Delay and cost-balanced communication resource management for IoT-empowered distribution grid energy dispatch

The combination of internet of things (IoT), 5G, and power line communication (PLC) provides real-time and low-cost data transmission services to meet the quality of service (QoS) requirements for distribution grid energy dispatch. However, the IoT-empowered communication resource management system faces challenges in optimizing delay and traffic cost for distribution grid energy dispatch. There is a contradiction between the long-term performance guarantee and short-term optimization objectives, compounded by competition for communication resources. In this paper, we construct the minimization problem of the weighted sum of data transmission delay and traffic cost. Utilizing Lyapunov optimization, we aim to decouple the long-term constraint of average queuing delay with the short-term optimization objective. Then, a delay and cost-balanced communication resource management algorithm based on two-layer iterative matching is proposed. It optimizes the communication mode selection by I-to-2 bidding matching in a large timescale and subchannel allocation by many-to-many deferred acceptance matching in a small timescale. The simulation data present that the proposed algorithm excels in reducing data transmission delay, minimizing traffic cost, and decreasing queuing delay.

1 Introduction

The internet of things (IoT) has a broad development prospect in the field of distribution grid energy dispatch. By connecting distribution grid operators with energy users and electric equipment (Tariq et al., 2020; Liao et al., 2023a; Fizza et al., 2023; Liu et al., 2023; Safdar Malik et al., 2023; Zhu et al., 2024), IoT provides dynamic data acquisition and real-time state perception of key electric equipment. Then, these collected data can be uploaded to the edge server or cloud server for deep state analysis and intelligent energy dispatch (Wang et al., 2023; Yao et al., 2023). Among various communication technologies, fiber optic technology cannot adapt to the wide coverage requirement of IoT due to the high deployment cost (Chagnon, 2019; Liao et al., 2023b; Lin et al., 2023). Wireless fidelity (WiFi) relying on the industrial, scientific, and medical (ISM) band is susceptible to interference and privacy issues (Schwung et al., 2023). In comparison, 5G and power line communication (PLC) emerge as feasible candidates (López et al., 2019; Pal et al., 2021; Zhou et al., 2022). Coverage by using a dedicated frequency band, but it causes extra traffic costs for grid operators (Qian et al., 2022; Zhou et al., 2024; Zhou et al., 2023a). On the other hand, PLC has the advantages of low cost and flexible development, but it suffers from lower communication capacity. How to combine 5G and PLC to support the real-time energy dispatch of the distribution grid from a delay and cost balance perspective remains an open issue (Xu et al., 2021; Zhang et al., 2023; Ruby et al., 2023).

Communication resource management refers to the effective and reasonable configuration, monitoring, scheduling, and optimization of various resources of communication systems to meet the quality of service (QoS) requirements (Guo et al., 2021; Ding et al., 2022; Gu et al., 2022; Wang et al., 2023). When combining 5G and PLC with IoT, communication mode selection and subchannel allocation are two important research topics of communication resource management. Particularly, communication mode selection should be optimized in a large timescale because the frequently switching communication mode results in large overheads. On the other hand, subchannel allocation should be optimized in a small timescale, considering the temporal-varying characteristics of the channel state (Xiang et al., 2022; Bigdeli et al., 2023). Despite the great research efforts initiated by previous studies, how to realize scalable, reliable, stable, and adaptable communication resource management still faces several technical challenges.

First, the optimization of data transmission delay and traffic cost is contradictory to each other. Although 5G has lower latency, it significantly increases the total traffic cost, particularly under the scenario of second-level data collection (Gu et al., 2021). The switching between 5G and PLC should be dynamically adjusted in accordance with various parameters including delay, traffic cost, and channel quality. Second, severe competition for communication resources is inevitable when the number of IoT devices is overwhelming. The small-timescale subchannel allocation optimization of a device is not only affected by the large-timescale mode selection results but also related to decisions of other competing devices. This incurs further difficulty in the multi-timescale resource management problem (Leng et al., 2023). Finally, short-term optimization based on information lacking foresight leads to long-term performance deterioration. The long-term queuing delay requirement imposed by real-time energy dispatch is considered an example. The optimum policy to balance delay and cost may come at the expense of larger cumulative queue backlog, which deteriorates the long-term queuing delay performance (Huang et al., 2023).

There exist several studies on subchannel allocation in IoT. Zhou et al. (2020) launched an algorithm based on online learning, utilizing the context-aware multi-armed bandit framework to dynamically distribute channels in a 5G network, which has shown exceptional performance, particularly in large-scale network scenarios. Ning et al. (2019) proposed a blended framework for computational task offloading, designed to enhance real-time traffic handling within 5G network infrastructures. The goal is to maximize the sum offloading rate. Do and Lehnert (2011) proposed a PLC channel allocation protocol that considers the individual channel quality of each user, enabling precise calculations for the required transmission resources. Han et al. (2023) investigated an advanced channel allocation strategy involving dynamic two-step random access optimization to enhance the access success probability. Wang et al. (2018) proposed an innovative algorithm for joint power and channel allocation, with the objective of maximizing the sum rate for cellular users. However, these works overlook severe competition for communication resources caused by massive IoT devices. Dewa et al. (2021) proposed a distributed channel assignment algorithm that efficiently finds the optimal channel configuration using the concept of belief propagation. Li et al. (2023) proposed a multi-agent device-to-device (D2D) communication resource allocation algorithm based on the advantage actor critic (A2C) to dynamically and adaptively output the resource allocation scheme of D2D users. However, these works overlook severe competition for communication resources caused by massive IoT devices. The developed optimization approaches have the disadvantages of high complexity, slow convergence, and instability under resource competition.

Matching theory provides a feasible tool to address combinatorial optimization problems involving large-number participants. Meshgi et al. (2017) studied the channel allocation problem of multi-user multi-channel cellular networks and proposed a channel allocation scheme based on stable matching to effectively improve the system capacity. Islam et al. (2016) proposed a channel allocation method based on stable matching to effectively reduce delay and improve system throughput for D2D communications underlying cellular networks. Csercsik and Jorswieck (2023) proposed a novel preallocation-based combinatorial auction approach to optimize the efficient allocation of channels for ultra-reliable low-latency communication (URLLC) services. Zhou et al. (2021) considered priority-aware resource coordination in a multi-unmanned aerial vehicle (UAV) communication system and jointly optimized a channel assignment and power allocation strategy under stringent resource availability constraints. These works simply assume all the resources are optimized in the same timescale and cannot be applicable to our scenario involving large-timescale communication mode selection and small-timescale subchannel allocation. Huang et al. (2015) proposed a multi-timescale matching model to enhance the matching degree between the available wind supply and the increasing EV charging demand within the microgrid. Huang et al. (2015) and Yu et al. proposed an innovative algorithm aimed at addressing challenges in resource allocation and task division within non-orthogonal multiple access edge computing-based power IoT. Wang et al. (2021) proposed a low-complexity algorithm to solve the formulated subchannel allocation problem using the matching theory, where the joint optimization of the task assignment and power allocation is performed at each iteration. Huang et al. (2022) proposed a beacon synchronization-based multi-channel dynamic time slot assignment method. The channel is allocated based on interference minimization from adjacent channels. However, these studies ignore the coupling between the long-term queuing delay guarantee with the short-term optimization of delay and cost balance.

Thus, we design a delay and cost-balanced communication resource management framework for IoT-empowered distribution grid energy dispatch. First, we present models of delay and traffic cost and formulate a delay and traffic cost optimization problem. The optimization objective is to minimize the weighted sum of transmission delay and traffic cost under the constraints of the subchannel allocation number, subchannel allocation quota, data transmission reliability, and long-term average queuing delay. Then, we decompose the formulated problem into two main subproblems, i.e., a large-timescale subproblem involving device communication mode selection and a small-timescale subproblem focusing on subchannel allocation, and solve them alternatively by the proposed delay and cost-balanced communication resource management algorithm based on two-layer iterative matching. The specific contributions include the following.

• Communication resource management with delay and traffic cost balancing: The proposed algorithm dynamically adjusts the optimization policy to trade off data transmission delay with traffic cost, which is an oversight in related works.

• Communication resource competition solution and complexity reduction: At each epoch, the large-timescale mode selection problem is addressed through the utilization of I-to-2 bidding matching. The small-timescale subchannel allocation problem is solved based on many-to-many deferred acceptance matching at each slot. This multi-timescale matching improves the convergence speed and complexity performances and the overheads caused by frequent switching in related works.

• Guarantee of long-term queuing delay: Based on Lyapunov optimization, we transform the long-term queuing delay constraint into a virtual queue. Then, the product of the virtual queue backlog and the queuing delay is added into the optimization objective. Particularly, devices with large queue backlog and queuing delay are given priority in matching so as to realize long-term queuing delay guarantee, which is a lack of consideration in related works.

The remainder of this paper is structured in the subsequent manner: An exposition of the system model and the formulation of the problem are explained in Section 2. The algorithm proposed, which relies on a two-tiered iterative matching process, is elucidated in Section 3. Section 4 is dedicated to demonstrating the outcomes derived from simulations. The conclusion of this study is presented in Section 5. The notations used in this paper are summarized in Table 1.

Table 1

Table 1. Summary of notations.

2 System model

Figure 1 introduces the proposed delay and cost-balanced communication resource management framework for IoT-empowered distribution energy dispatch, which includes the device layer, transmission layer, and edge layer. In the device layer, I IoT devices which support both PLC and 5G communication modes are deployed on electrical equipment including distributed photovoltaic, energy storage unit, power distribution equipment, and electrical vehicle charging pile to collect various types of data such as active power, reactive power, and temperature (Adnan et al., 2019; Ali et al., 2021). Define the set of IoT devices as $\mathcal{M}=\{m_1,\dots ,m_i,\dots ,m_I\}$. The transmission layer contains a PLC gateway and a 5G base station for data transmission, which support dual communication modes, i.e., PLC and 5G. An orthogonal frequency division multiplexing (OFDM)-based data transmission scheme is adopted. There exist J orthogonal subchannels, including J₁ PLC subchannels and J₂ 5G subchannels. Define the set of subchannels as $\mathcal{N}=\{n_1,\dots ,n_j,\dots ,n_J\}$, where n_j, j = 1, …, J₁ are PLC subchannels, and n_j, j = J₁ + 1, …, J are 5G subchannels. The data collected by IoT devices are uploaded to the edge layer via a selected communication mode and allocated subchannels, i.e., either PLC subchannels or 5G subchannels. The edge layer contains an edge server that processes the data uploaded from the device layer. The edge server also optimizes communication resource management in terms of communication mode selection and subchannel allocation.

Device communication mode selection and subchannel allocation are optimized in different timescales. Particularly, to avoid frequent switching of the communication mode and reduce overheads, in a large timescale, i.e., epoch, mode selection is optimized, while in a small timescale, i.e., time slot, subchannel allocation is optimized (Sezer and Gezici, 2016; Yu et al., 2021; Li et al., 2023; Zhou et al., 2023b). We consider a duration which contains T slots. Each slot lasts a duration τ. Define the slot’s set as $\mathcal{T}=\{1,\dots ,t,\dots ,T\}$ and the epoch’s set as $\mathcal{V}=\{1,\dots ,v,\dots ,V\}$. Each epoch contains consecutive T₀ slots. The relationship between V and T satisfies T = T₀V. The slot’s set in the v-th epoch is denoted as $\mathcal{T}(v)=\{(v-1)T_0+1,(v-1)T_0+2,\dots ,v{T}_0\}$.

Figure 1

Figure 1. Delay and cost-balanced communication resource management framework for IoT-empowered distribution energy dispatch.

Define ${\mathit{x}}_i(v)=\left\{x_i^{\text{PLC}}(v),x_i^{5\text{G}}(v)\right\}$ as the set of optimization variables of large timescale device communication mode selection, where $x_i^{\mathit{PLC}}(v)$ and $x_i^{5G}(v)$ are the indicator variables of the 5G communication mode and PLC mode, respectively. $x_i^{\text{PLC}}(v)=1$ indicates that device m_i selects the PLC mode to upload data to the edge server in the v-th epoch; otherwise, $x_i^{\text{PLC}}(v)=0$. Similarly, $x_i^{5\text{G}}(v)=1$ indicates that device m_i selects the 5G communication mode, and otherwise $x_i^{5\text{G}}(v)=0$. Define y_i,j(t) as the optimization variable of small-timescale subchannel allocation. y_i,j(t) = 1 indicates that in the t-th slot, the edge server allocates subchannel n_j to device m_i, and otherwise, y_i,j(t) = 0. Denote q_m as the quota of subchannel allocation, i.e., at most q_m subchannels can be allocated for each device per slot. Meanwhile, due to the limited number of subchannels in each communication mode, PLC subchannels can be allocated to at most J₁ devices, and 5G subchannels can be allocated to at most J₂ devices.

2.1 Data transmission model

In the t-th slot, the data transmission rate for device m_i on subchannel n_j is calculated as

$R_{i,j}\left(t\right)=N_s\min \left(R_j^{\text{max}},⌊{\mathrm{l}\mathrm{o}\mathrm{g}}_2\left(1+\frac{P_{i,j}\left(t\right)g_{i,j}\left(t\right)}{{\mathrm{\Gamma }}_i}\right)⌋\right),(1)$

where ⌊⋅⌋ represents that the number is rounded down to the nearest integer. N_s is the OFDM symbol rate. $R_j^{\text{max}}$ (bits/symbol) is the maximum transmitted bits per symbol for subchannel n_j, which is determined based on the modulation method, signal-to-noise ratio, frequency selective fading, computational complexity, and other factors to guarantee signal quality. Γ_i is the signal-to-interference-plus-noise ratio (SINR) gap coefficient, and g_i,j(t) is the subchannel gain, which are calculated as

${\mathrm{\Gamma }}_i\approx \frac{{\left[Q^{-1}\left(P_e/4\right)\right]}^2}{3},(2)$

$g_{i,j}\left(t\right)=\frac{|H_{i,j}\left(t\right){|}^2}{N_j^{\text{EMI}}\left(t\right)+N_0},(3)$

where P_e is the target bit error rate. Q⁻¹(⋅) is the inverse function of $Q(x)=\frac{1}{2\pi }{\int }_x^{\infty }{e}^{t^2/2}dt$. H_i,j(t) is the frequency response of device m_i on subchannel n_j. N₀ is Gaussian noise. $N_j^{\text{EMI}}(t)$ is the electromagnetic interference generated by the operation of the electrical equipment. We use the alpha steady-state function to describe electromagnetic interference (Zhou et al., 2016), and its characteristic function is given by

$\mathrm{l}\mathrm{g}f\left(x\right)=\left\{\begin{array}{cc}-{\theta }^{\nu }|x{|}^{\nu }\left[1-j\eta \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left(x\right)\mathrm{t}\mathrm{a}\mathrm{n}\frac{\pi \nu }{2}\right]+j\mu x\hfill & ,\nu \ne 1\hfill \\ -\theta |x|\left[1-j\eta \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left(x\right)\frac{2}{\pi }\mathrm{l}\mathrm{g}|x|\right]+j\mu x\hfill & ,\nu =1\hfill \end{array}\right.,(4)$

where ν ∈ (0, 2) is the characteristic index. η ∈ [−1, 1] is a skewed parameter that determines the slope. θ > 0 is a scale parameter used to measure the dispersion. μ ∈ R is a positional parameter. When $\nu \in \left(\mathrm{1,2}\right]$, μ represents the average value; when $\nu \in \left(\mathrm{0,1}\right]$, μ represents the median. sign(⋅) is the sign function.

Define the SINR of device m_i on subchannel n_j as

$SIN{R}_{i,j}\left(t\right)=\frac{P_{i,j}\left(t\right)g_{i,j}\left(t\right)}{{\mathrm{\Gamma }}_i}.(5)$

To ensure reliable data transmission, the SINR constraint is given by

$SIN{R}_{i,j}\left(t\right)\ge SIN{R}_{\text{min}},(6)$

where SINR_min represents the lower bound of SINR.

2.2 Transmission delay and the traffic cost model

The data stored at m_i is modeled as a device-side data queue, the backlog of which evolves as

$L_i\left(t+1\right)=L_i\left(t\right)+A_i\left(t\right)-D_i\left(t\right),(7)$

where A_i(t) is m_i’s collected data amount in the t-th slot. D_i(t) is m_i’s throughput, i.e., the amount of data leaving L_i(t), which is calculated as

$D_i\left(t\right)=\min \left\{L_i\left(t\right)+A_i\left(t\right),\tau {\displaystyle \sum _{j=1}^J}{y}_{i,j}\left(t\right)R_{i,j}\left(t\right)\right\}.(8)$

Therefore, in the t-th slot, the data transmission delay from m_i to the edge server is given by

${\tau }_i\left(t\right)=\min \left\{\tau ,\frac{L_i\left(t\right)+A_i\left(t\right)}{{\sum }_{j=1}^J{R}_{i,j}\left(t\right)}\right\}.(9)$

Since the PLC network belongs to the power grid assets, there is no additional traffic cost when using PLC for data transmission. On the other hand, although 5G provides a higher transmission rate, it belongs to the assets of the telecommunication operator. Extra traffic cost is required when using 5G for data transmission, which is given by

$C_i\left(t\right)=x_i^{5\text{G}}\left(v\right)e^{5\text{G}}\left(v\right)D_i\left(t\right),(10)$

where e^5G(v) represents the unit cost of transmitting single bit data through the 5G subchannel at the v-th epoch.

2.3 Queuing delay model

For the data queue, we normally expect the mean rate of data queue to be stable. L_i(t) is mean rate stable if

$\underset{T\to \infty }{\lim }\frac{\mathbb{E}\left\{|L_i\left(t\right)|\right\}}{T}=0.(11)$

Queuing delay is defined as the ratio obtained by dividing the average quantity of data backlogged in the queue by the mean rate at which data arrive. Then, the queuing delay of data transmission at device m_i is given by

${\tau }_i^{\text{que}}\left(t\right)=\frac{L_i\left(t\right)}{{\widehat{A}}_i\left(t\right)},(12)$

where ${\widehat{A}}_i(t)$ is the average data arrival rate of m_i, which is calculated as

$\widehat{A_i}\left(t\right)=\frac{1}{t-1}{\displaystyle \sum _{s=1}^{t-1}}{A}_i\left(s\right).(13)$

To avoid a large queue backlog and meet the low-delay requirement of energy dispatch, a constraint of the long-term average queuing delay over T slots is given by

$\underset{T\to \infty }{\lim }\frac{1}{T}{\displaystyle \sum _{t=1}^T}{\tau }_i^{\text{que}}\left(t\right)\le {\tau }_{i,\mathrm{m}\mathrm{a}\mathrm{x}}^{\text{que}},(14)$

where ${\tau }_{i,\mathrm{m}\mathrm{a}\mathrm{x}}^{\text{que}}$ represents the average queuing delay threshold.

2.4 Problem formulation

The optimization problem is a joint minimization problem that aims to jointly minimize data transmission delay and traffic cost through the large-timescale optimization of device communication mode selection and the small-timescale optimization of subchannel allocation. The constraints of the subchannel allocation number, subchannel allocation quota, data transmission reliability, and long-term average queuing delay are taken into account. The data transmission delay and traffic cost joint minimization problem is formulated as

$\begin{array}{ll}\hfill & \mathbf{P}\mathbf{1}:\underset{\left\{{\mathit{x}}_i\left(v\right),y_{i,j}\left(t\right)\right\}}{\min }\underset{T\to \infty }{\lim }\frac{1}{T}{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{i=1}^I}\left[{\tau }_i\left(t\right)+\alpha C_i\left(t\right)\right]\hfill \\ \hfill \text{s.t.}& C_1:x_i^{\text{PLC}}\left(v\right),x_i^{5\text{G}}\left(v\right)\in \left\{\mathrm{0,1}\right\},\forall m_i\in \mathcal{M},\forall v\in \mathcal{V},\hfill \\ \hfill & C_2:x_i^{\text{PLC}}\left(v\right)+x_i^{5\text{G}}\left(v\right)=1,\forall m_i\in \mathcal{M},\forall v\in \mathcal{V},\hfill \\ \hfill & C_3:0\le {\displaystyle \sum _{i=1}^I}{x}_i^{\text{PLC}}\left(v\right)\le J_1,\forall v\in \mathcal{V},\hfill \\ \hfill & C_4:0\le {\displaystyle \sum _{i=1}^I}{x}_i^{5\text{G}}\left(v\right)\le J_2,\forall v\in \mathcal{V},\hfill \\ \hfill & C_5:0\le {\displaystyle \sum _{j=1}^J}\left[x_i^{\text{PLC}}\left(v\right)y_{i,j}\left(t\right)+x_i^{5\text{G}}\left(v\right)y_{i,j}\left(t\right)\right]\hfill \\ \hfill & \le q_m,\forall m_i\in \mathcal{M},\forall t\in \mathcal{T},\forall v\in \mathcal{V}\hfill \\ \hfill & C_6:{\displaystyle \sum _{i=1}^I}\left[x_i^{\text{PLC}}\left(v\right)y_{i,j}\left(t\right)+x_i^{5\text{G}}\left(v\right)y_{i,j}\left(t\right)\right]\hfill \\ \hfill & \le 1,\forall n_j\in \mathcal{N},\forall t\in \mathcal{T},\forall v\in \mathcal{V}\hfill \\ \hfill & C_7:SIN{R}_{i,j}\left(t\right)\ge SIN{R}_{\text{min}},\forall m_i\in \mathcal{M},\forall n_j\in \mathcal{N},\forall t\in \mathcal{T},\hfill \\ \hfill & C_8:\underset{T\to \infty }{\lim }\frac{1}{T}{\displaystyle \sum _{t=1}^T}{\tau }_i^{\text{que}}\left(t\right)\le {\tau }_{i,\mathrm{m}\mathrm{a}\mathrm{x}}^{\text{que}},\hfill \end{array}(15)$

where α represents the weight of traffic cost. C₁ is the constraint of the large-timescale device communication mode selection variable. C₂ indicates that the device can only choose one of the communication modes in an epoch. C₃ indicates that PLC channels can be allocated to at most J₁ devices. C₄ indicates that 5G subchannels can be allocated to at most J₂ devices. C₅ is the constraint on the number of subchannels allocated to one device in each slot. C₆ indicates that each subchannel can be allocated to at most one device. C₇ is the constraint of the data transmission reliability requirement. C₈ is the constraint of long-term average queuing delay.

2.5 Problem transformation

The formulated joint optimization problem is a stochastic problem with a long-term perspective, which cannot be solved in polynomial time because the long-term constraint of average queuing delay is coupled with the short-term tradeoff between queuing delay and traffic cost per slot. Therefore, we utilize Lyapunov optimization to provide a tractable solution by transforming the problem based on the virtual queue concept. Specifically, virtual queue O_i(t) corresponding to C₈ evolves as

$O_i\left(t+1\right)=\max \left\{O_i\left(t\right)+{\tau }_i^{\text{que}}\left(t\right)-{\tau }_{i,\mathrm{m}\mathrm{a}\mathrm{x}}^{\text{que}},0\right\}.(16)$

If O_i(t) is mean rate stable, C₈ holds automatically. Based on O_i(t), P1 is rewritten as

$\begin{array}{ll}\hfill & \mathbf{P}\mathbf{2}:\underset{\left\{{\mathit{x}}_i\left(v\right),y_{i,j}\left(t\right)\right\}}{\min }{\displaystyle \sum _{i=1}^I}\left[{\tau }_i\left(t\right)+\alpha C_i\left(t\right)+O_i\left(t\right){\tau }_i^{\text{que}}\left(t\right)\right]\hfill \\ \hfill \text{s.t.}& C_1\sim C_7.\hfill \end{array}(17)$

3 Delay and cost-balanced communication resource management algorithm based on two-layer iterative matching

The optimization problem formulated in (17) involves both large and small timescales. To address it, we propose a delay and cost balanced communication resource management algorithm based on two-layer iterative matching, which is shown in Figure 2. First, the initial optimization problem has been broken down into a communication mode selection subproblem in large-timescale epoch and a subchannel allocation subproblem in a small-timescale slot. Next, we propose a large-timescale communication mode selection algorithm based on I-to-2 bidding matching to select the communication mode at each epoch. Here, I-to-2 indicates that the matching is implemented in a bidding fashion between I devices and two communication modes. On this basis, based on the many-to-many deferred acceptance matching algorithm, a small-timescale subchannel allocation algorithm is proposed to match devices with subchannels based on bilateral preferences.

Figure 2

Figure 2. Schematic diagram of the delay and cost-balanced communication resource management algorithm based on two-layer iterative matching.

3.1 Large-timescale communication mode selection based on I-to-2 bidding matching

In this subsection, the proposed large-timescale communication mode selection algorithm based on I-to-2 bidding matching is introduced. It establishes a stable matching between I devices and two communication modes through iterative bidding. As the communication mode selected by a device in a large-timescale epoch influences the data transmission delay and traffic cost of multiple slots in that epoch, the large-timescale decision-making is coupled with future performance of small-timescale optimization. To address the issue of the lack of a priori knowledge of future performance, historical data transmission delay and historical traffic cost are used to construct the preference value of device toward the communication mode. Then, a device selects its most preferred communication mode based on the preference values.

However, due to the constraint of the subchannel number, matching competition among devices occurs if the device number selecting the PLC mode exceeds J₁, or the device number selecting the 5G communication mode exceeds J₂. Bidding matching can effectively solve the competition between devices, improve the convergence speed, and reduce the complexity by lowering the preference value so as to enforce devices giving up competing for the same communication mode. The proposed algorithm adopts iterative bidding to resolve competition among devices toward communication mode selection. Specifically, a bidding price is introduced to reduce the preference value of a device toward the competing communication mode at each iteration, thereby forcing some devices to choose the other communication mode and quit competition. Moreover, the bidding price can be dynamically adjusted according to the virtual queue backlog and queuing delay to provide higher priority for devices with a larger queue backlog and queuing delay. The specific implementation procedures are summarized in Algorithm 1, which are introduced below.

3.1.1 Initialization

Define the preference values of device m_i for selecting the PLC mode and 5G communication mode as ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$, respectively. The bidding prices for device m_i to select the PLC mode or 5G communication mode are defined as $p_i^{\text{PLC}}(v)$ and $p_i^{5\text{G}}(v)$.

Represent the set of devices queuing for matching as Π, the set of devices that issue requests to PLC mode as Λ^PLC, and the set of devices that issue requests to 5G communication mode as Λ^5G. Initialize $\mathbf{\Pi }=\mathcal{M}$, Λ^PLC =∅, Λ^5G =∅, ${\gamma }_i^{\text{PLC}}(0)=\rho$, and ${\gamma }_i^{5\text{G}}(0)=\rho$, $\forall m_i\in \mathcal{M}$, where ρ is a predefined constant.

Algorithm 1.Large-timescale communication mode selection based on I-to-2 bidding matching.

1: For v= 1, 2, …, V, do

2:   Phase 1: Initialization

3:   Initialize $\mathbf{\Pi }=\mathcal{M}$, Λ^PLC=∅, Λ^5G=∅, ${\gamma }_i^{\text{PLC}}(0)=\rho$, and ${\gamma }_i^{5\text{G}}(0)=\rho$.

4:   Phase 2: 5G and PLC preference value calculation

5:  Calculate ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$ based on (18) and (19).

6:  while Π≠ ∅, do

7:    Phase 3: 5G and PLC preference list construction

8:    Construct P_i based on ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$.

9:    Phase 4: I-to-2 matching

10:    $m_i\in \mathcal{M}$ sends matching request to its most preferred communication mode based on ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$.

11:    if |Λ^PLC| ≤ J₁, then

12:      m_i∈ Λ^PLC selects the PLC mode and sets the corresponding $x_i^{\text{PLC}}(v)=1$.

13:      Update Π= Π\Λ^PLC

14:    end if

15:    if |Λ^5G| ≤ J₂, then

16:      m_i∈ Λ^5G selects the 5G communication mode and sets the corresponding $x_i^{5\text{G}}(v)=1$.

17:      Update Π= Π\Λ^5G

18:    end if

19:    Phase 5: bidding matching and preference value update

20:    if |Λ^PLC| > J₁, then

21:    m_i∈ Λ^PLC starts bidding and updates ${\gamma }_i^{\text{PLC}}(v)$ based on Eq. (20) and (22).

22:    if $\exists m_i\in {\mathbf{\Lambda }}^{\text{PLC}},{\gamma }_i^{\text{PLC}}(v)<{\gamma }_i^{5\text{G}}(v)$, then

23:      m_i sends matching request to the 5G communication mode and updates Λ^PLC= Λ^PLC\m_i.

24:     end if

25:   end if

26:   if |Λ^5G| > J₂, then

27:    m_i∈ Λ^5G starts bidding and updates ${\gamma }_i^{5\text{G}}(v)$ based on Eq. (21) and (23).

28:    if $\exists m_i\in {\mathbf{\Lambda }}^{5\text{G}},{\gamma }_i^{5\text{G}}(v)<{\gamma }_i^{\text{PLC}}(v)$, then

29:      m_i sends matching request to the PLC mode and updates Λ^5G= Λ^5G\m_i.

30:    end if

31:   end if

32:   Repeat the above steps until Π=∅.

33:  end while

34:end for

3.1.2 5G and PLC preference value calculation

The preference values ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$ are calculated by the edge server. We utilize the historical performance to calculate the preference values ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$, which are represented as Eq. 18, Eq. 19, respectively. Here, Eq. 18 is considered an example. The first term of the numerator, i.e., ${\gamma }_i^{\text{PLC}}(v-1)\left({\sum }_{z=1}^{v-1}{x}_i^{\text{PLC}}(z)+1\right)$, represents the accumulative preference value of m_i for PLC until the (v − 1)-th epoch, while the second term of the numerator, i.e., $x_i^{\text{PLC}}(v)\frac{{\sum }_{t=(v-1)T_0}^{v{T}_0}{\tau }_i(t)}{T_0}$, represents the average transmission delay of m_i within the v-th epoch. The denominator, i.e., ${\sum }_{z=1}^v{x}_i^{\text{PLC}}(z)+1$, represents the total number of selecting PLC mode of m_i until the v-th epoch. Eq. 19 is defined similarly.

${\gamma }_i^{\text{PLC}}\left(v\right)=\frac{{\gamma }_i^{\text{PLC}}\left(v-1\right)\left({\sum }_{z=1}^{v-1}{x}_i^{\text{PLC}}\left(z\right)+1\right)-x_i^{\text{PLC}}\left(v\right)\frac{{\sum }_{t=\left(v-1\right)T_0}^{v{T}_0}{\tau }_i\left(t\right)}{T_0}}{{\sum }_{z=1}^v{x}_i^{\text{PLC}}\left(z\right)+1},(18)$

${\gamma }_i^{5\text{G}}\left(v\right)=\frac{{\gamma }_i^{5\text{G}}\left(v-1\right)\left({\sum }_{z=1}^{v-1}{x}_i^{5\text{G}}\left(z\right)+1\right)-x_i^{5\text{G}}\left(v\right)\frac{{\sum }_{t=\left(v-1\right)T_0}^{v{T}_0}\left({\tau }_i\left(t\right)+\alpha C_i\left(t\right)\right)}{T_0}}{{\sum }_{z=1}^v{x}_i^{5\text{G}}\left(z\right)+1}.(19)$

3.1.3 5G and PLC preference list construction

Denote the 5G and PLC preference list of device m_i as P_i. Each device constructs the preference list by arranging its preference values ${\gamma }_i^{\text{PLC}}(v)$ and ${\gamma }_i^{5\text{G}}(v)$ in a descending order. The communication mode with the largest preference value is prioritized to be selected, which ranks top in the preference list.

3.1.4 I-to-2 matching

Each device m_i ∈ Π issues a matching request to its most preferred communication mode based on its preference list. Denote the number of devices selecting the PLC mode as |Λ^PLC|, which is the number of elements in the set Λ^PLC. Similarly, the number of devices selecting the 5G communication mode is |Λ^5G|. When |Λ^PLC| ≤ J₁, devices selecting the PLC mode, i.e., m_i ∈ Λ^PLC, are matched successfully with the PLC mode, i.e., $x_i^{\text{PLC}}(v)=1$. Then, the devices which are successfully matched with the PLC mode are removed from the set of unmatched devices, i.e., Π = Π\Λ^PLC. Similarly, when |Λ^5G| ≤ J₂, devices selecting the 5G mode, i.e., m_i ∈ Λ^5G, are matched successfully with the 5G communication mode, i.e., $x_i^{5\text{G}}(v)=1$. Then, the devices which are successfully matched with the 5G mode are removed from the set of unmatched devices, i.e., Π = Π\Λ^5G.

3.1.5 Bidding matching and preference value update

When |Λ^PLC|≥ J₁ or |Λ^5G|≥ J₂, competition of communication mode selection occurs, and C₃ or C₄ cannot be satisfied. To address the competition issues, bidding matching is proposed to iteratively reduce the preference value based on the bidding price. Moreover, the bidding price can be dynamically adjusted to enable larger preference for devices with a large queuing delay and virtual queue backlog.

To enable higher priority for devices with a larger virtual queue backlog and queuing delay, the bidding price is negatively proportional to an historical virtual queue backlog and queuing delay. The bidding prices of device m_i toward PLC and 5G modes are given by

$p_i^{\text{PLC}}\left(v\right)=\frac{{\beta }^{\text{PLC}}{\gamma }_i^{\text{PLC}}\left(v\right)}{{\sum }_{t=\left(v-1\right)T_0}^{v{T}_0}{O}_i\left(t\right){\tau }_i^{\text{que}}\left(t\right)},(20)$

$p_i^{5\text{G}}\left(v\right)=\frac{{\beta }^{5\text{G}}{\gamma }_i^{5\text{G}}\left(v\right)}{{\sum }_{t=\left(v-1\right)T_0}^{v{T}_0}{O}_i\left(t\right){\tau }_i^{\text{que}}\left(t\right)},(21)$

where β^PLC and β^5G denote the bidding price coefficients for the PLC and 5G communication modes, respectively. Taking (20) as an example, the numerator represents the bidding step size, and the denominator represents the historical virtual queue backlog and queuing delay.

The device m_i reduces its preference values for the PLC and 5G communication modes by subtracting the bidding prices, which are given by

${\gamma }_i^{\text{PLC}}\left(v\right)={\gamma }_i^{\text{PLC}}\left(v\right)-p_i^{\text{PLC}}\left(v\right),(22)$

${\gamma }_i^{5\text{G}}\left(v\right)={\gamma }_i^{5\text{G}}\left(v\right)-p_i^{5\text{G}}\left(v\right).(23)$

Since the bidding price is negatively related to the virtual queue backlog and queuing delay, devices with worse historical performances will have a larger preference value and higher priority to be matched.

Then, repeat 3), 4), and 5) until Π =∅.

In 3), i.e., the procedure of 5G and PLC preference list construction, devices reconstruct the preference list based on the updated preference values. The subtraction of bidding price lowers the preference value and changes the ranking of communication modes in the preference list. For example, device m_i which used to select PLC in the previous iteration may select 5G in the current iteration because the preference value toward PLC is reduced, and the PLC mode becomes less attractive than 5G. In this way, bidding price enforces some devices to withdraw matching, thereby resolving communication mode selection competition.

3.2 Small-timescale subchannel allocation based on many-to-many deferred acceptance matching

Based on the large-timescale optimization results of communication mode selection, the small-timescale subchannel allocation problem is decomposed into a PLC subchannel allocation subproblem and a 5G subchannel allocation subproblem, which can be solved simultaneously by the proposed many-to-many deferred acceptance matching. The objective is to minimize the weighted sum of data transmission delay and traffic cost by establishing a bilateral matching relationship between devices and subchannels. Some definitions of the algorithm put forward are described below.

Definition 1 (Bilateral preference relation): For the matching between devices and subchannels, the complete, reflective, and transitive bilateral relation between devices and subchannels, i.e.,“ ≻,” is expressed” through the bilateral preference relation, which indicates the extent of mutual preference. It is introduced to compare the preferences as

$m_i{\succ }_{n_j}{n}_{j\prime }\iff {\omega }_{i,j}\left(t\right)>{\omega }_{i,j^{\prime }}\left(t\right),(\mathrm{24a})$

$n_j{\succ }_{m_i}{m}_{i^{\prime }}\iff {\lambda }_{i,j}\left(t\right)>{\lambda }_{i^{\prime },j}\left(t\right),(\mathrm{24b})$

where ⇔ means equivalence. $m_i{\succ }_{n_j}{n}_j^{\prime }$ means that the device m_i prefers the subchannel n_j more than the subchannel n_j′ because ω_i,j′(t) is smaller than the preference value ω_i,j(t). $n_j{\succ }_{m_i}{m}_{i^{\prime }}$ means that the subchannel n_j prefers the device m_i more than the device m_i’ because λ_i′,j(t) is smaller than the preference value λ_i,j(t).

Definition 2 (bilateral matching): The small-timescale subchannel allocation is a bilateral matching ϕ with constraints of device quota and transmission reliability, i.e.,

$\varphi \left(m_i\right)\subseteq \mathcal{N}\text{and}|\varphi \left(m_i\right)|\le q_m,\forall n_j\in \mathcal{N},(\mathrm{25a})$

$\varphi \left(n_j\right)\subseteq \mathcal{M}\text{and}|\varphi \left(n_j\right)|\le 1,\forall m_i\in \mathcal{M},(\mathrm{25b})$

$\varphi \left(m_i\right)\subseteq \mathcal{N}\text{and}SIN{R}_{i,j}\left(t\right)\ge SIN{R}_{\mathit{min}},\forall m_i\in \mathcal{M},(\mathrm{25c})$

$n_j\in \varphi \left(m_i\right)\iff m_i\in \varphi \left(n_j\right),(\mathrm{25d})$

where (25a) ensures that at most q_m subchannels can be allocated to m_i. (25b) indicates that each subchannel can be allocated to at most one device. (25c) indicates that the SINR of the subchannel allocated to m_i needs to meet the requirement of transmission reliability. (25d) means that the subchannel n_j is matched to the device m_i if m_i is matched to n_j.

Definition 3 (stable matching): If the matching ϕ satisfies individual rationality criteria and is not disrupted by any pair, it is deemed to be stable.

Based on the above definitions, we propose the small-timescale subchannel allocation algorithm based on many-to-many deferred acceptance matching. Algorithm 2 encapsulates the detailed procedural steps for implementation.

Algorithm 2.Small-timescale subchannel allocation based on many-to-many deferred acceptance matching.

1:for t= (v− 1)T₀+ 1, (v− 1)T₀+ 2, …, vT₀ do

2:   Phase 1: Grouping and initialization

3:   Initialize Θ_i(t) =∅ and y_i,j= 0.

4:   Phase 2: Bilateral preference value calculation

5:   $\forall m_i\in \mathcal{M}$ calculates its preference value toward n_j based on (26) and (28).

6:   $\forall n_j\in \mathcal{N}$ calculates its preference value toward m_i based on (27) and (29).

7:   Phase 3: Bilateral partial preference list construction

8:   m_i and n_j construct ${\mathcal{F}}_i^D$ and ${\mathcal{F}}_j^C$ based on C₇ and large-timescale optimization results.

9:   Phase 4: Device and 5G subchannel bilateral deferred acceptance matching

10:   $\forall m_i\in {\mathcal{M}}^{5\text{G}}$ sends matching proposals to its most preferred $\left(q_m-|{\mathrm{\Theta }}_i(t)|\right)$ 5G subchannel in ${\mathcal{F}}_i^D$.

11:   for n_j, j= J₁+ 1, …, J do

12:    if C₆ is satisfied then

13:     Derive stable matching between devices and 5G subchannels.

14:    end if

15:    if C₆ is not satisfied then

16:     if y_i,j= 0 then

17:      n_j selects the device m_i with the largest preference rejects the other devices and sets y_i,j(t) = 1.

18:     else

19:        n_j compares m_i’ with m_i and selects the device with the largest preference value.

20:        n_j rejects the other devices and renews the tentative matching relationship.

21:     end if

22:    end if

23:    Remove the devices which are temporarily matched with 5G subchannels from ${\mathcal{F}}_j^C$. Remove the 5G subchannels which have rejected m_i from ${\mathcal{F}}_i^D$.

24:    Repeat the above steps until no 5G subchannel remains.

25:   end for

26:   Phase 5: Device and PLC subchannel bilateral deferred acceptance matching

27:   Perform the bilateral deferred acceptance matching between devices and PLC subchannel similarly.

28: end for

3.2.1 Grouping and initialization

According to the large-timescale optimization results of communication mode selection, devices are divided into two groups. Among them, the devices that select the PLC mode belong to the set ${\mathcal{M}}^{\text{PLC}}$, and the devices that select the 5G communication mode belong to the set ${\mathcal{M}}^{5\text{G}}$. Define Θ_i(t) as the set of PLC subchannels that are currently matched with m_i. Denote |Θ_i(t)| as the size of Θ_i(t), i.e., the number of subchannels allocated to m_i. Initialize y_i,j(t) = 0 and Θ_i(t) =∅.

3.2.2 Bilateral preference value calculation

According to the grouping results, $\forall m_i\in {\mathcal{M}}^{\text{PLC}}$, the preference values of m_i toward the PLC subchannel n_j are calculated by the edge server, which is defined as the reciprocal of the data transmission delay, i.e.,

${\omega }_{i,j}\left(t\right)=\frac{x_i^{\text{PLC}}\left(v\right)}{{\tau }_i\left(t\right)},j=1,\dots ,J_1.(26)$

Considering higher priority for devices with a large virtual queue backlog and queuing delay, the preference value of the PLC subchannel n_j toward m_i is defined as the product of the virtual queue backlog and queuing delay, which is given by

${\lambda }_{i,j}\left(t\right)=x_i^{\text{PLC}}\left(v\right)O_i\left(t\right){\tau }_i^{\text{que}}\left(t\right),j=1,\dots ,J_1.(27)$

Similarly, $\forall m_i\in {\mathcal{M}}^{5\text{G}}$, combined with the extra traffic cost of using 5G subchannels, the preference value of m_i toward 5G subchannel n_j is defined as

${\omega }_{i,j}\left(t\right)=\frac{x_i^{5\text{G}}\left(v\right)}{{\tau }_i\left(t\right)+\alpha C_i\left(t\right)},j=J_1,\dots ,J.(28)$

The preference value of the 5G subchannel n_j toward m_i is given by

${\lambda }_{i,j}\left(t\right)=x_i^{5\text{G}}\left(v\right)O_i\left(t\right){\tau }_i^{\text{que}}\left(t\right),j=J_1,\dots ,J.(29)$

3.2.3 Bilateral partial preference list construction

Unlike the large-timescale matching in communication mode selection, the preference list of subchannel allocation is partial because subchannels which cannot meet the minimum SINR requirement are removed from the preference list. Assuming that device m_i selects the 5G communication mode, the set of available 5G subchannels for m_i is defined as ${\mathcal{N}}_i(t)=\left\{n_j|n_j\in \mathcal{N},SIN{R}_{i,j}(t)\ge SIN{R}_{\text{min}},j=J_1+1,\dots ,J\right\}$.

Then, m_i constructs the partial preference list of 5G subchannels, i.e., ${\mathcal{F}}_i^D$, by sorting the preference values of 5G subchannels of set ${\mathcal{N}}_i(t)$ in descending order. Next, each 5G subchannel constructs the preference list of devices based on (29). The partial preference list of the subchannel n_j is defined as ${\mathcal{F}}_j^C$. The bilateral preference lists between devices and PLC subchannels are constructed similarly.

3.2.4 Device and 5G subchannel bilateral deferred acceptance matching

Bilateral deferred acceptance is used to derive a stable matching between devices and 5G subchannels.

Step 1. $m_i\in {\mathcal{M}}^{5\text{G}}$ sends matching proposals to its most preferred $\left(q_m-|{\mathrm{\Theta }}_i(t)|\right)$ 5G subchannels in its preference list ${\mathcal{F}}_i^D$.

Step 2. Each 5G subchannel, i.e., n_j, j = J₁ + 1, …, J, calculates the total number of received matching proposals. If the matching proposals received by all 5G subchannels meet the constraint C₆, then a stable matching between devices and 5G subchannels is derived. The bilateral deferred acceptance matching is terminated. Otherwise, if the constraint C₆ is not satisfied, execute Step 3.

Step 3. Assume that n_j receives more than one matching proposals. If n_j has not established a tentative matching relationship with any device in previous iterations, it selects the device with the largest preference, e.g., m_i, and rejects the other devices. Then, a tentative matching relationship is established between n_j and m_i, i.e., y_i,j(t) = 1.

If n_j has established a tentative matching relationship with some device in previous iterations, e.g., m_i’, it compares m_i’ with m_i and selects the device with the largest preference value. Next, it rejects other devices and renews the tentative matching relationship. Therefore, devices which have been matched with subchannels in previous iterations may get rejected in later iterators if better matching candidate appears, which stands for the meaning of deferred acceptance.

Step 4. The devices which are temporarily matched with 5G subchannels are removed from the set ${\mathcal{F}}_j^C$. Meanwhile, the 5G subchannels which have rejected m_i are removed from the set ${\mathcal{F}}_i^D$. Then, go back to Step 1 and reperform bilateral matching for the rejected devices until no 5G subchannel remains.

3.2.5 Device and PLC subchannel bilateral deferred acceptance matching

The bilateral deferred acceptance matching between devices and PLC subchannels is performed similarly as that of 5G. The iterative process between n_j and m_i is repeated until no PLC subchannel remains. The proposed algorithm divides devices into two groups based on the large-timescale communication mode selection result and allows parallel implementation of two matchings. This dramatically reduces matching complexity and convergence performance compared to existing approaches.

4 Simulation results

Within this segment, the efficacy of the algorithm put forward is assessed via simulation-based analysis. An IoT-empowered distribution energy dispatch scenario containing 10 IoT devices is set. The quota of subchannel allocation q_m is set as 10. There are 128 orthogonal subchannels, including 100 PLC subchannels and 28 5G subchannels. The alpha steady-state function is used to describe electromagnetic interference. Table 2 presents the parameters used for the simulation (Liao et al., 2020; Zhang P. et al., 2023). Two existing algorithms are compared with the algorithm put forward. The first algorithm is the resource allocation scheme based on the fire algorithm (RAF), which minimizes the weighted sum of transmission delay and traffic cost and ignores the large-timescale optimization of communication mode selection (Liu et al., 2019). The second algorithm is the resource allocation algorithm based on one-to-many matching (RAOM), which neglects the traffic cost optimization (Yuan et al., 2019). Both comparison algorithms do not consider the long-term average queuing delay constraint.

Table 2

Table 2. Simulation parameters (Seo, 2012).

Figure 3 shows the weighted sum of data transmission delay and traffic cost versus time slot. With the device number escalating from 100 to 300, the weighted sum performances of the proposed algorithm, RAF, and RAOM exhibit enhancements of 20.82%, 53.78%, and 37.47%, respectively. The algorithm put forward considers the optimization of the communication mode selection and subchannel allocation in a multi-timescale. In a large timescale, by updating the bidding price, the proposed algorithm resolves the conflicts among devices. In a small timescale, the proposed algorithm calculates the preference value based on the data transmission delay, traffic cost, virtual queue backlog, and queuing delay. The proposed algorithm constructs the partial preference list, according to the data transmission reliability requirement, and executes the grouping matching based on the large-timescale decisions. This effectively reduces the complexity of matching iteration and improves the weighted sum of data transmission delay and traffic cost while satisfying the long-term average queuing delay constraint. RAF ignores the large-timescale communication mode selection, leading to the high complexity and worse weighted sum performance. RAOM does not consider traffic cost optimization, and its performance is the worst.

Figure 3

Figure 3. Weighted sum of data transmission delay and traffic cost versus time slot (I =100).

Figure 4 shows the weighted sum of data transmission delay and traffic cost versus the number of devices. With the device number escalating from 10 to 110, the weighted sum performances of the proposed algorithm, RAF, and RAOM exhibit enhancements of 20.82%, 53.78%, and 37.47%, respectively. When I = 110, compared with RAF and RAOM, the proposed algorithm reduces the weighted sum performance by 33.13% and 53.65%, respectively. The algorithm put forward addresses the conflicts through the dynamic bidding in a large timescale and the bilateral deferred acceptance matching in a small timescale, which can achieve the stable two-layer iterative matching strategies among devices.

Figure 4

Figure 4. Weighted sum of data transmission delay and traffic cost versus the number of devices.

Figure 5 shows the traffic cost versus proportion of the 5G subchannel. As the proportion of the 5G subchannel increases from 15% to 60%, the traffic cost of the proposed algorithm increases at a slower pace compared to that of RAF and RAOM. When the proportion of 5G subchannel is 60%, the traffic cost of the proposed algorithm is 34.03% and 53.35% lower than those of RAF and RAOM, respectively. The proposed algorithm considers the trade-off between data transmission delay and traffic cost, avoiding the problem of high traffic cost due to the excessive selection of 5G channels when the 5G subchannel number is high.

Figure 5

Figure 5. Traffic cost versus proportion of the 5G subchannel.

Figure 6 shows the data transmission delay and traffic cost versus α. The simulation result shows that the traffic cost increases gradually with α, while the data transmission delay decreases contrarily. When α increases from 100 to 900, the data transmission delay is reduced by 95.25%, and the traffic cost is increased by 55.45%. The increase in α makes the proposed algorithm tend to optimize the transmission delay. Therefore, a dynamic tradeoff is achieved between data transmission delay and traffic cost by adaptively adjusting α in the proposed algorithm.

Figure 6

Figure 6. Data transmission delay and traffic cost versus α.

Figure 7 shows the box plots of the virtual queue backlog. Compared with RAF and RAOM, the proposed algorithm reduces the median virtual queue backlog by 23.73% and 30.08%, respectively. The proposed algorithm transforms the long-term constraint of average queuing delay into the stability of virtual queue based on Lyapunov optimization. Moreover, it considers the virtual queue of queuing delay into the preference value calculation and effectively solves the competition problem among devices.

Figure 7

Figure 7. Box plots of the virtual queue backlog.

Figure 8 shows the weighted sum of data transmission delay and traffic cost versus SINR_min. As SINR_min increases, the weighted sum performances of the three algorithms gradually increase. The proposed algorithm achieves smallest increment. This is due to the decrease in available channels caused by the increase in SINR_min, resulting in an overall performance degradation. The proposed algorithm can optimize the communication resource allocation strategies based on the alternately iterative matching between the large timescale and small timescale. In addition, the proposed algorithm enhances the optimality of matching through the bidding and deferred acceptance mechanisms.

Figure 8

Figure 8. Weighted sum of data transmission delay and traffic cost versus SINR_min.

5 Conclusion

In this paper, we addressed the joint minimization problem of data transmission delay and traffic cost. The delay and cost-balanced communication resource management algorithm based on two-layer iterative matching is proposed to satisfy the constraints of the subchannel allocation number, subchannel allocation quota, data transmission reliability, and long-term average queuing delay by jointly optimizing the large-timescale communication mode selection and small-timescale subchannel allocation. Compared with the RAF and RAOM algorithm, the proposed algorithm reduces the weighted sum of data transmission delay and traffic cost by 43.22% and 22.13%, respectively. Particularly, the proposed algorithm can efficiently guarantee the long-term average queuing delay constraint. Compared with RAF and RAOM, the proposed algorithm reduces the median virtual queue backlog by 23.73% and 30.08% and achieves the best queuing delay performance.

The large-scale access of IoT devices causes an explosion of data for distribution energy dispatch. Limited computing resources of the edge server cannot meet the data processing demands. A potential solution is to combine edge computing with cloud computing, thereby constructing a cloud-edge collaborative computing framework to improve the data processing capacity. However, this increases the optimization complexity of communication resource allocation. How to reasonably allocate computing resources to meet the data processing requirements with different service priority is also an open issue. Therefore, future work will focus on the joint optimization of cloud-edge collaborative communication and computing resources to further improve the data processing performance for IoT-empowered distribution grid energy dispatch.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.

Author contributions

ZS: conceptualization, formal analysis, funding acquisition, investigation, methodology, software, validation, writing–original draft, and writing–review and editing.

Funding

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This work was supported by the China Southern Power Grid Technology Project under the grant number 03600KK52220019 (GDKJXM20220253).

Conflict of interest

Author ZS was employed by Guangdong Power Grid Co., Ltd.

The authors declare that this study received funding from China Southern Power Grid Technology Project. The funder had the following involvement in the study: study design, collection, interpretation of data, the writing of this article, and the decision to submit it for publication.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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