ERAM-EE: Efficient resource allocation and management strategies with energy efficiency under fog–internet of things environments

ABSTRACT

Due to technological advancements, most devices are generating a significant amount of data which needs appropriate technology to handle the data generated by IoT devices. Fog computing addresses this challenges in a decentralised manner. This paper proposes an efficient resource allocation and management strategies with energy efficiency (ERAM-EE) to effectively allocate available resources in Fog-enabled networks. The ERAM-EE algorithm utilises the channel gain matrix of the interconnected network to assign IoT devices to Fog nodes (FNs) through resource blocks (RBs) with three stages. In the initial stage, one FN is assigned to each IoT device through a single RB by calculating the maximum value of the channel gain. In the subsequent stage, the remaining RBs are assigned to unassigned FNs for future task-offloading processes. Finally, the unassigned RBs are allocated to IoT devices by calculating the maximum channel gain of the Fog–IoT networks. Simulated results indicate that the ERAM-EE scheme confirms that each IoT device is mapped with minimum one FN and RB for effective task scheduling and resource management. Analysis reveals that the ERAM-EE method achieved an increase in EE of up to 7, 8, and 18 Mbit/J compared to existing schemes for varying IoT devices, FNs and RBs respectively.

KEYWORDS:

• Fog computing
• internet of things network
• energy efficiency
• resource allocation
• resource management

1. Introduction

Over the past few years, extensive studies have been conducted on mobile Cloud computing, establishing it as the most widely used method for managing computationally effective programmes due to its abundant computation and storage resources. With the advent of the Internet of Things (IoT), future networks are expected to incorporate millions of resource-constrained devices (Ali et al., 2018; Dang et al., 2022; Hosseinpour et al., 2021; Prakasam et al., 2020). However, achieving a high transmission rate is challenging due to the significant distance between IoT devices and data centres, leading to inevitable issues such as congestion, delay, and energy consumption (Dubey et al., 2022; Kumar et al., 2023b). In response to the limitations of mobile Cloud computing, edge computing emerged as an enhancement.

In general, various applications, such as virtual reality in healthcare and driverless cars, are expected to arise, necessitating efficient service performance. These applications typically require the transfer of data to a distant Cloud server due to their ample computing and storage capacity, meeting the increasing demand from distant Cloud data centres. Cloud computing, being a centralised paradigm, encounters challenges for IoT applications concerning computational complexity, latency, interoperability, dependability, and bandwidth due to the large number of devices. Latency, defined as the time lag between sending and receiving data, can significantly impact the performance and response of IoT applications. Over the past several years, Fog-enhanced IoT systems have been employed to handle applications requiring extensive processing (Zhang et al., 2021), potentially limiting the growth of Cloud computing. Issues associated with Fog computing (FC) include heavy workloads, traffic jams, delays, energy consumption, and unstable wireless connections caused by deep vanishing (Ruan et al., 2022). Compared to traditional network architecture, a Fog computing network might offer improved Quality-of-Service (QoS) for nearby IoT devices and increased utilisation of network resources (Cao et al., 2019). The concept of Fog computing, introduced by Cisco in January 2014, represents an alternative to Cloud computing. This method capitalises on the proliferation of computing devices and the data they generate by establishing specific resources for processing at the network's edge. Fog computing is associated with Fog nodes (FNs) positioned closer to devices, situated between the devices and the Cloud. Fog refers to Clouds closer to computing devices, facilitating the early processing of data/tasks generated by edge devices. The primary goal is to bring the system's processing power closer to the network's edge, reducing latency. A non-orthogonal multiple access-based optimisation technique manages numerous devices and FNs to reduce overall network energy consumption and increase efficiency (Mostafa et al., 2022). This method decentralises data centres, thereby reducing response times. In recent years, Fog computing has been proposed to further decrease latency and enhance energy efficiency (EE) by deploying massive, flexible FNs and servers at the network's edge. Efficient resource reallocation poses a typical challenge, with extensive literature, particularly leveraging game theory, due to its distributed nature.

Given the prevailing circumstances, energy conservation emerges as the primary challenge for Fog-based IoT networks, particularly since many devices have limited energy for routine processes without intervention (Chaudhary et al., 2022). In this context, network EE becomes a crucial metric in Fog-IoT networks, serving as a measure of the network's overall performance. EE (bit/J) is defined as the ratio between network transmission rates and power consumption. Mahmud et al. (Mahmud et al., 2018) proposed a clustering and geometric-based power management solution to enhance network EE, ensuring load balancing and minimising the likelihood of outages in various cellular networks. While this solution contributes to improving Cloud computing performance, the need for more decentralised and effective solutions persists. Fog computing, positioned as an intermediary layer connecting IoT devices to the Cloud, serves as a highly virtualised, virtual Cloud-like technology providing end users and Cloud servers with data, computation, storage, and networking services (Agarwal et al., 2016). It optimises the use of computational resources, offering data, software, and infrastructure at a lower cost while maintaining security, dependability, and adaptability. In the face of increased throughput and bandwidth consumption, maintaining load balancing and data consistency with reduced complexity becomes imperative to meet current end-user demands (Sethi et al., 2022).

Within the domain of data centres, one of the primary challenges is the management of energy consumption, which is a crucial factor that affects the operation and maintenance of Cloud computing (Katal et al., 2023). Traditional cellular systems face issues with clients at the cell edge, which necessitates a greater number of resource blocks (RBs) and more time for data uploads.

This, in turn, can potentially lead to a reduction in service quality. The aforementioned issue is further emphasised by the relay scheme proposed for cooperative device-to-device (D2D) networks, which relies on channel gain and transmission link distance. In uplink scenarios, several researchers have suggested methods for selecting relays that utilise D2D communication to minimise resource usage and processing time (Duguma et al., 2022; Jiang et al., 2016; Shah et al., 2015). The resource allocation algorithm for D2D communication is foundational to 5G networks and plays a crucial role in D2D communications (Ranjan et al., 2022). Spectrum allocation and power adjustment optimise the entire Fog network. The buffer-assisted max-link relay selection in cooperative networks enhances the diversity gain of conventional cooperative protocols and facilitates flexible channel state information-based transmission (Tian et al., 2015). To address the challenge of EE in the Fog–IoT environment, the authors introduced a mixed-task paradigm that involves binary and partial offloading. They also employed a novel optimisation approach to enhance the devised scheme (Chen et al., 2020). A strategy to enhance transmission bandwidth efficiency in 5G systems leverages direct communication between User Equipment (UEs) in close proximity, thereby reducing the radio resources needed to transmit content to the base station (Militano et al., 2015). Taking advantage of advancements in artificial intelligence, a deep learning-based method was implemented for relay selection, with the aim of improving data transmission and reducing power consumption in cellular D2D networks (Abdulazeez & Askar, 2023; Zhang et al., 2019). Numerous algorithms have been designed to decrease energy consumption in data centres while maximising user utility and reducing energy consumption during task offloading to servers. Table 1 provides an overview of existing literature related to task scheduling, offloading and resource management strategies within Fog–IoT environments.

Table 1. Review of various literature on task offloading and resource allocation in Fog computing.

S. No	Literature	Contribution(s)	Algorithm and metrics	Limitation(s)
1	(Talaat et al., 2019)	Addressed issues in various Quality-of-services in Fog environments	Effective load-balancing mechanism Average waiting time Failure rate CPU utilisation	Holdups in FNs cache and data length is varied
2	(Hajam & Shabir, 2023a)	Created a Fog network task scheduling technique to reduce the task's overall cost	Greedy task offloading spider monkey optimisation mechanism Energy consumption Degree of imbalance	Multi-objective functions have limited memory and bandwidth resources
3	(Hajam & Shabir, 2023b)	Presented a mathematical approach for solving optimisation issues and evaluating performance during heuristic setup	Spider monkey optimisation strategy Average cost and service time	Task offloading strategy was not employing load-balancing mechanism, which increases latency
4	(Hussein & Mousa, 2020)	Reduced response time of Internet of Things applications by balancing activities on Fog nodes	Ant colony optimisation and particle swarm optimisation Mean response time Degree of imbalance	There is no coordination between Internet of Things devices and dynamic IoT devices may cause Fog node load to be imbalanced
5	(Hosseini et al., 2023)	Used federated learning to conduct latency-sensitive operations based on a priority queue and optimise service while using the least amount of energy	Greedy knapsack offloading algorithm Mean response time Energy efficiency	This strategy offloads a range of activities for processing rather than a single job, increasing reaction time and energy usage for individual operations
6	(Mahini et al., 2021)	Offered practical Internet of Things applications with a focus on a game theory perspective	Game theory Availability Offloading	Increase in the number of tasks processing will increase the processing time.
7	(Dang & Seong, 2021)	Created Internet of Things–Fog–Cloud environments using an adaptive task-offloading technique to provide the lowest possible service provisioning latency	Fog resource-aware adaptive task-offloading reduction ratio latency Mean time for resource mapping	Achieving less response time in different Fog networks is a challenging task
8	(Li et al., 2014)	Combined optimal power allocation and splitting ratio allotment schemes to satisfy optimal degree and power consumption	Iterative algorithm for power allocation Energy efficiency Average splitting ratio	A remote user needs a co-operative signal to enhance data rate
9	(Shruthi et al., 2022)	Formulated the resource allocation concerns in Fog computing using a weighted sum method in a multi-objective approach	Weighted greedy knapsack-based allocation algorithm Power consumption Execution payload	All task functions with variable lengths use a fixed number of Fog nodes; keeping all Fog nodes active during processing uses more energy
10	(Atiq et al., 2023)	Provided a dependable Fog computing architecture for Internet of Things transportation with effective resource management	Reliable resource allocation and management Latency Power consumption	Due to the limited communication range of Internet of Things devices, execution failure may occur

1.1. Motivation

The research suggests that current task offloading and resource allocation techniques primarily focus on reducing the energy consumption of FNs rather than prioritising their effective utilisation. Only a few algorithms consider resource sharing as an alternative for specific task scheduling and offloading in Fog networks with dedicated resources. These approaches often lack an optimal resource allocation technique to address latency, complexity, and data rate issues. The existing literature aims to identify the most effective resources for task offloading, highlighting a research gap. To address this gap, an efficient resource allocation and management strategies with energy efficiency (ERAM-EE) algorithm is proposed, which aims to optimise network EE. Our approach is motivated by the goal of improving average network energy efficiency while ensuring sufficient resource availability and storage capacity on FNs. We propose this technique to establish an efficient method for resource allocation in task offloading within Fog-IoT networks. Moreover, our emphasis on practical task offloading with the highest average network EE arises from the need to consistently serve IoT devices in Fog environments. The study aims to determine the optimal distribution of allocated resources among IoT devices and FNs, leveraging the proposed algorithm to maximise network EE.

1.2. Research contributions

There is a pressing need to implement an effective algorithm for resource allocation, management, and task offloading in IoT-Fog networks. This study addresses this gap by exploring a novel approach to the energy-efficient resource allocation issue in FC, ensuring that task scheduling and offloading are dependent on bandwidth. Prior to assigning task offloading, the states of FNs are assessed, taking into consideration the energy levels of FNs. The primary objective of this research is to analyse and enhance resource allocation algorithms developed for Fog computing systems. The study identifies a reduction in resource utilisation due to unequal task-offloading requests and processing. This inequity is exacerbated by the reluctance of many FNs to freely share resources. Consequently, tasks are often offloaded to a few assigned FNs, resulting in substantial power consumption and congestion among those FNs. Given the distributed nature of Fog-enabled networks and the limited energy resources of many IoT devices, there is a significant demand for efficient resource allocation and management schemes. The notable contributions of this research paper include:

• Proposing ERAM-EE to effectively assign and manage available resources in Fog-enabled networks.

• Generating and utilising the channel gain matrix to allocate RBs to each IoT device and FNs.

• Conducting RB and FN allocation for each IoT device by computing the maximum value in the channel gain matrix. This allocation process unfolds in three steps.

  • o Varying RBs while keeping FNs and IoT devices constant.

  • o Varying IoT devices while keeping RBs and FNs constant.

  • o Varying FNs while keeping RBs and IoT devices constant.

• Proposing an ERAM-EE scheme for optimising energy efficiency at every time instant, subject to various constraints.

• Ensuring, at the end of the process, that:

  • o All IoT devices are connected to at least one FN through the available RB for effective task offloading.

  • o No FN is overloaded and no single RB is congested.

The remainder of this paper is organised as follows. In Section 2, an overview of the system model utilised and problem formulation is addressed. The proposed ERAM-EE is explained along with use case model in section 3. Section 4 deals with an experimental analysis and performance comparison with existing methods. The conclusion and feature scope for further research are dealt in section 5.

2. System model

This section presents a model aimed at optimising resource allocation and management, encompassing IoT devices (K), FNs (N), and RBs (M).

2.1. Network model

The Fog network efficiently handles significant volumes of data with low latency by locally storing and processing a substantial amount of data, leveraging the Fog server for enhanced computing capabilities. While the Cloud server offers infinite resources, it operates within a centralised model for data processing, relying on remote data centres. In contrast, the Fog network operates under a decentralised model, allowing for data processing closer to edge devices and thus reducing latency. The Fog network is particularly advantageous in scenarios that require real-time responses, such as video surveillance, autonomous vehicles, e-health, and industrial control systems (Kumar et al., 2023a). As a result, in the Fog-enabled Cloud network, the network model is divided into three layers: the IoT device layer, the Fog layer, and the Cloud layer, as illustrated in Figure 1.

Figure 1. Network model.

The task requests are initiated by IoT devices, which include intelligent home appliances, intelligent transportation devices, and monitoring devices. The fog layer efficiently manages these task requests from IoT devices through appropriate resource allocation and management strategies to facilitate efficient task offloading. The FNs, located in close proximity to the edge IoT devices, encounter similar computational complexities as the Cloud server. FNs receive tasks/data from IoT devices, process and forward them to the Cloud layer for storage, while simultaneously updating results to enhance security. FNs, being safeguarded, execute some processing locally, minimising the need to send data to the Cloud and thus saving bandwidth. The placement of each FN and IoT device within the infrastructure is randomly distributed. IoT devices are denoted as k, where k ∈ K = {1, 2, 3, … , K}. Each IoT device generates l_k(t) bits of data packets at time t. These data packets must be allocated to various nearby FNs for effective task offloading. IoT devices possess the necessary task details, including the size of all accessible local FNs. Upon receiving information with the required offloading details from device k, the assigned FNs manage the data, computing the average energy consumption before recurring the computing capabilities to IoT device k.

The task-offloading decisions depend on computing resources and energy consumption. The proposed algorithm selects candidate FNs with non-zero computation capability at time t, denoted as m, where m ∈ M = {1, 2, … , M}, each possessing different essential characteristics. In the proposed network model, the bandwidth BW is shared among multiple RBs, divided into N, and the bandwidth for an individual RB is denoted as B = BW/N. FNs in this context may receive task processing requests from numerous IoT devices, prompting the use of the coordinated multiple-point method for improved transmission. Additionally, each IoT device is exclusively assigned a single FN through a single RB, preventing transmission interference among different IoT devices. The signal-to-noise ratio (SNR) of RBs (n) from FNs (m) to IoT devices (k) can be computed using Equation (1). (1) $\mathrm{SN}{R}_{n,m,k}(t)=\frac{P_{n,m,k}(t)|h_{n,m,k}(t){|}^2}{{\sigma }^2}$(1) Where $P_{n,m,k}(t)$ denotes the transmission power of IoT device (k) to FN (m) through RB (n) at time t, $h_{n,m.k}(t)=l_{k.m}(t)\ast g_{n,m,k}(t)$ denotes the respective channel gain, and $l_{k,m}(t)=c\ast s_{k,m}\ast d_{m,k}^{-\alpha }(t)$ represents the large-scale fading factor, influenced by the distance between the IoT node and FN. Here, “c” is the median path gain for 1 km distance, s_k,m is the shadowing notation with zero mean and standard deviation of σ_sh, d_m,k(t) is the distance between FN (m) and IoT device (k), and α is the path loss value. The small-scale fading index is represented as g_n,m,k(t) for an independent complex Gaussian random variable with a mean value of zero and variance of 1.

2.2. Average energy efficiency

Given that IoT devices are designed to operate in remote areas for extended periods without human intervention, it is crucial to accurately assess the power and energy consumption of processors for the development of energy-efficient IoT–Fog–Cloud networks. The average energy consumption and network efficiency are discussed, along with mathematical representations. The power consumption of smaller devices is often measured in W, while larger devices typically have power consumption measured in KW. For example, intelligent thermostats, lighting systems, and appliances can be remotely controlled and optimised for EE with minimal energy consumption. The energy consumption of each device is monitored, analysed, and adjusted based on user preferences and environmental conditions through the integration of IoT devices with Fog networks. The power consumption of the Fog–Cloud layer depends on the tasks generated by IoT devices and their completion time.

The Shannon Fano channel capacity theorem defines the transmission rate (r) for IoT device (k) to FN (m) through RB (n) at an incident t as given by Equation (2). (2) $r_{n,m,k}(t)=B{\log }_2(1+\mathrm{SN}{R}_{n.m.k}(t))$(2) Where “B” represents the bandwidth allocated for each RB. To ensure transmission quality, IoT device (k) must maintain the required transmission rate, expressed by the condition (3) $\sum _{n=1}^N\sum _{m=1}^M{r}_{n,m,k}(t)\ge R_k^{min}$(3) The overall network transmission rate at time “t” is derived from Equation (4). (4) $R_{\mathrm{tot}}(t)=\sum _{k=1}^K\sum _{n=1}^N\sum _{m=1}^M{a}_{k,m}{b}_{n,m}{r}_{n,m,k}(t)$(4) Where a_m,k∈ {0, 1} represents the binary connection status between IoT device (k) and FN (m). When a_m,k is equal to 1, there is no connection. Similarly, b_n,m∈ {0, 1} represents the binary connection status between RB (n) and FN (m). A value of 1 for b_n,m indicates a connection, while 0 indicates no connection.

The mean network rate, denoted as $\overline{R}{}_{\mathrm{tot}}(t),$ is determined by Equaton (4) (5) $\overline{R}{}_{\mathrm{tot}}(t)=\underset{T\to \mathrm{\infty }}{lim}sup\frac{1}{T}\sum _{t=1}^{T}E[R_{\mathrm{tot}}(t)]$(5) where, E[.] denotes the expectation computation. The overall transmission power of FNs for effective task offloading is represented using Equation (6) (6) $P_t(t)=\sum _{k=1}^K\sum _{n=1}^N\sum _{m=1}^M{a}_{k,m}{b}_{n,m}{P}_{n,m,k}(t)/P_m^{\mathrm{af}}$(6) In addition, the power budget for FN (m)'s transmission power should not be exceeded. Thus, we have (7) $\sum _{k=1}^K\sum _{n=1}^N{a}_{k,m}{b}_{n,m}{p}_{k,n,m}(t)\le p_m^{max}$(7) Therefore, the overall processing power is obtained through eqns. (6) and (7), and it is given by (8) $P_c(t)=\sum _{k=1}^K\sum _{n=1}^N\sum _{m=1}^M{a}_{k,m}{b}_{n,m}{\eta }_m{\theta }_m{l}_k(t)$(8) where θ_m is the FN m's energy use per CPU cycle (J/cycle). Furthermore, the processing and transmission power that FNs use together comprise their entire usage. (9) $P_{\mathrm{tot}}(\text{t})=P_t(\text{t})+P_c(\text{t})$(9) The mean value of the power consumption is obtained from Equation (9) as follows. (10) ${\overline{P}}_{\mathrm{tot}}(t)=\underset{T\to \mathrm{\infty }}{lim}sup\frac{1}{T}\sum _{t=1}^{T}E[P_{\mathrm{tot}}(t)]$(10) The average EE is obtained from eqns. (5) and (10), and it can be computed using Equation (11) (11) ${\overline{\eta }}_{\mathrm{EE}}=\frac{{\overline{R}}_{\mathrm{tot}}(\mathbf{a},\mathbf{b},\mathbf{p})}{{\overline{P}}_{\mathrm{tot}}(\mathbf{a},\mathbf{b},\mathbf{p})}$(11) From Equation (11), it is clear that the EE of the network can be maximised by optimising the power consumption of the FNs connected in the Fog–IoT network.

2.3. Processing and response time

The latency, also known as response time, is a metric that combines both transmission delay and processing delay during task offloading. In this context, the IoT devices are represented as k and belong to the set k ∈ K = {1, 2, 3, … , K}. These devices rely on the FN to offload tasks through the RBs in response to task requests. The processing time (T_p) is defined as the time it takes for the FN to execute each query received from the IoT devices through specific RBs. This can be calculated using Equation (12). (12) $T_p=T_c-T_o$(12) Where T_c represents the task completion time, and T_o represents the initial task arrival time for the specific task offloading. The overall time it takes to transfer data between the IoT device and the FN, in both directions, is referred to as response time or overall latency. This can be determined using Equation (13) (13) $T_R=T_P+T_d$(13) Where T_d represents the transmission time required to transfer the task from the IoT device to the FN and vice versa. To further refine the analysis Equation (12) can be substituted into Equation (13), resulting in the final response time as given by Equation (14). (14) $T_R=T_c-T_o+T_d$(14)

2.4. Problem formulation and objective functions

In the Fog–IoT network discussed in this article, the tasks generated by IoT devices undergo offloading and processing by an FN. This presents a multi-objective optimisation problem to minimise EE and optimise the channel gain value. To address the challenges encountered during task offloading, there are two distinct objective functions:

1. Channel gain optimisation – The optimal channel gain value for the FN is selected for task offloading using a maximum gain-based channel matrix computation to enhance task processing efficiency.

2. EE minimisation – EE is minimised by effectively assigning and mapping IoT nodes to the FN through RBs, achieved by the proposed ERAM-EE algorithm. This approach ensures efficient resource allocation and management during task processing.

The multi-objective function for the problem formulation in distributed Fog–IoT networks is defined by eqns. (15) and (16), subject to the constraints specified in Equation (17): (15) $\begin{array}{rl}\text{Opt}({\text{H}}_{\text{f}})& =\text{max }\{\text{R}{\text{B}}_1,\text{ R}{\text{B}}_2,\dots \dots .,\text{R}{\text{B}}_{\text{n}}\}\end{array}$(15) (16) $\begin{array}{rl}min({\overline{\eta }}_{\text{EE}})& =\text{select }(\text{max }\{\text{R}{\text{B}}_1,\text{ R}{\text{B}}_2,\dots \dots .,\text{R}{\text{B}}_{\text{m}}\})\text{ with appropriate IoTs and FNs}.\end{array}$(16) Subject to the following constraints: (17) $\begin{array}{l}\text{C}1:\text{R}{\text{B}}_{\text{m}}>{\text{K}}_{\text{k}}\\ \text{C}2:{\text{K}}_{\text{k}}>\text{F}{\text{N}}_{\text{n}}\\ \text{C}3:{\text{H}}_{\text{f}}\to 1max\text{value}\\ \text{C}4:\text{R}{\text{B}}_{\text{m}}\to 1(\text{K }\mathrm{\&}\text{ FN})\\ \text{C}5:\text{F}{\text{N}}_{\text{n}}\ge 1(\text{K }\mathrm{\&}\text{ RB})\\ \text{C}4:{\text{K}}_{\text{k}}\ge 1(\text{RB }\mathrm{\&}\text{ FN})\end{array}$(17)

3. Proposed efficient resource allocation and resource management strategies with energy efficiency algorithm

The selection of the most suitable FN for connected IoT devices is facilitated by the proposed ERAM-EE algorithm, ensuring effective task offloading. Each IoT device is assigned an RB, which is subsequently allocated to the FN for efficient task offloading, thereby maintaining transmission performance.

The optimisation of QoS in the network is achieved by assigning high EE RBs to their corresponding FNs. Assuming the Fog-enabled network comprises M FNs, N RBs, and K IoT devices, where M, K, and N are chosen such that M ≤ K ≤ N. Based on these values, 3D channel gain matrices are generated in the form of H(K, N, M), where h(k, n, m) represents the channel gain for the k^th IoT devices offloading tasks to the m^th FN through n^th RB. To execute this allocation, the following steps are undertaken, as outlined in the proposed ERAM-EE algorithm presented in algorithm 1.

Table

Algorithm 1

Proposed Efficient Resource Allocation and Management Strategies with Energy Efficiency (ERAM-EE)

Initialise: Fk = {ϕ}, Rm = { ϕ }, k  = {12,3, … , K}, m = {1,2,3, … , M}, n = {1,2,3, … ,N}

Begin

// Step 1: Assigning each IoT device with minimum single FN through one RB for optimal task offloading

for k = 1, 2, 3, … , K

create H (N, M, K) matrix

maximise hn,m,k using the channel gain value of H matrix

compute Rm = Rm + {n} and Fk = Fk + {m}

update N = N–{n} and K = K–{k}

remove H(:,:,k) from H matrix

assign H(n,:,: ) → 0

if |K|  = 0 then

break

endif

end for

// Step 2: Assigning an RB to each FN to guarantee that each FN has at least one RB

for k = 1, 2, 3, … , K

create H^’(N–K, M–x, K)

maximise h’n,m,k using the channel gain value of H’ Matrix

compute Rm = Rm + {n} and Fk = Fk + {m}

update N = N–{n}

remove H’(n,:,: ) form H’ Matrix

assign H’(:,m,: ) → 0

if |M| = 0 then

break

endif

end for

// Step 3: Assigning the remaining unassigned RBs to IoT devices for effective task offloading

for k = 1, 2, 3, … , K

create H”(N–K–M–X, M, K)

maximise h”n,m,k using the channel gain value of H’” Matrix

update N = N–{n}

remove H” (n,:,: )

if |N| = 0 then

break

endif

end for

end

3.1. Working principles of the efficient resource allocation and management strategies with energy efficiency algorithm

The operational principles underlying the various steps of the proposed ERAM-EE algorithm are dealt in this section.

Step 1: Assigning each IoT device to one FN through RB – This step confirms that each device is assigned at least one FN through one RB. It is achieved by selecting the maximum value from the matrix h(n, m, k) and allocating the corresponding RB (n) to the FN (m) for the associated IoT device (k). Once the RB is assigned to the IoT device, the corresponding H matrix of IoT device k is removed, and the rows related to RB (n) in the channel gain matrices are set to zero. Consequently, it can be inferred that there is an absence of RBs for M –×(where 1 ≤ x ≤ M) FNs, and N – K available RBs are available.

Step 2: Assigning an RB to each FN – Each FN may simultaneously serve multiple devices with different RBs; hence, each FN must be assigned at least one RB. The RB-IoT assignment generates the H(K, N, M – x) matrices. From these matrices, the maximum value for the corresponding FN (m) and RB (n) is identified, and the respective FN (m) is assigned to the connected IoT device (k). The rows and columns corresponding to RB n and FN m are then removed from the matrix. Consequently, it is evident that N – K – M + X RBs are still available for M FNs and K IoT devices.

Step 3: Assigning remaining unassigned RBs to IoT devices – After the execution of the above two steps, a new H”(K, N – K – M + X, M) channel gain matrix is generated. By selecting the highest value from this matrix, the corresponding FN m and RB n can be assigned to the associated IoT device k, and this process continues until all RBs are assigned in the network.

3.2. Use case for the proposed efficient resource allocation and management strategies with energy efficiency algorithm

The application of the proposed ERAM-EE algorithm is illustrated through numerical examples to enhance comprehension. Consider a Fog-enabled network comprising two FNs, five RBs, and three IoT devices. A channel gain matrix H is generated with randomly assigned channel gains ranging from 0 to 1. The resulting channel gain matrices, H, for three IoT devices after applying Step 1 of the proposed ERAM-EE algorithm are as follows. $H_1=\left[\begin{array}{c}\mathrm{0.810.90}\\ \mathrm{0.120.91}\\ \mathrm{0.630.09}\\ \mathrm{0.270.54}\\ \mathrm{0.950.96}\end{array}\right],H_2=\left[\begin{array}{c}\mathrm{0.150.97}\\ \mathrm{0.950.48}\\ \mathrm{0.800.14}\\ \mathrm{0.420.91}\\ \mathrm{0.790.95}\end{array}\right],H_3=\left[\begin{array}{c}\mathrm{0.650.03}\\ \mathrm{0.840.93}\\ \mathrm{0.670.75}\\ \mathrm{0.740.39}\\ \mathrm{0.650.17}\end{array}\right]$By implementing Step 1 of the proposed ERAM-EE algorithm, we have established a connection between each IoT device and at least one FN through one RB, ensuring optimal task offloading. This step involves identifying the highest value, hn,m,k, from the matrices and assigning RB (n) to the respective FN (m) for the associated IoT device (k). In the provided use case, the maximum channel gain value is 0.97, located in the 1st row, 2^nd column of the H2 matrix. This corresponds to the 2^nd IoT device, utilising the 1st RB and connecting to the 2nd FN. This process is iterated under various conditions, and as a result of Step 1 of the proposed ERAM-EE algorithm, the channel gain matrices are updated as follows. $H_1=\left[\begin{array}{c}\mathrm{0.810.90}\\ \mathrm{0.120.91}\\ \mathrm{0.630.09}\\ \mathrm{0.270.54}\\ 00\end{array}\right],H_2=\left[\begin{array}{c}00\\ \mathrm{0.950.48}\\ \mathrm{0.800.14}\\ \mathrm{0.420.91}\\ \mathrm{0.790.95}\end{array}\right]$Upon closer examination of the matrices, it is evident that FN 2 is initially connected to IoT device 2 through RB 1. However, if FN 2 is not present in the set of FNs, the step can be reiterated. In such a case, RB 1 in all matrices is set to 0. The matrix corresponding to IoT device 2 is then deleted, and the channel gain matrix H_k is updated accordingly. Following this process, the next assignment is determined. Specifically, h₅₂ of IoT device 1 is the maximum, leading to the assignment of RB 5 and FN 2 to IoT device 1. Similarly, h₂₂ of IoT device 3 is the maximum, resulting in the assignment of RB 2 and FN 2 to IoT device 3. Consequently, each IoT device is allocated at least one FN with one RB. In this instance, FN 2 assigns RBs 1, 5, and 2 to IoT devices 2, 1, and 3, respectively. As a result, the updated channel gain matrix H₃ is as follows, $H_3=\left[\begin{array}{c}00\\ 00\\ \mathrm{0.670.75}\\ \mathrm{0.740.39}\\ 00\end{array}\right]$The result of the proposed ERAM-EE at the conclusion of the step for the provided use case, illustrating the mapping of one FN through an RB for each device, is depicted in Figure 2.

Figure 2. Mapping of one Fog node through one resource block for each Internet of Things device.

Step 2 of the proposed ERAM-EE algorithm entails assigning an RB to each FN to ensure that each FN possesses at least one RB. The new matrix, denoted as H’, is generated with the available parameters after Step 1, where K = {1,2,3}, M = {1}, N = {3,4}. The resulting matrix is presented below. $H_1^{\mathrm{\prime }}=\left[\begin{array}{c}0.63\\ 0.27\end{array}\right],H_2^{\mathrm{\prime }}=\left[\begin{array}{c}0.80\\ 0.42\end{array}\right],H_3^{\mathrm{\prime }}=\left[\begin{array}{c}0.67\\ 0.74\end{array}\right]$In this step, the initial procedure involves identifying the highest element value among the three matrices. In the given scenario, the maximum value is observed at h₁₁ for device 2. Consequently, RB 1 of IoT device 2 is assigned to FN 1. Similarly, h₁₂ for device 3 has the highest value, leading to the assignment of RB 2 and FN 1 to IoT device 3. At this point, only a few RBs are yet to be assigned; specifically, RB 3 remains unassigned. The result of the proposed ERAM-EE at the conclusion of Step 2 for the provided use case, which involves the allocation of the remaining RB to the unassigned FN for the IoT device, is illustrated in Figure 3.

Figure 3. Mapping of resource blocks to unassigned Fog nodes.

In Step 3, the process involves assigning the remaining unassigned RBs to IoT devices using RB–IoT device assignment. The updated matrix, denoted as H’”, is generated with the following parameters: K = {1,2,3}, N = {4}, M = {1,2}. The resulting matrices for each IoT device are: ${\text{H}}_1^{{}^{\mathrm{\prime \prime }}}=[0.270.54]$, ${\text{H}}_2^{{}^{\mathrm{\prime \prime }}}=[0.420.91]$, and ${\text{H}}_3^{{}^{\mathrm{\prime \prime }}}=[0.740.39]$.

In this step, the initial procedure involves identifying the highest element value among the three matrices. In this particular case, the maximum value is observed at h₁₁ for device 2. As a result, FN 2 is assigned to IoT device 2 through RB 4. Consequently, it can be concluded that all resources are effectively assigned for task offloading using the proposed ERAM-EE method. Achieving the resource allocation for the network of IoT devices, where K₁= {5}, K₂= {1,3,4}, K₃= {2}, and FN allocation F₁= {3}, F₂= {1,2,4,5} of RB allocation, signifies the successful completion of the resource allocation process. The outcome of the proposed ERAM-EE at the conclusion of Step 3 for the provided use case, which includes the mapping of unassigned RBs to the IoT device for efficient task offloading, is illustrated in Figure 4.

Figure 4. Mapping of unassigned resource blocks to the Internet of Things devices.

The proposed ERAM-EE algorithm operates effectively under the condition where the number of RBs is greater than the number of IoTs and FNs. In such a configuration, the resources utilised between IoTs and FNs are more abundant. The final output of the use case, as depicted in Figure 4, clearly specifies that IoT 2 is connected with both FN 1 and FN 2, utilising three RBs. This configuration signifies a robustness in the system, indicating that even in the event of RB or FN failures or if some are occupied, task processing can efficiently proceed with the assistance of the remaining resources. This approach not only enhances task processing resilience but also contributes to reducing network congestion and interference.

4. Results and discussion

In this section, we present the simulation environment details, experimental analysis, performance comparison with existing methods, and computational complexity.

4.1. Simulation environment

The proposed ERAM-EE algorithm is simulated and its performance is analysed within a Fog-IoT network. The simulation considers the necessary components such as IoT devices, RBs, and FNs to validate its effectiveness. FNs are randomly distributed to create the Fog network, and RBs are allocated to the optimised FNs based on the provided channel gain matrices of IoT devices. The simulation configurations, under which the network operates, are outlined in Table 2.

Table 2. Parameters for simulation.

Parameter	Value
Number of Internet of Things devices	0–12
Number of Fog nodes	0–9
Number of resource blocks	0–9
Bandwidth of resource blocks	15kHz
Path loss (α, reference distance = 1 km)	3.2
Max transmission power of resource block	0.3W
Max transmission rate	20kbps
Optimum energy consumption per CPU Cycle (θ) Fog nodes	1100 J/cycle
The central processing unit for 1-b data ()	10^–9
Noise power	–140dBm
Large-scale fading factor	1
Amplification efficiency	98–102%
Minimum transmission rate	20kbps
Shadow fading standard deviation σ	8dB

For simulation purposes, the assumed configuration includes 9 FNs, 12 IoT devices, and 9 RBs. The simulation is designed to emulate a real-time Fog computing scenario. The input for this simulation consists of Channel Gain Matrices that correspond to the network. In real-time scenarios, both FN failures and the idle behaviour of IoT devices are encountered. Failing to address these cases separately can significantly impact the system's throughput. The algorithm proposed in this paper is designed to handle random deactivation and failure scenarios for both IoT devices and FNs.

The algorithm's output comprises two matrices: F_k, representing the allocation of FNs and IoT devices, and R_b, corresponding to the allocation of FNs and RBs. Finally, the EE of the Fog–IoT network, as computed by the ERAM-EE algorithm, serves as the conclusive output.

4.2. Experimental analysis and performance comparison

The proposed ERAM-EE algorithm is analysed in a configured Fog–IoT network, and simulations are conducted using MATLAB 2022a. The performance of the proposed ERAM-EE algorithm is evaluated by comparing it with the following algorithms.

1. Random Resource Optimum Power Allocation (RR-OPA) scheme: Enhances transmission efficiency by randomly distributing available RBs (Li et al., 2014).

2. Optimal Resource Equal Power Allocation (OR-EPA) scheme: Allocates resources equally with optimal power, without considering task length and priority (He et al., 2014).

3. Energy-Efficient Candidate Node Selection (EE-CN) method: Optimises energy efficiency by improving the task scheduling method (Huang et al., 2020).

4.2.1. Energy efficiency

The analysis of network Energy Efficiency (EE) metrics involves varying the number of IoT nodes, Fog Nodes (FNs), and RBs. The performance is assessed under three scenarios. In the initial scenario, the EE of the proposed ERAM-EE scheme is simulated for a Fog-enabled network with constant values of 2 FNs and 5 RBs, while the number of IoT devices ranges from 5 to 11. The obtained results for this scenario are compared with existing methods such as RR-OPA (Li et al., 2014), OR-EPA (He et al., 2014), and EE-CN (Huang et al., 2020) and presented in Figure 5.

Figure 5. Energy efficiency vs the number of Internet of Things devices.

From Figure 5, it is observed that the EE of all schemes gradually increases with the increase in the number of IoT devices. This increase is attributed to the growth in the transmission rate as the number of IoT devices expands. Notably, the proposed ERAM-EE algorithm demonstrates an enhanced EE, reaching up to 7 Mbit/J compared to the existing EE-CN (Huang et al., 2020) algorithm. This improvement is achieved by performing multiple tasks in a single FN, identifying the highest channel gain path, and optimising the association between RBs and FNs for associated IoT devices. The proposed ERAM-EE method exhibits an incremental improvement in EE, reaching up to 18.42% compared to the existing EE-CN (Huang et al., 2020) method. This incremental change is attributed to the optimisation of the mapping between FNs and RBs for corresponding IoT devices, achieved by computing the highest channel gain path. This optimisation increases the transmission rate, ultimately enhancing the EE of the Fog-enabled network.

In the second scenario, the EE of the proposed ERAM-EE scheme is simulated with a fixed value of 5 RBs and 3 IoT devices, while the number of Fog Nodes (FNs) is varied from 3 to 9. The results obtained in this scenario are compared with existing schemes such as RR-OPA (Li et al., 2014), OR-EPA (He et al., 2014), and EE-CN (Huang et al., 2020) and illustrated in Figure 6. From Figure 6, it is clear that the total power consumption of the Fog network increases as the number of FNs grows, resulting in a decrease in EE. Therefore, as the number of FNs increases, the network's EE decreases for all schemes. However, the proposed ERAM-EE algorithm demonstrates superior EE compared to the existing methods. The improved performance of the ERAM-EE algorithm can be attributed to its real-time task scheduling for tasks received from devices via unassigned free FNs and RBs. As a result, the EE of the proposed ERAM-EE decreases from 24 Mbit/J at F = 3 to 18 Mbit/J at F = 9, while the EE of the EE-CN (Huang et al., 2020) method decreases from 20 Mbit/J at F = 3 to 10 Mbit/J at F = 9. The proposed ERAM-EE method achieves a significant improvement in EE ranging from 16.77% to 80% compared to the existing EE-CN (He et al., 2014) scheme. This demonstrates the effectiveness of the proposed ERAM-EE algorithm in optimising EE in different FN scenarios.

Figure 6. Energy efficiency vs the number of Fog nodes.

In the last scenario, the EE of the proposed ERAM-EE algorithm is simulated with a fixed number of 2 FNs and 3 IoT devices, while the number of RBs varies from 2 to 9. The simulation results obtained for this scenario are compared with existing schemes, namely RR-OPA (Li et al., 2014), OR-EPA (He et al., 2014), and EE-CN (Huang et al., 2020), as illustrated in Figure 7.

Figure 7. Energy Efficiency vs the number of resource blocks.

From the observations in Figure 7, it is clear that Energy Efficiency (EE) increases as the number of Resource Blocks (RBs) increases across all schemes. This correlation is due to the fact that an increase in RBs leads to a wider bandwidth, resulting in higher transmission rates and thus improved EE. It is worth noting that the proposed ERAM-EE algorithm consistently outperforms existing methods in terms of EE. The ERAM-EE algorithm excels by strategically selecting the optimal RBs for task offloading from IoT devices to FNs. The algorithm shows an increase in EE of up to 18 Mbit/J compared to the existing EE-CN (Huang et al., 2020) scheme, demonstrating an improvement of 28.57%. This enhancement can be attributed to the algorithm's ability to identify the path with the highest channel gain and optimise the assignment between RBs and FNs for the individual IoT devices.

The above scenarios clearly demonstrate that the average EE of the ERAM-EE algorithm consistently outperforms existing methods such as RR-OPA (Li et al., 2014), OR-EPA (He et al., 2014), and EE-CN (Huang et al., 2020). This improvement in average EE can be attributed to the strategic allocation of IoT devices to specific FNs through designated RBs, which is achieved by computing the highest channel gain value for resource allocation and task scheduling. The ERAM-EE scheme excels in assigning optimal resources and managing available resources with minimal power consumption, thereby enhancing EE in Fog-IoT networks. In contrast, the EE-CN (Huang et al., 2020) scheme relies solely on channel gain values for optimal resource allocation without systematically assigning RBs to the requested IoT devices. The RR-OPA (Li et al., 2014) method lacks consideration for cooperation among FNs during task allocation, and the OR-EPA (He et al., 2014) scheme involves prioritised task-offloading allocation with random resources, potentially leading to increased task allocation time and energy consumption. In summary, the proposed ERAM-EE algorithm demonstrates superior EE in the given Fog network compared to existing schemes, highlighting its efficacy in improving system performance.

4.2.2. Response time and processing time

The response time and processing time of the ERAM-EE algorithm are analysed by varying the number of task requests received from IoT devices. For analytical purposes, we consider 50, 100, 150, 200, and 250 task requests. We compare the algorithm's performance with existing schemes, namely RR-OPA (Li et al., 2014), OR-EPA (He et al., 2014), and EE-CN (Huang et al., 2020), to establish the superiority of the proposed scheme. The processing time, computed using Equation (12), is illustrated in Figure 8, along with that of the existing schemes.

Figure 8. Processing time vs number of task requests.

From Figure 8, it is observed that OR-EPA (He et al., 2014) required high processing time to effectively allocate the RBs, and schedule and offload the task requests received from IoT devices. The proposed ERAM-EE scheme requires less processing time to allocate and manage the RBs for effective task offloading and it allocates the same resources quickly as compared with existing OR-EPA (He et al., 2014), RR-OPA (Li et al., 2014) and EE-CN (Huang et al., 2020) by 1.7 sec, 0.7 sec and 0.4 sec, respectively. This is due to balancing and immediate assignment of the RBs for the IoT devices for task transmission. The total time required and response time to allocate and process the task received from the IoT devices by assigned FN through RBs are simulated for the proposed ERAM-EE method and illustrated in Figure 9. The total response time of the proposed method is compared with existing schemes.

Figure 9. Response time vs number of task requests.

Based on Figure 9, it is clear that the proposed ERAM-EE scheme performs better than the existing schemes. It efficiently allocates RBs to IoT devices and their corresponding FNs, allowing for a quick response to tasks from IoT devices. In comparison to the existing schemes such as OR-EPA (He et al., 2014), RR-OPA (Li et al., 2014), and EE-CN (Huang et al., 2020), the proposed scheme completes the entire process faster by 1.9 sec, 0.9 sec, and 0.6 sec, respectively. By determining the highest channel gain value, the scheme achieves optimal resource allocation, which may result in a few extra RBs in the Fog-IoT network. These additional RBs are used for parallel task offloading. This efficient resource allocation is what contributes to the reduced response time achieved by the proposed ERAM-EE scheme compared to existing methods.

4.2.3. Mapping of internet of things devices, fog nodes, and resource blocks

This subsection discusses the mapping between FNs with RBs and IoT devices with FNs. Figure 10 illustrates the mapping between IoT devices and FNs facilitated by the proposed ERAM-EE algorithm. As each IoT device can chose numerous FNs for task transfer, and each FN can serve various IoT devices, the resource utilisation of FNs is enhanced. For instance, the task request generated by IoT device 5 can be offloaded by multiple FNs, such as FN 1 and FN 3. Simultaneously, FN 4 is ready to execute task requests raised by numerous IoT devices, including IoT 1, IoT 4, IoT 7, and IoT 9. This scenario highlights the flexibility of offloading tasks from an IoT device to multiple FNs, each with its respective RBs, and the capacity of a single FN to process tasks from multiple IoT devices.

Figure 10. Association of Fog nodes vs Internet of Things devices.

Similarly, Figure 11 illustrates that RBs can efficiently offload tasks to the respective IoT devices using the associated FNs. For example, FN 3 may receive task-offload requests through various RBs, such as RB 2, RB 5, RB 7, and RB 11. This approach minimises interference among IoT devices and enhances RB utilisation.

Figure 11. Association of Fog nodes vs resource blocks.

4.3. Computational complexity analysis

The computational complexity of the RR-EPA (Li et al., 2014) can be calculated as Ο(N + M + K) + Ο(N²), optimising power and allocating RBs randomly. On the other hand, the EE-CN (Huang et al., 2020) scheme optimises RB assignment in a planned manner through candidate node selection with a computational complexity of Ο(N × K × (M² × M (K + M))) + Ο(N). The OR-OPA (He et al., 2014) scheme, which allocates transmission power equally and allocates suitable RBs to FNs, has a computational complexity of Ο(N + M + K) + Ο(N). However, the computational complexity of the ERAM-EE scheme is Ο(N × M × (M² – N × (K + M – M’))), where M’ denotes the failed RBs. The proposed model identifies suitable RBs for specific IoT devices. It is observed that the computational complexity of existing methods is higher than that of the proposed ERAM-EE method.

Not only do the functionalities offered by the proposed ERAM-EE framework prove useful for Fog–IoT applications, but the hardware and infrastructure requirements are also crucial. In larger areas of the Fog–IoT network, using costly specialised hardware as FNs is impractical due to the significant expense involved. Therefore, frameworks that are platform-independent, have low hardware requirements and can leverage inexpensive nodes like Raspberry Pis are preferred over those with demanding hardware requirements. Additionally, low hardware requirements enable the utilisation of “leftover” processing capacity from IoT devices placed within a specific area that are not robust enough to support high-performance frameworks. To save maintenance costs, the routers should also be power-efficient. Furthermore, the FN is available as a virtual machine that can be installed in a virtualisation environment and operates on consumer routers similar to those supplied by telecom companies. Since the proposed algorithm will be applied in FNs, which are a type of wireless device like Raspberry Pis, maintenance and replacement are easily manageable by administrators and cost-effective. Since Fog computing is decentralised, the proposed ERAM-EE algorithm works in the Fog layer, which also has the same environment for processing data in a decentralised manner to reduce complexity and latency issues. In the future, the identification and replacement of faulty resources are easier in this proposed method, as the number of RBs is kept higher than the number of IoT devices compared to other methods, enhancing the robustness of Fog networks.

5. Conclusion

This paper presents the implementation of the ERAM-EE framework in Fog networks. The system operates within a finite system bandwidth and allocates multiple RBs with equal bandwidth for utilisation by FNs. The algorithm uses a candidate mechanism that takes channel gain matrices as inputs to allocate at least one FN and RB to each terminal device. A candidate node is selected from the candidate set, representing an FN with a non-zero computing capacity. Resource allocation in real-time Fog systems addresses challenges such as malfunctioning FNs and inactive IoT devices. The ERAM-EE algorithm is designed to optimise task offloading with efficient RBs in a Fog-IoT network, with a goal of maximising EE compared to existing methods. The results show that the proposed ERAM-EE algorithm achieves incremental improvements in EE, up to 7, 8, and 18 Mbit/J compared to existing schemes for varying IoT devices, FNs and RBs respectively. The proposed ERAM-EE fog based approach will reduce the volume of data processing and storage in the cloud, which may reduce the bandwidth consumption and related payloads. Also, it will improve the response and process time. Due to this, the latency may be reduced. However, a major limitation of the proposed ERAM-EE lies in the heterogeneous and dynamic nature of IoT devices. Additionally, constraints related to CPU memory and processing power hinder the performance of the network, especially in heterogeneous IoT environments. Future work will focus on incorporating suitable modifications and new algorithms alongside ERAM-EE to address these limitations and manage dynamic situations by scaling up the Fog network within a larger Fog–Cloud environment.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The Open Access Fee is funded by Vellore Institute of Technology, Vellore, India.