover, the slicing resource allocation algorithm proposed in this paper for different energy flow services exhibits scalability to accommodate additional energy flow services. To ensure that energy flow monitoring services can only be transmitted and processed on devices and channels meeting their security requirements, the following two inequality constraints are proposed:

$$\begin{array}{cc}\hfill & {}^{x}l_k\le {\displaystyle \frac{{\omega }_k^n}{{\zeta }^x}},\forall k\in L,\forall x\in \{e,g,h,c,\dots ,X\}\hfill \\ \hfill & {}^{x}n_i\le {\displaystyle \frac{{\omega }_k^l}{{\zeta }^x}},\forall i\in N,\forall x\in \{e,g,h,c,\dots ,X\}\hfill \end{array}$$

(1)

where x denotes the energy flow slice type, while e, g, h, and c represent the power, gas, heat, and cooling energy flow monitoring network slices, respectively. X represents all types of energy flow monitoring services. $l_k^x$ and $n_i^x$ indicate whether the channel l and the monitoring equipment n are connected to the energy flow slice x, where “1” denotes connection and “0” denotes disconnection. ${\omega }_k^l$ and ${\omega }_k^n$ denote the security levels of channel l and equipment n, respectively, while ${\zeta }^x$ represents the security level of slice x.

The network topology must maintain radial connectivity to prevent data circulation, which can be expressed as follows:

$$\sum _{k\in L}{}^{x}l_k=\sum _{i\in N}{}^{x}n_i-1,\forall x\in \{e,g,h,c,\dots ,X\}$$

(2)

To ensure connectivity between terminals and the CC for each energy flow slice, the following constraint is formulated:

$$-1+{}^{x}l_p\le {}^{x}n_i-{}^{x}n_j\le 1-{}^{x}l_p,\forall p=(i,j)\in L$$

(3)

where p denotes the transmission channel from device i to device j.

Furthermore, the throughput constraint of the edge relay server is expressed as follows:

$$R_i^{SUM}\ge \sum _{e,g,c,h}^x{}^{x}R_i^{\mathsf{rc}},i\in \left(1,2,\dots ,N^R\right)$$

(4)

where $R_i^{SUM}$ denotes the maximum throughput of edge relay server $R_i$, and ${}^{x}R_i^{\mathsf{rc}}$ represents the throughput value transmitted from $R_i$ to the CC under energy flow slice x.

Upon completion of energy flow slicing, each slice incorporates the following monitoring data transmission modes. The entire process of data monitoring proposed in this article can be expressed as follows: first, integrated data transmission sends part of the monitoring tasks to other data monitoring devices for processing through the already integrated data monitoring equipment. Secondly, the edge monitoring station uploads part of the tasks to the edge relay server, and the edge relay server shares some tasks with other nearby relay servers for collaborative processing. Then, the edge monitoring station transmits data to the cloud control center via the edge relay server using non-orthogonal multiple access transmission. Finally, the cloud control center processes the data.

(1) Integrated Data Transmission: since traditionally independent energy flow monitoring resources are now jointly utilized, this integration is defined as collaborative monitoring task processing. Therefore, the joint signal transmission throughput ${}^{x}R_{i,j}^{\mathsf{ss}}$ between $S_i$ within slice x is expressed as follows:

$${}^{x}R_{i,j}^{\mathsf{ss}}=W_i{\displaystyle \frac{{}^x\mathit{\omega }_i\left({}^{x}d_i/{}^{x}T\right)}{{\sum }_{e,g,h,c}^y{}^y\mathit{\omega }_i\left({}^{y}d_i/{}^{y}T\right)}}{log}_2\left(1+{\displaystyle \frac{P_{i,j}^{ss}{h}_{i,j}^{ss}}{{\sigma }^2}}\right)$$

(5)

where $W_i$ represents the aggregate transmission bandwidth from $S_i$ to $S_j$ across all slices, and ${}^x\mathit{\omega }_i$ denotes the priority coefficient of energy flow slice x. ${}^{x}d_i$ denotes the total volume of monitoring data transmitted to $S_i$ within slice x that requires processing, ${}^{x}T$ represents the time scale for data monitoring in energy flow slice x, $P_{i,j}^{ss}$ indicates the transmission power, $h_{i,j}^{ss}$ stands for the channel gain, and ${\sigma }^2$ is the variance of additive white Gaussian noise.

The integrated signal transmission task volume ${}^{x}d_{i,j}^{\mathsf{ss}}={}^{x}t_i^1{}^{x}R_{i,j}^{\mathsf{ss}}$, and the transmission energy consumption ${}^{x}Z_i^{\mathsf{ss}}$ are expressed as follows:

$${}^{x}Z_i^{\mathsf{ss}}={}^{x}t_i^1\sum _M^{k=1}{P}_{i,k}^{ss}$$

(6)

where ${}^{x}t_i^1$ denotes the transmission duration. The integrated signal transmission model between $R_i$ follows a similar pattern to $S_i$.

The energy consumption ${}^{x}Z_i^s$ for data processing by $S_i$ within slice x is formulated as follows:

$${}^{x}Z_i^s={\displaystyle \frac{k_i^s{c}_i^s{\left({}^{x}d_i^s+{\sum }_M^{k=1}{}^{x}d_{k,i}^s\right)}^3}{{\left({}^{x}T-{}^{x}t_i^1\right)}^2}}$$

(7)

where $k_i^s$ denotes the effective capacitance coefficient on $S_i$, $c_i^s$ represents the number of CPU cycles allocated for computation, and ${}^{x}d_{k,i}^s$ indicates the data transmitted from other edge monitoring platforms to $S_i$ for integrated processing.

(2) Relay server-assisted data processing: to reduce the monitoring data processing load on the cloud control center, the edge communication station offloads part of the collected terminal monitoring data to the edge relay server for processing. The throughput expression follows a similar form to Equation (5), while the data processing energy consumption resembles Equation (7). The monitoring task transmission volume is expressed as ${}^{x}d_i^r={}^{x}t_i^2{}^{x}R_i^{sr1}$, where ${}^{x}t_i^2$ denotes the transmission duration. The transmission energy consumption ${}^{x}Z_i^{\mathsf{sr}}$ is formulated as follows:

$${}^{x}Z_i^{\mathsf{sr}}={}^{x}t_i^2{P}_i^{sr1}$$

(8)

(3) Non-Orthogonal Multiple Access data transmission: to enhance data transmission performance, non-orthogonal multiple access technology is adopted for data transmission between edge monitoring stations and the cloud control center. The edge monitoring station simultaneously sends data to both the cloud control center and the edge relay server. The edge relay server first decodes the portion of information from the edge monitoring station intended for the cloud, removes it, and then decodes the portion intended for itself. $S_i$ simultaneously transmits data requiring CC processing to both the CC and $R_i$, with the transmission energy consumption formulated as ${}^{x}Z_i^{\mathsf{sc}}={}^{x}t_i^3{P}_i^{sc}$. In energy flow slice x, the energy consumption for data transmission from $R_i$ to the CC is denoted as ${}^{x}Z_i^{\mathsf{rc}}={}^{x}t_i^4{P}_i^{rc}$, and the throughput is expressed as follows:

$$R_i^{rc}={\displaystyle \frac{W_i{}^x\mathit{\omega }_i\left({}^{x}d_i/{}^{x}T\right)}{2{\sum }_{e,g,h,c}^y{}^y\mathit{\omega }_i\left({}^{y}d_i/{}^{y}T\right)}}ln\left(1+G_i+{\displaystyle \frac{{}^{x}P_i^{\mathsf{rc}}{h}_i^{rc}}{{\sigma }^2}}\right)$$

(9)

where $G_i=P_i^{sc}{h}_i^{sc}/\left(P_i^{sr2}{h}_i^{sc}+{\sigma }^2\right)$. $P_i^{sc}$ denotes the transmission power from $S_i$ to the CC, and $h_i^{sc}$ represents the corresponding channel gain.

If the throughput received by the CC does not meet the minimum requirement ${}^{x}R_i^{\mathsf{rc}}⩾R_{i,0}$, the CC will be in a shutdown state, resulting in a power constraint:

$${}^{x}P_i^{\mathsf{rc}}⩾{\displaystyle \frac{N_0}{h_i^{rc}}}\left(e^{{\displaystyle \frac{2R_{i,0}}{{}^{x}W_i}}}-1-{\displaystyle \frac{P_i^{dc}{h}_i^{dc}}{P_i^{dc}{h}_i^{dc}+N_0}}\right)$$

(10)

According to the NOMA transmission principle, the throughput from $R_i$ to the CC must not exceed that from $S_i$ to the CC. Therefore, the power constraint for data transmission to the CC within energy slice x can be derived as follows:

$${\displaystyle \frac{P_i^{sr}{h}_i^{sr}}{h_i^{rc}}}-{\displaystyle \frac{N_0{P}_i^{sc}{h}_i^{sc}}{h_i^{rc}\left(P_i^{sr}{h}_i^{sc}+{\sigma }^2\right)}}{\ge }^x{P}_i^{rc}$$

(11)

where $P_i^{sr}$ denotes the transmit power from $S_i$ to $R_i$, and $h_i^{sr}$ represents the channel gain.

2.3. Optimal Slice Resource Allocation Problem Formulation

Building upon the monitoring resource slicing allocation model, this section formulates the low-cost resource slicing allocation problem. This problem constitutes a two-stage optimization process: the first stage maximizes energy flow slice service connectivity, while the second stage minimizes slice data monitoring costs.

(1) First Stage: to meet the practical requirements of diverse energy flow monitoring services, including low-energy resource allocation under varying time scales and monitoring data processing task volumes. The network slicing method proposed in this paper is based on diverse energy flow monitoring services, with the objective of maximizing the optimization of energy flow slice service connectivity. The objective function of the service connectivity maximization problem for energy flow slicing is formulated as follows:

$$\begin{array}{cc}\hfill & max\sum _{e,g,h,c}^x{}^x\mathit{\omega }_i\sum _N^i{}^{x}n_i\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.\left(1\right),\left(2\right),\left(3\right)\hfill \end{array}$$

(12)

(2) Second Stage: the slice data monitoring cost comprises two components: the first part includes both the energy consumption cost for data transmission in energy flow slicing ${}^{x}Z_1$ and the energy consumption cost for data processing ${}^{x}Z_2$. To address the non-convexity of the cost problem, auxiliary variable ${}^{x}Z_i^{\mathsf{rc}}$ is introduced to replace ${}^{x}P_i^{\mathsf{rc}}$, yielding ${}^{x}Z_1$ and ${}^{x}Z_2$ as follows:

$$\begin{array}{c}\hfill {}^{x}Z_1={}^{x}b_1\sum _{e,g,c,h}^x\sum _{N^E}^{i=1}\left[{}^{x}t_i^1\sum _M^{k=1}{P}_{i,k}^{ss}+{}^{x}t_i^3\sum _M^{k=1}{P}_{i,k}^{rr}+{}^{x}Z_i^{\mathsf{rc}}+\right.\\ \hfill \left.{}^{x}t_i^2{P}_i^{sr}+{}^{x}t_i^3{P}_i^{sc}+{}^{x}t_i^3{P}_i^{sr}\right]\end{array}$$

(13)

$${}^{x}Z_2={}^{x}b_2{k}_i^s{c}_i^s\sum _{e,g,h,c}^x\sum _{N^E}^{i=1}\left[{}^{x}Z_i^s+{}^{x}Z_i^r\right]$$

(14)

where ${}^{x}b_1$ and ${}^{x}b_2$ represent the unit energy consumption costs for data transmission and data processing in energy-flow slice x, respectively. Given the real-time requirements of data monitoring, the time scale considered for data transmission in this study is orders of magnitude smaller than the fluctuation period of energy prices. Therefore, after accounting for the impact of time-varying energy prices, the aforementioned parameters are treated as fixed values. Therefore, the slice data monitoring cost can be expressed as $Z_{\mathrm{Total}}={}^{x}Z_1+{}^{x}Z_2$.

In summary, the second-stage minimization of slice data monitoring cost can be expressed as follows:

$$\begin{array}{cc}min\hfill & Z_{\mathrm{Total}}\hfill \\ \mathrm{s}.\mathrm{t}.\hfill & -\sum _{e,g,c,h}^x{}^{x}W_{i}ln\left(1+G_i+{\displaystyle \frac{{}^{x}Z_i^{\mathsf{rc}}{h}_i^{rc}}{{}^{x}t_i^4{\sigma }^2}}\right)\ge -R_i^{SUM}\hfill \\ \hfill & 0\le {}^{x}t_i^1,{}^{x}t_i^2,{}^{x}t_i^3,{}^{x}t_i^4\le {}^{x}T\hfill \\ \hfill & {}^{x}Z_i^{\mathsf{rc}}\ge {\displaystyle \frac{{\sigma }^2}{h_i^{rc}}}\left(e^{{\displaystyle \frac{2R_{i,0}}{{}^{x}W_i}}}-1-{\displaystyle \frac{P_i^{sc}{h}_i^{sc}}{P_i^{sc}{h}_i^{sc}+{\sigma }^2}}\right){}^{x}t_i^4\hfill \\ \hfill & {}^{x}Z_i^{\mathsf{rc}}\le {\displaystyle \frac{P_i^{sr}{h}_i^{srx}{t}_i^4}{h_i^{rc}}}-{\displaystyle \frac{N_0{P}_i^{sc}{h}_i^{sc}{t}_i^4}{h_i^{rc}\left(P_i^{sr}{h}_i^{sc}+{\sigma }^2\right)}}\hfill \\ \hfill & {}^{x}D_i={}^{x}d_i^c+{}^{x}d_i^r+{}^{x}d_i^s+\sum _M^{k=1}{}^{x}d_{i,k}^{\mathsf{ss}}+\sum _M^{k=1}{}^{x}d_{i,k}^{\mathsf{rr}}\hfill \\ \hfill & {}^{x}T={}^{x}t_i^1+{}^{x}t_i^2+{}^{x}t_i^3+{}^{x}t_i^4+{\displaystyle \frac{c_i^c{d}_i^c}{f^{MAX}}}\hfill \end{array}$$

(15)

The data transmission energy consumption cost component is a linear function with respect to ${}^{x}t_i^1$, ${}^{x}t_i^2$, ${}^{x}t_i^3$, and ${}^{x}Z_i^{\mathsf{rc}}$; thus, this part is convex. The data processing energy consumption cost component, due to the constraints of time and total monitoring data volume, is a joint convex function of ${}^{x}d_i^s$, ${}^{x}t_i^1$, and ${\sum }_M^{k=1}{d}_{k,i}^s$. For the first constraint component, since it is inherently a strictly concave function, both sides are multiplied by $-1$ to maintain convexity of the constraint. The remaining constraints are all linear; thus, the overall constraint set exhibits convexity. In summary, the sliced data monitoring cost optimization problem constitutes a convex optimization problem. This ensures that the global optimal solution can be efficiently obtained using convex optimization methods.

3. Proposed Method

To address the low-cost resource slicing allocation problem proposed in the previous section, this section further presents the MRSA algorithm. Since the first stage optimization problem constitutes a Mixed-Integer Linear Programming problem, it can be solved using commercially available solvers. As the second stage optimization problem has been transformed into a convex problem, let $\left({}^{x}t_i^{1^{*}},{}^{x}t_i^{2^{*}},{}^{x}t_i^{3^{*}},{}^{x}t_i^{4^{*}},{}^{x}t_i^{5^{*}},{}^{x}d_i^{s^{*}},{}^{x}d_i^{r^{*}},{}^{x}d_i^{c^{*}},{}^{x}P_i^{r{c}^{*}}\right)$ denote the optimal solution to the optimization problem. The Lagrangian function can be expressed as follows:

$$\begin{array}{cc}\hfill & L=Z_{\mathrm{Total}}-\hfill \\ \hfill & \sum _N^{i=1}\left[{}^x\alpha _i\left({}^{x}W_{i}ln\left(1+G_i+{\displaystyle \frac{{}^{x}Z_i^{rc}{h}_i^{rc}}{{}^{x}t_i^4{\sigma }^2}}\right)-R_i^{SUM}\right)+\right.\hfill \\ \hfill & {}^x\beta _i{}^{x}t_i^1+{}^x\chi _i{}^{x}t_i^2+{}^x\delta _i{}^{x}t_i^3+{}^x\mathit{\epsilon }_i{}^{x}t_i^4+\hfill \\ \hfill & {}^{x}v_i\left({}^{x}Z_i^{rc}-{\displaystyle \frac{{\sigma }^2}{h_i^{rc}}}\left(e^{{\displaystyle \frac{2R_{i,0}}{{}^{x}W_i}}}-1-{\displaystyle \frac{P_i^{sc}{h}_i^{sc}}{P_i^{sc}{h}_i^{sc}+{\sigma }^2}}\right){}^{x}t_i^4\right)+\hfill \\ \hfill & {}^x\phi _i\left({\displaystyle \frac{P_i^{sr}{h}_i^{srx}{t}_i^4}{h_i^{rc}}}-{\displaystyle \frac{N_0{P}_i^{sc}{h}_i^{scx}{t}_i^4}{h_i^{rc}\left(P_i^{sr}{h}_i^{sc}+{\sigma }^2\right)}}-Z_i^{rc}\right)+\hfill \\ \hfill & {}^x\theta _i\left(-{}^{x}T+{}^{x}t_i^1+{}^{x}t_i^2+{}^{x}t_i^3+{}^{x}t_i^4+{\displaystyle \frac{c_i^{cx}{d}_i^c}{f^{MAX}}}\right)+\hfill \\ \hfill & \left.{}^x\zeta _i\left({}^{x}d_i^c+{}^{x}d_i^r+{}^{x}d_i^s+\sum _M^{k=1}{}^{x}d_{i,k}^{ss}+\sum _M^{k=1}{}^{x}d_{i,k}^{rr}-{}^{x}D_i\right)\right]\hfill \end{array}$$

(16)

Let $\left(v_i^{*},{\lambda }_i^{*},{\omega }_i^{*},{\mu }_i^{*},{\sigma }_i^{*},{\eta }_i^{*},{\phi }_i^{*},{\gamma }_i^{*},{\mathit{\epsilon }}_i^{*},{\psi }_i^{*}\right)$ denote the optimal solution to the dual problem. The dual problem of the slice data monitoring cost minimization is formulated as follows:

$$\begin{array}{cc}max\hfill & D\left({}^x\alpha _i,{}^x\beta _i,{}^x\chi _i,{}^x\delta _i,{}^x\nu _i,{}^x\phi _i,{}^x\mathit{\epsilon }_i,{}^x\theta _i,{}^x\zeta _i\right)\hfill \\ \hfill & {}^x\alpha _i\ge 0,{}^x\beta \ge 0,{}^x\chi _i\ge 0,{}^x\delta _i\ge 0,\hfill \\ \mathrm{s}.\mathrm{t}.\hfill & {}^x\theta _i\ge 0,{}^x\nu _i\ge 0,{}^x\phi _i\ge 0,{}^x\mathit{\epsilon }_i\ge 0,\hfill \\ \hfill & {}^x\zeta _i\ge 0\left(i=1,2,\dots ,N^E\right)\hfill \end{array}$$

(17)

According to the Lagrangian dual decomposition principle:

$${}^{x}t_i^{4^{*}}={\displaystyle \frac{h_i^{rcx}{W}_i^x{\alpha }_i}{{}^{x}B_i{h}_i^{rc}+\left(1+G_i\right){\sigma }^2\left({}^{x}b_1-{}^x\nu _i-{}^x\phi _i\right)}}$$

(18)

The energy consumed for data transmission from $R_i$ to CC within slice x is given by:

$${}^{x}Z_i^{rc}={\displaystyle \frac{{}^{x}B_i{}^{x}t_i^{4^{*}}}{{}^{x}b_1-{}^{x}v_i-{}^x\phi _i}}$$

(19)

When integrated data transmission exists between $S_i$ within slice x, the transmission duration and task volume are given by:

$${}^{x}t_i^{t^{*}}={\displaystyle \frac{\sqrt{{}^x\mathit{\epsilon }_i}{}^{x}T}{{}^{x}R_{i,k}^{ss}\sqrt{{}^{x}b_1{k}_k^s{c}_k^{s^3}}+\sqrt{{}^x\mathit{\epsilon }_i}}}$$

(20)

$${}^{x}d_{i,k}^{s^{*}}={}^{x}t_i^{1^{*}x}{R}_{i,k}^{ss}$$

(21)

The integrated data transmission between $R_i$ follows similarly.

When no integrated data transmission exists between $R_i$ within slice x, ${}^{x}t_i^{2^{*}}$ is expressed as follows:

$${}^{x}t_i^{2^{*}}={\displaystyle \frac{\left({}^{x}T-{}^{x}t_i^{{*}^{*}}\right)}{1+{}^{x}R_i^{sr1}\sqrt{\frac{2{}^{x}b_1{k}_k^r{c}_k^{r^3}}{{}^x\chi _i+{}^x\theta _i-{}^{x}b_2{P}_i^{sr1}}}}}$$

(22)

The data volumes transmitted from $S_i$ to $R_i$ and CC within slice x are formulated as follows:

$${}^{x}d_i^{r^{*}}={}^{x}t_i^{2^{*}x}{R}_i^{sr1}$$

(23)

$${}^{x}d_i^{c^{*}}={}^{x}t_i^{3^{*}x}{R}_i^{sr}$$

(24)

Since the total monitored data volume received by $S_i$ is ${}^{x}D_i$, ${}^{x}d_i^{s^{*}}$ can be expressed as follows:

$${}^{x}d_i^{s^{*}}={}^{x}D_i-{}^{x}d_i^{c^{*}}-{}^{x}d_i^{r^{*}}-\sum _M^{k=1}{}^{x}d_{i,k}^{s{s}^{*}}-\sum _M^{k=1}{}^{x}d_{i,k}^{r^{*}}$$

(25)

Given that the time scale for each energy-flow slice is ${}^{x}T$, ${}^{x}t_i^{3^{*}}$ can be formulated as follows:

$${}^{x}t_i^{3^{*}}={}^{x}T-{}^{x}t_i^{1^{*}}-{}^{x}t_i^{2^{*}}-{}^{x}t_i^{4^{*}}-{\displaystyle \frac{c_i^c{}^{x}d_i^{c^{*}}}{f^{MAX}}}$$

(26)

The Lagrange multiplier update is expressed as follows:

$$\begin{array}{cc}\hfill & {}^x\alpha _i(k+1)={}^x\alpha _i\left(k\right)-{}^x\mu _1\left[{}^{x}W_{i}ln\left(1+G_i+{\displaystyle \frac{{}^{x}Z_i^{rc}{h}_i^{rc}}{{}^{x}t_i^4{\sigma }^2}}\right)-R_i^{SUM}\right]\hfill \\ \hfill & {}^x\beta _i(k+1)={}^x\beta _i\left(k\right)-{}^x\mu _2{}^{x}t_i^1\hfill \\ \hfill & {}^x\chi _i(k+1)={}^x\chi _i\left(k\right)-{}^x\mu _3{}^{x}t_i^2\hfill \\ \hfill & {}^x\delta _i(k+1)={}^x\delta _i\left(k\right)-{}^x\mu _4{}^{x}t_i^3\hfill \\ \hfill & {}^x\mathit{\epsilon }_i(k+1)={}^x\mathit{\epsilon }_i\left(k\right)-{}^x\mu _5{}^{x}t_i^4\hfill \\ \hfill & {}^{x}v_i(k+1)={}^{x}v_i\left(k\right)-{}^x\mu _6\left(Z_i^{rc}-{\displaystyle \frac{{\sigma }^2}{h_i^{rc}}}\left(e^{{\displaystyle \frac{2R_{i,0}}{x^x{W}_i}}}-1-{\displaystyle \frac{P_i^{sc}{h}_i^{sc}}{P_i^{sc}{h}_i^{sc}+{\sigma }^2}}\right){}^{x}t_i^4\right)\hfill \\ \hfill & {}^x\phi _i(k+1)={}^x\phi _i\left(k\right)-{}^x\mu _7\left({\displaystyle \frac{P_i^{sr}{h}_i^{srx}{t}_i^4}{h_i^{rc}}}-{\displaystyle \frac{N_0{P}_i^{sc}{h}_i^{scx}{t}_i^4}{h_i^{rc}\left(P_i^{sr}{h}_i^{sc}+{\sigma }^2\right)}}-{}^{x}Z_i^{rc}\right)\hfill \end{array}$$

(27)

where ${}^x\mu$ denotes the iteration step size, and the iterative process terminates when the dual function D satisfies a convergence criterion within an extremely small tolerance threshold.

In summary, the CC first performs energy-flow slicing on the integrated data monitoring network based on the terminal energy equipment information detected by $S_i$. It then optimizes the resource allocation within the four slices (electricity, gas, heat, and cooling) through coordinated optimization between CC and $S_i$ to solve the low-cost resource slicing allocation problem, with the pseudocode presented in Algorithm 1.

Algorithm 1: Monitoring resource slicing allocation algorithm

Input:    Integrated network topology information: ${\omega }_k^l$, ${\omega }_k^n$, $N^T$, $N^E$, $l_k^x$, $n_i^x$,

Monitoring equipment parameters: $P_{i,j}^{ss}$, $P_{i,j}^{rr}$, $P_{i,j}^{sc}$, $P_{i,j}^{sr}$, $C_i^s$, $C_i^r$, $C_i^c$, ${}^{x}b_1$,

Transmission channel parameters: ${}^{x}W_i$, $h_{i,j}^{ss}$, $h_{i,j}^{rr}$, $h_{i,j}^{sc}$, $h_{i,j}^{sr}$, $h_{i,j}^{rc}$,

Energy flow monitoring parameters: ${}^{x}D_i$, ${}^{x}T$.

Output: Energy flow slicing topology information: $G^x$, $x\in \{e,g,h,c\}$,

Intra-slice resource allocation information: P, I, $t^{k-1}$,

Sliced data monitoring cost: $Z_{TOTAL}$.

If      $S_i$ detects changes in terminal energy device information:

$S_i$ sends terminal information to CC;

CC optimizes energy flow slicing according to Equation (12);

Repeat:

Initialize ${\alpha }_i$, ${\beta }_i$, ${\chi }_i$, ${\delta }_i$, ${ϵ}_i$, $v_i$, ${\phi }_i$,

Initialize ${\mu }_1$, ${\mu }_2$, ${\mu }_3$, ${\mu }_4$, ${\mu }_5$, ${\mu }_6$, ${\mu }_7$;

CC broadcasts ${\alpha }_i,{\beta }_i,{\chi }_i,{\delta }_i,{ϵ}_i,v_i,{\phi }_i$ to $S_i$;

If $S_i$ receives iteration factors Then:

Perform local optimization according to Equations (18)–(26);

If P, L, t changed:

Update P, L, t;

End;

If CC receives updated P, L, t Then:

Update ${\alpha }_i,{\beta }_i,{\chi }_i,{\delta }_i,{ϵ}_i,v_i,{\phi }_i$ Equation (27);

Until: energy consumption cost change $<\mathrm{threshold}$

End;

After calculation, for X network slices with $N^x$ monitoring stations each, the time complexity under precision $\mathcal{E}$ is: $T_{\mathrm{MRSA}}=O\left({\displaystyle \frac{1}{\mathit{\epsilon }}}X{N}^x\right)$. Therefore, the above complexity analysis demonstrates that the MRSA algorithm’s complexity is polynomial-level, making it a scalable and efficient solution suitable for real-time or near-real-time resource allocation in integrated energy systems.

4. Case Study

To validate the effectiveness of the proposed method, tests were conducted on an integrated energy system in a region of China, whose physical network comprises a distribution grid, gas network, heating network, and cooling network. The system configuration includes four renewable energy nodes, one combined cooling, heating, and power unit, 16 load nodes, and two energy storage nodes. The data monitoring network of this system consists of one cloud control center and six edge monitoring stations, with each edge monitoring station connected to the CC through an edge relay server. According to the energy flow types, the network slicing for energy flow monitoring services in this integrated energy system is categorized into electrical slices, gas slices, heating slices, and cooling slices. The monitoring data resources used in this study are derived from the average of the total volume of monitoring data requiring processing across multiple time periods within the integrated energy system demonstration park of China.

The unit energy consumption costs for data transmission and data processing are denoted as ${}^{x}b_1=10\mathrm{USD}/\mathrm{MW}$ and ${}^{x}b_2=15\mathrm{USD}/\mathrm{MW}$, respectively. The integrated transmission power from $S_1$ to $S_6$ is C, while that from $S_3$ to $S_4$ is 1 MW. The integrated transmission power from $R_1$ to $R_5$ is $P_{1,6}^{rr}=0.5\mathrm{W}$, and that from $R_3$ to $R_4$ is $P_{3,4}^{rr}=0.8\mathrm{MW}$. The parameters related to data monitoring channels and equipment are listed in

Table 1. Parameter configuration of data monitoring equipment.

Parameter	Device 1	Device 2	Device 3	Device 4	Device 5	Device 6
$P_i^{ST}$ (MW)	2	8	5	6	3	4
$P_i^{SC}$ (MW)	5	6	1	5	4	6
$P_i^{dc}$ (MW)	6	7	2	5	1	5
$k_i^S$	$2\times {10}^{-28}$	$1\times {10}^{-28}$	$3\times {10}^{-28}$	$5\times {10}^{-28}$	$4\times {10}^{-28}$	$4\times {10}^{-28}$
$c_i^S$ (cycles/bit)	$6\times {10}^3$	$2\times {10}^3$	$4\times {10}^3$	$1\times {10}^3$	$8\times {10}^3$	$3\times {10}^3$
$k_i^r$	$8\times {10}^{-28}$	$2\times {10}^{-28}$	$7\times {10}^{-28}$	$4\times {10}^{-28}$	$4\times {10}^{-28}$	$9\times {10}^{-28}$
$c_i^r$ (cycles/bit)	$5\times {10}^3$	$3\times {10}^3$	$4\times {10}^3$	$1\times {10}^3$	$1\times {10}^3$	$4\times {10}^3$
$W_i$ (MHz)	16	18	20	25	19	17
$c_i^c$ (cycles/bit)	$2\times {10}^3$	$4\times {10}^3$	$4\times {10}^3$	$5\times {10}^3$	$1\times {10}^3$	$6\times {10}^3$

, while the energy flow monitoring parameters are presented in

Table 2. Parameter configuration of energy flow.

Parameter	Electrical	Gas	Heating	Cooling
${}^{x}T$ (s)	60	900	1000	500
${}^{x}d_1$ (MB)	0	0	8	5
${}^{x}d_2$ (MB)	0	10	5	0
${}^{x}d_3$ (MB)	5	0	0	0
${}^{x}d_4$ (MB)	10	8	9	3
${}^{x}d_5$ (MB)	6	0	5	0
${}^{x}d_6$ (MB)	15	0	0	0

.

4.1. Effectiveness Analysis

To validate the effectiveness of the MRSA algorithm in solving the low-cost resource slicing allocation problem, this section conducts simulation verification. The integrated and sliced network topology is illustrated in Figure 2, where Figure 2a through Figure 2d represent the electrical, gas, heating, and cooling energy flow slices, respectively. Figure 2 demonstrates that all physical terminals of the energy flow slices can establish communication channels with the CC while achieving maximized energy-flow service connectivity.

The power convergence characteristics of $R_i$ within each slice are illustrated in Figure 3. As shown in Figure 3a through Figure 3d, the power of $R_i$ exhibits stable convergence characteristics across all slice types, including electricity, gas, heat, and cooling slicing. Moreover, due to the smaller time scale and larger task volume in electric power slice monitoring, Figure 3a clearly shows that the relay server power within the electric slice is significantly higher than in the other three energy flow slices.

Figure 4 illustrates the convergence of monitoring costs for sliced data. As shown in Figure 4a, the energy consumption costs of data transmission converge across the four energy flow slices. Similarly, Figure 4b demonstrates the convergence of energy consumption costs for data processing in the four energy flow slices. Therefore, the proposed MRSA algorithm effectively addresses the low-cost resource slicing allocation problem.

Figure 5 illustrates the allocation of data monitoring resources within and between slices. As shown in Figure 5a, the inter-slice allocation of communication bandwidth is presented. Due to the smaller time scale of the electrical slice and the larger volume of data monitoring tasks, 66.7% of the total communication bandwidth is allocated to the electrical slice. Figure 5b illustrates the intra-slice allocation of data monitoring tasks. It can be observed that 89.7% of the data monitoring tasks are processed by the edge monitoring station, 8.8% are handled by the edge relay server, and only 1.4% of the tasks are executed on the cloud control center. Therefore, the proposed MRSA algorithm effectively promotes the rational allocation of data monitoring resources among energy flow monitoring services with different requirements, while alleviating the task processing burden on the cloud control center.

4.2. The Impact of Communication Parameters

This section examines the impact of terminal energy monitoring task volume, communication bandwidth, and Gaussian noise variations on the slice data monitoring cost, with the results presented in Figure 6. Figure 6a demonstrates that the sliced data monitoring cost gradually increases with the growing task volume of terminal energy monitoring in the integrated energy system. Figure 6b reveals that the monitoring cost decreases progressively as the communication bandwidth expands. Figure 6c indicates that higher noise levels lead to a corresponding increase in the sliced data monitoring cost.

4.3. Algorithm Comparison

To evaluate the performance of the proposed MRSA algorithm, this section compares it with the existing WCCRA [17] and JCCRA [12] algorithms.

In the WCCRA algorithm, edge monitoring stations collect terminal information and process monitoring data at both the edge and the cloud. However, WCCRA does not involve relay server-assisted computation nor does it incorporate joint and sliced allocation of monitoring resources. Therefore, to test the effectiveness of edge relay servers and the resource integration and slicing allocation method, the typical cloud-edge collaborative system architecture of WCCRA is used for comparison. In the JCCRA algorithm, the edge monitoring station collects all data requiring monitoring within its actual service range, including electricity, gas, cooling, and heating. Among these, both the edge monitoring stations and edge relay servers can perform edge processing on the monitoring data. Additionally, the cloud control center also participates in data processing. The JCCRA algorithm coordinates and allocates the resources of all three components. To evaluate the advantages of the proposed MRSA algorithm in terms of data monitoring device integration and sliced resource allocation, the JCCRA algorithm and its corresponding typical architecture are used for comparison.

Under the condition of the same task volume for energy terminal data processing, the data monitoring costs of different algorithms are compared, as shown in Figure 7. The simulation results demonstrate that the proposed MRSA algorithm allocates limited resources on-demand to corresponding data monitoring tasks through energy flow slicing and resource allocation operations. During the iterative process, tasks tend to be executed on equipment with lower energy consumption. Moreover, the edge relay servers in the data monitoring network can assist in task processing. These advantages enable the MRSA algorithm to achieve a 42.9% reduction in data monitoring costs compared to the WCCRA algorithm and a 29.8% reduction compared to the JCCRA algorithm. Therefore, the proposed MRSA algorithm in this study effectively reduces signal processing costs.

The power magnitudes of edge relay servers in different algorithms are compared in

Table 3. Power comparison of edge relay servers in different algorithms.

Relay Server ID	MRSA	JCCRA [12]	WCCRA [17]
1	$2.10\times {10}^{-4}$ MW	$3.36\times {10}^{-4}$ MW	/
2	$1.38\times {10}^{-4}$ MW	$1.07\times {10}^{-4}$ MW	/
3	$8.13\times {10}^{-1}$ MW	$8.89\times {10}^{-1}$ MW	/
4	$1.98\times {10}^{-1}$ MW	$3.15\times {10}^{-1}$ MW	/
5	$5.96\times {10}^{-2}$ MW	$8.35\times {10}^{-2}$ MW	/
6	$3.52\times {10}^{-1}$ MW	$8.77\times {10}^{-1}$ MW	/

. Due to collaborative data processing in the sliced communication network, relay servers with lower data processing costs experience an increase in power allocation, while those with higher data processing costs see a reduction. This power distribution strategy contributes to the overall decrease in data monitoring costs. It is worth noting that, to investigate the impact of relay power on data monitoring costs, the network architecture of the WCCRA algorithm used for comparison in this study does not include relay servers.

The comparison of data transmission costs and data monitoring costs among different algorithms is shown in Figure 8. As the slicing allocation algorithm enables the sharing and dynamic reallocation of monitoring resources, computational tasks are more inclined to be scheduled to devices with lower costs. Building on this, with the assistance of edge relays in task processing, the data monitoring costs are further reduced. Therefore, compared to the JCCRA and WCCRA algorithms, the proposed MRSA algorithm demonstrates superior performance in both data transmission costs and data processing costs.

5. Conclusions

This study has investigated the resource slicing allocation problem for data monitoring in integrated energy systems and has proposed a communication network slicing framework specifically designed for heterogeneous energy flow. Based on this network slicing framework, a monitoring data transmission strategy integrating edge computing with network slicing has been proposed, along with its corresponding cost representation methodology. The simulation results have demonstrated that the MRSA algorithm enables dynamic resource slicing allocation of monitoring networks according to the data monitoring requirements of heterogeneous energy flows. The proposed methodology has been demonstrated to effectively fulfill fundamental monitoring requirements for physical terminals in integrated energy systems while maximizing utilization of existing resources, thereby significantly reducing data monitoring costs. Furthermore, the proposed approach significantly reduces the computational load on cloud control centers and enables rational allocation of data monitoring resources. In future research, more efficient optimization algorithms will be investigated for long-term information transmission optimization scenarios to reduce algorithmic time complexity and enhance adaptability to large-scale integrated energy systems.