# Energy Consumption Optimization of an IoT Monitoring Center Based on a Max-Min Ant Colony Algorithm

Authors: Yinghua Tong
Journal: Wireless Communications and Mobile Computing
 (2023)

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## Abstract

As a result of the green IoT, application layer users are increasingly seeking more services, and it is particularly important to reduce the energy consumption of an IoT monitoring center while ensuring service reliability. In this paper, the max-min ant colony algorithm is proposed to effectively solve the problems of user service reliability and energy consumption optimization of an IoT monitoring center. First, the service reliability of the application layer users is modeled based on a Markov chain, and the quantitative reliability performance indicators are given. Second, an optimization model between the user service reliability and the energy consumption of an IoT monitoring center is established. Finally, the optimization problem is solved based on the improved max-min ant system. Simulation experimental results show that compared with the improved FFD algorithm, the average power consumption of the max-min ant colony algorithm can be reduced by up to 7.14%.


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## Body

## 1. Introduction

The continuous development of IoT technology has promoted its application in intelligent environment monitoring, military, smart medicine, and other areas. A functional block diagram of an IoT monitoring system [1] is shown in Figure 1. The core network of the IoT is responsible for item identification, data collection, and transmission. An IoT monitoring center is composed of an IoT data center and IoT computing platform, which is responsible for the deployment and installation of the hardware environment, software operating system, and middleware, to flexibly and rapidly deploy virtual machines, achieve unified data storage, and separate computing and processing. The various business needs of application layer users are provided in the form of web services.Figure 1
Functional block diagram of an IoT-based monitoring center.The user services at the application layer run on the servers of the IoT-based monitoring center as virtual machines, which often causes service failure due to CPU device failure, hardware failure, and human factors, rendering the service unreliable. In addition, users have various requirements for different service reliabilities. For example, virtual machines corresponding to user service 1 at the application layer need to run with a reliability of 0.99 on the servers for three days. The virtual machines corresponding to user service 2 need to run with a reliability of 0.999 on the servers for seven days. A single virtual machine runs and does not guarantee high-reliability service requirements. Redundant deployment of virtual machines is bound to increase the energy consumption of the IoT monitoring center. At the same time, with the fine-grained monitoring of an IoT monitoring system, the number of servers in the IoT monitoring center continues to increase, and although the development of industry business is promoted, the resulting high energy consumption and high cost problems have attracted widespread attention from monitoring enterprises. Therefore, to ensure the reliability of user services at the application layer, minimizing the energy consumption of the monitoring center and building a reliable, green, and energy-saving IoT monitoring system are becoming the focus of people’s attention.Under the premise of meeting the reliability of user services, the energy consumption of the monitoring center is minimized, which can be abstracted into a multidimensional bin-packing problem. This problem has proven to be an NP-hard problem and is generally solved using approximation approaches, linear programming methods, and metaheuristic algorithms [2]. Classical discrete bin-packing approximation approaches include the improved First Fit Decreasing (FFD) algorithm and Best Fit Decreasing (BFD) algorithm because the approximation algorithm is based on greedy algorithms, which are often highly centralized. The time complexity of the linear programming methods increases exponentially. Metaheuristic algorithms construct candidate solution spaces according to certain rules and accept suboptimal solutions in the iterative process with a certain probability, which can jump out of local optima [3]. Common metaheuristic algorithms include genetic algorithms, simulated annealing algorithms, ant colony algorithms, and tabu search algorithms.The ant colony algorithm is a bionic swarm intelligence algorithm. It is a heuristic search algorithm inspired by the ant foraging principle. It has characteristics, such as robustness, positive feedback, and distributed parallel computing. Although the ant colony algorithm has the above advantages, it always fails to obtain the optimal solution or takes too long to solve the optimal solution for massive data and easily falls into the local optimum. To avoid the above problems, the improved max-min ant colony algorithm is proposed on the basis of the basic ant colony algorithm, which is mainly based on the fact that the pheromone concentration on each path has a maximum and minimum value, and each update ensures that the pheromone concentration is within the interval range of [min, max]. The minimum pheromone concentration can improve exploration, while the maximum pheromone concentration can ensure the exploitation of ants. The pheromone concentration evaporates every time, but after each evaporation, only the pheromone on the optimal path increases, and it is going to converge faster. In this paper, we apply the improved max-min ant colony algorithm to solve the multidimensional bin-packing problem and compare it with the improved FFD algorithm. The results indicate that the average power consumption of the max-min ant colony algorithm can be reduced by up to 7.14%.


### 1.1. Related Work

Many mechanisms have been proposed to enhance the energy efficiency and reliability of the IoT monitoring center. The energy consumption models of the IoT monitoring center components are pivotal for ensuring the optimal design of the internal facilities and limiting the energy consumption of the IoT monitoring center. The reliability model of the IoT monitoring center is also important since the end-user’s satisfaction depends on the availability of the IoT monitoring center services. Many studies analyzed the energy consumption models of the IoT monitoring center’s major load sections and discussed the reliability modeling aspects of the IoT monitoring center.


#### 1.1.1. IoT Monitoring Center Energy Consumption Modeling

The energy consumption models of the IoT monitoring center are needed to provide solutions for increasing the energy efficiency. The proposed power consumption models of the servers are classified into four groups based on the characteristics of the proposed power hand energy consumption models, namely, the additive power model, baseline-active model, regression model, and utilization-based model.(1) Additive Power Model. The proposed power consumption models of the servers are based on the additive power model. In [4], the server power consumption model was proposed considering the power consumption of the CPU and memory unit. In [5], the power consumption of the motherboards can be regarded as the conduction loss of the server. Chatzipapas et al. [6] indicated that the overall power consumption of the server includes the idle power consumption of the server. Alan et al. proposed a detailed model of the data transfer server power consumption in [7], considering CPU utilization, memory access rate, hard disk I/O request rate, and network I/O request rate.(2) Baseline-Active Power Model. The proposed power consumption models of the servers are based on the baseline-active power model. In IoT monitoring centers, the servers are not always in active state because the servers can also be switched to idle mode. In [8], the power consumption of the server is expressed as the sum of the baseline power and active power.(3) Regression Model. The regression models of server power consumption are mostly adopted in research, which considers the power consumption and the performance indicators of each functional unit, namely, the CPU, memory, and disk. One aspect of energy model is the possibility of attributing energy consumption to “energy users,” such as applications and virtual machines. The energy modeler’s main role is to assign energy consumption values to the energy user from the values obtained at the host level. Rules establish how the host energy consumption is assigned to each energy user. In [9], the host energy consumption is divided into CPU utilization and idle energy utilization. The server power consumption has been modeled as a linear power consumption concerning their individual utilization of the CPU, disk, and I/O ports in [10]. Kansal et al. presented a model of server power consumption considering CPU utilization, the number of missing last-level caches, and the number of bytes that were read and written, as discussed in [11]. Costa and Hlavacs proposed a generalized power consumption model of the server based on its component performance counters, such as CPU cycles per second, cache per second, and cache misses per second [12]. Beloglazov et al. presented a nonlinear model of servers that performs better than regression models [13]. Zhang et al. [14] proposed a high-order polynomial model of server power consumption, and demonstrated that the cubic polynomial model is the best choice.(4) Utilization-Based Power Model. Most of the system utilization-based power models consider CPU utilization as their metric in modeling the server’s power consumption. Elnozahy et al. presented the earliest CPU utilization-based server power model in [15]. Previous studies [16, 17] have been conducted from the perspective of reducing energy consumption. Singh et al. proposed a novel secure FAES-AOMDV protocol. This algorithm composes the AOMDV protocol for multiple route discoveries along with the K-nearest neighbor for nearest neighbor node selection and uses the false key-build advanced encryption standard (FAES) encryption scheme for the cryptography method. The proposed scheme offers a higher throughput along with lower end-to-end delay and energy consumption. Furthermore, the rate of success of the proposed scheme is to guarantee and ensure that packet delivery to the destination is very high through multiple paths and in a more secured manner [18]. Vimal et al. [19] proposed a hybrid model for mitigating jamming and energy monitoring using the MOACO model along with the double Q-learning model. The model has been proposed with the IoT model that involves data aggregation and energy-constrained devices with optimization techniques to enhance utilization and the network throughput with energy enhancement. Cluster-based data utilization is proposed with the Q-learning algorithm, and it enhances the intercluster data aggregation. A hybrid model has been proposed in the CR node using the greedy algorithm with intranetwork to enhance green communication. The proposed model enhances the network lifetime, residual energy, and throughput.


#### 1.1.2. The Reliability Modeling of IoT Monitoring Centers

In [20], the Uptime Institute’s classification system is the pioneer in research to standardize the IoT monitoring center design and describe the redundancy of its underlying power supply systems, which is used for the reliability modeling of IoT monitoring center.(1) Reliability Indices for User Service. In [21], user service reliability refers to the readiness of an IoT monitoring center system to deliver the promised IT service to a user. In [22], the service reliability is also emphasized since the probability of fulfilling the service requests without latency is characterized by this index. A similar reliability index called “loss of workload probability” is proposed based on the server outage probability in [23]. Different reliability model approaches have been used for the IoT monitoring center. All modeling methods can be divided into analytical approaches and simulation-based approaches.(2) Analytical Approaches. In [24], a fault tree analysis-based failure-aware virtual machine migration technique was proposed to develop a fault-tolerant cloud IoT monitoring center. Cut set theory was applied to analyze the reliability of the IoT monitoring center’s network topologies in [25, 26]. Bennaceur and Kloul [27] investigated the different interactions between IoT monitoring center subsystems (electrical, thermal, and network) and their impact on IoT monitoring center reliability. Production trees were used to address the reliability issues of production systems.(3) Simulation-Based Approaches. Along with analytical models, simulation-based approaches are also common for IoT monitoring center reliability assessment. The state space models, including the Markov and Monte Carlo models, are used for reliability modeling. Markov models have been used for reliability modeling of IoT monitoring centers in [28]. The Monte Carlo approach is one of the most commonly used simulation-based approaches for IoT monitoring center reliability modeling. In [29, 30], a reliability assessment was performed for both 480 V AC distribution architecture and 380 V DC architecture for IoT monitoring centers complying with the Tier IV standard. The Monte Carlo simulation method was used to perform the reliability calculations. Aibin and Walkowiak [31] proposed a novel optimization approach that employs a machine learning Monte Carlo tree search algorithm for the simulation of future traffic to provide efficient and reliable operation of inter-IoT monitoring center networks based on optical technologies. In [32], the distribution functions for server reliability were analyzed, and the TTFs and TTRs for individuals and groups of servers were quantified. In [33], stochastic Petri nets were used for reliability modeling of the IoT monitoring center.


### 1.2. Contributions

The energy consumption of the IoT monitoring center has been modeled to reduce energy consumption, increasing the energy efficiency and thus reducing the operational cost of the IoT monitoring centers. Reliability indices for user services have been given, and the reliability of the IoT monitoring center has been modeled to prevent unwanted interruptions in the services, hence enhancing the service availability to satisfy the service with the clients. The trade-off between reducing the energy consumption of the IoT monitoring center and ensuring higher reliability of user services is an operational challenge, which is not addressed properly in previous literature. This paper fills the research gaps for making a trade-off between the energy efficiency of IoT monitoring centers and the reliability of user services. The main contributions of this paper are as follows:(i)
A reliability model based on the Markov user service is established, and a quantitative analysis of user service reliability is realized(ii)
An optimization model to minimize the energy consumption of the IoT monitoring center is proposed under the constraint of the user service reliability index of the application layer(iii)
The optimization problem is solved based on the improved max-min ant system to minimize the energy consumption of the monitoring centerThe remainder of this paper is organized as follows: in Section2, related concepts are discussed. Section 3 presents the reliability of user services and its model. In Section 4, the energy consumption optimization model of an IoT monitoring center based on user service reliability is presented. In Section 5, the optimization problem between the reliability of user service and energy consumption of an IoT monitoring center based on the max-min ant colony algorithm is discussed. Section 6 presents the experimental results and discussion. Section 7 concludes the paper.


## 1.1. Related Work

Many mechanisms have been proposed to enhance the energy efficiency and reliability of the IoT monitoring center. The energy consumption models of the IoT monitoring center components are pivotal for ensuring the optimal design of the internal facilities and limiting the energy consumption of the IoT monitoring center. The reliability model of the IoT monitoring center is also important since the end-user’s satisfaction depends on the availability of the IoT monitoring center services. Many studies analyzed the energy consumption models of the IoT monitoring center’s major load sections and discussed the reliability modeling aspects of the IoT monitoring center.


### 1.1.1. IoT Monitoring Center Energy Consumption Modeling

The energy consumption models of the IoT monitoring center are needed to provide solutions for increasing the energy efficiency. The proposed power consumption models of the servers are classified into four groups based on the characteristics of the proposed power hand energy consumption models, namely, the additive power model, baseline-active model, regression model, and utilization-based model.(1) Additive Power Model. The proposed power consumption models of the servers are based on the additive power model. In [4], the server power consumption model was proposed considering the power consumption of the CPU and memory unit. In [5], the power consumption of the motherboards can be regarded as the conduction loss of the server. Chatzipapas et al. [6] indicated that the overall power consumption of the server includes the idle power consumption of the server. Alan et al. proposed a detailed model of the data transfer server power consumption in [7], considering CPU utilization, memory access rate, hard disk I/O request rate, and network I/O request rate.(2) Baseline-Active Power Model. The proposed power consumption models of the servers are based on the baseline-active power model. In IoT monitoring centers, the servers are not always in active state because the servers can also be switched to idle mode. In [8], the power consumption of the server is expressed as the sum of the baseline power and active power.(3) Regression Model. The regression models of server power consumption are mostly adopted in research, which considers the power consumption and the performance indicators of each functional unit, namely, the CPU, memory, and disk. One aspect of energy model is the possibility of attributing energy consumption to “energy users,” such as applications and virtual machines. The energy modeler’s main role is to assign energy consumption values to the energy user from the values obtained at the host level. Rules establish how the host energy consumption is assigned to each energy user. In [9], the host energy consumption is divided into CPU utilization and idle energy utilization. The server power consumption has been modeled as a linear power consumption concerning their individual utilization of the CPU, disk, and I/O ports in [10]. Kansal et al. presented a model of server power consumption considering CPU utilization, the number of missing last-level caches, and the number of bytes that were read and written, as discussed in [11]. Costa and Hlavacs proposed a generalized power consumption model of the server based on its component performance counters, such as CPU cycles per second, cache per second, and cache misses per second [12]. Beloglazov et al. presented a nonlinear model of servers that performs better than regression models [13]. Zhang et al. [14] proposed a high-order polynomial model of server power consumption, and demonstrated that the cubic polynomial model is the best choice.(4) Utilization-Based Power Model. Most of the system utilization-based power models consider CPU utilization as their metric in modeling the server’s power consumption. Elnozahy et al. presented the earliest CPU utilization-based server power model in [15]. Previous studies [16, 17] have been conducted from the perspective of reducing energy consumption. Singh et al. proposed a novel secure FAES-AOMDV protocol. This algorithm composes the AOMDV protocol for multiple route discoveries along with the K-nearest neighbor for nearest neighbor node selection and uses the false key-build advanced encryption standard (FAES) encryption scheme for the cryptography method. The proposed scheme offers a higher throughput along with lower end-to-end delay and energy consumption. Furthermore, the rate of success of the proposed scheme is to guarantee and ensure that packet delivery to the destination is very high through multiple paths and in a more secured manner [18]. Vimal et al. [19] proposed a hybrid model for mitigating jamming and energy monitoring using the MOACO model along with the double Q-learning model. The model has been proposed with the IoT model that involves data aggregation and energy-constrained devices with optimization techniques to enhance utilization and the network throughput with energy enhancement. Cluster-based data utilization is proposed with the Q-learning algorithm, and it enhances the intercluster data aggregation. A hybrid model has been proposed in the CR node using the greedy algorithm with intranetwork to enhance green communication. The proposed model enhances the network lifetime, residual energy, and throughput.


### 1.1.2. The Reliability Modeling of IoT Monitoring Centers

In [20], the Uptime Institute’s classification system is the pioneer in research to standardize the IoT monitoring center design and describe the redundancy of its underlying power supply systems, which is used for the reliability modeling of IoT monitoring center.(1) Reliability Indices for User Service. In [21], user service reliability refers to the readiness of an IoT monitoring center system to deliver the promised IT service to a user. In [22], the service reliability is also emphasized since the probability of fulfilling the service requests without latency is characterized by this index. A similar reliability index called “loss of workload probability” is proposed based on the server outage probability in [23]. Different reliability model approaches have been used for the IoT monitoring center. All modeling methods can be divided into analytical approaches and simulation-based approaches.(2) Analytical Approaches. In [24], a fault tree analysis-based failure-aware virtual machine migration technique was proposed to develop a fault-tolerant cloud IoT monitoring center. Cut set theory was applied to analyze the reliability of the IoT monitoring center’s network topologies in [25, 26]. Bennaceur and Kloul [27] investigated the different interactions between IoT monitoring center subsystems (electrical, thermal, and network) and their impact on IoT monitoring center reliability. Production trees were used to address the reliability issues of production systems.(3) Simulation-Based Approaches. Along with analytical models, simulation-based approaches are also common for IoT monitoring center reliability assessment. The state space models, including the Markov and Monte Carlo models, are used for reliability modeling. Markov models have been used for reliability modeling of IoT monitoring centers in [28]. The Monte Carlo approach is one of the most commonly used simulation-based approaches for IoT monitoring center reliability modeling. In [29, 30], a reliability assessment was performed for both 480 V AC distribution architecture and 380 V DC architecture for IoT monitoring centers complying with the Tier IV standard. The Monte Carlo simulation method was used to perform the reliability calculations. Aibin and Walkowiak [31] proposed a novel optimization approach that employs a machine learning Monte Carlo tree search algorithm for the simulation of future traffic to provide efficient and reliable operation of inter-IoT monitoring center networks based on optical technologies. In [32], the distribution functions for server reliability were analyzed, and the TTFs and TTRs for individuals and groups of servers were quantified. In [33], stochastic Petri nets were used for reliability modeling of the IoT monitoring center.


## 1.1.1. IoT Monitoring Center Energy Consumption Modeling

The energy consumption models of the IoT monitoring center are needed to provide solutions for increasing the energy efficiency. The proposed power consumption models of the servers are classified into four groups based on the characteristics of the proposed power hand energy consumption models, namely, the additive power model, baseline-active model, regression model, and utilization-based model.(1) Additive Power Model. The proposed power consumption models of the servers are based on the additive power model. In [4], the server power consumption model was proposed considering the power consumption of the CPU and memory unit. In [5], the power consumption of the motherboards can be regarded as the conduction loss of the server. Chatzipapas et al. [6] indicated that the overall power consumption of the server includes the idle power consumption of the server. Alan et al. proposed a detailed model of the data transfer server power consumption in [7], considering CPU utilization, memory access rate, hard disk I/O request rate, and network I/O request rate.(2) Baseline-Active Power Model. The proposed power consumption models of the servers are based on the baseline-active power model. In IoT monitoring centers, the servers are not always in active state because the servers can also be switched to idle mode. In [8], the power consumption of the server is expressed as the sum of the baseline power and active power.(3) Regression Model. The regression models of server power consumption are mostly adopted in research, which considers the power consumption and the performance indicators of each functional unit, namely, the CPU, memory, and disk. One aspect of energy model is the possibility of attributing energy consumption to “energy users,” such as applications and virtual machines. The energy modeler’s main role is to assign energy consumption values to the energy user from the values obtained at the host level. Rules establish how the host energy consumption is assigned to each energy user. In [9], the host energy consumption is divided into CPU utilization and idle energy utilization. The server power consumption has been modeled as a linear power consumption concerning their individual utilization of the CPU, disk, and I/O ports in [10]. Kansal et al. presented a model of server power consumption considering CPU utilization, the number of missing last-level caches, and the number of bytes that were read and written, as discussed in [11]. Costa and Hlavacs proposed a generalized power consumption model of the server based on its component performance counters, such as CPU cycles per second, cache per second, and cache misses per second [12]. Beloglazov et al. presented a nonlinear model of servers that performs better than regression models [13]. Zhang et al. [14] proposed a high-order polynomial model of server power consumption, and demonstrated that the cubic polynomial model is the best choice.(4) Utilization-Based Power Model. Most of the system utilization-based power models consider CPU utilization as their metric in modeling the server’s power consumption. Elnozahy et al. presented the earliest CPU utilization-based server power model in [15]. Previous studies [16, 17] have been conducted from the perspective of reducing energy consumption. Singh et al. proposed a novel secure FAES-AOMDV protocol. This algorithm composes the AOMDV protocol for multiple route discoveries along with the K-nearest neighbor for nearest neighbor node selection and uses the false key-build advanced encryption standard (FAES) encryption scheme for the cryptography method. The proposed scheme offers a higher throughput along with lower end-to-end delay and energy consumption. Furthermore, the rate of success of the proposed scheme is to guarantee and ensure that packet delivery to the destination is very high through multiple paths and in a more secured manner [18]. Vimal et al. [19] proposed a hybrid model for mitigating jamming and energy monitoring using the MOACO model along with the double Q-learning model. The model has been proposed with the IoT model that involves data aggregation and energy-constrained devices with optimization techniques to enhance utilization and the network throughput with energy enhancement. Cluster-based data utilization is proposed with the Q-learning algorithm, and it enhances the intercluster data aggregation. A hybrid model has been proposed in the CR node using the greedy algorithm with intranetwork to enhance green communication. The proposed model enhances the network lifetime, residual energy, and throughput.


## 1.1.2. The Reliability Modeling of IoT Monitoring Centers

In [20], the Uptime Institute’s classification system is the pioneer in research to standardize the IoT monitoring center design and describe the redundancy of its underlying power supply systems, which is used for the reliability modeling of IoT monitoring center.(1) Reliability Indices for User Service. In [21], user service reliability refers to the readiness of an IoT monitoring center system to deliver the promised IT service to a user. In [22], the service reliability is also emphasized since the probability of fulfilling the service requests without latency is characterized by this index. A similar reliability index called “loss of workload probability” is proposed based on the server outage probability in [23]. Different reliability model approaches have been used for the IoT monitoring center. All modeling methods can be divided into analytical approaches and simulation-based approaches.(2) Analytical Approaches. In [24], a fault tree analysis-based failure-aware virtual machine migration technique was proposed to develop a fault-tolerant cloud IoT monitoring center. Cut set theory was applied to analyze the reliability of the IoT monitoring center’s network topologies in [25, 26]. Bennaceur and Kloul [27] investigated the different interactions between IoT monitoring center subsystems (electrical, thermal, and network) and their impact on IoT monitoring center reliability. Production trees were used to address the reliability issues of production systems.(3) Simulation-Based Approaches. Along with analytical models, simulation-based approaches are also common for IoT monitoring center reliability assessment. The state space models, including the Markov and Monte Carlo models, are used for reliability modeling. Markov models have been used for reliability modeling of IoT monitoring centers in [28]. The Monte Carlo approach is one of the most commonly used simulation-based approaches for IoT monitoring center reliability modeling. In [29, 30], a reliability assessment was performed for both 480 V AC distribution architecture and 380 V DC architecture for IoT monitoring centers complying with the Tier IV standard. The Monte Carlo simulation method was used to perform the reliability calculations. Aibin and Walkowiak [31] proposed a novel optimization approach that employs a machine learning Monte Carlo tree search algorithm for the simulation of future traffic to provide efficient and reliable operation of inter-IoT monitoring center networks based on optical technologies. In [32], the distribution functions for server reliability were analyzed, and the TTFs and TTRs for individuals and groups of servers were quantified. In [33], stochastic Petri nets were used for reliability modeling of the IoT monitoring center.


## 1.2. Contributions

The energy consumption of the IoT monitoring center has been modeled to reduce energy consumption, increasing the energy efficiency and thus reducing the operational cost of the IoT monitoring centers. Reliability indices for user services have been given, and the reliability of the IoT monitoring center has been modeled to prevent unwanted interruptions in the services, hence enhancing the service availability to satisfy the service with the clients. The trade-off between reducing the energy consumption of the IoT monitoring center and ensuring higher reliability of user services is an operational challenge, which is not addressed properly in previous literature. This paper fills the research gaps for making a trade-off between the energy efficiency of IoT monitoring centers and the reliability of user services. The main contributions of this paper are as follows:(i)
A reliability model based on the Markov user service is established, and a quantitative analysis of user service reliability is realized(ii)
An optimization model to minimize the energy consumption of the IoT monitoring center is proposed under the constraint of the user service reliability index of the application layer(iii)
The optimization problem is solved based on the improved max-min ant system to minimize the energy consumption of the monitoring centerThe remainder of this paper is organized as follows: in Section2, related concepts are discussed. Section 3 presents the reliability of user services and its model. In Section 4, the energy consumption optimization model of an IoT monitoring center based on user service reliability is presented. In Section 5, the optimization problem between the reliability of user service and energy consumption of an IoT monitoring center based on the max-min ant colony algorithm is discussed. Section 6 presents the experimental results and discussion. Section 7 concludes the paper.


## 2. Related Concepts

### 2.1. Reliability

Definition 1 (reliability).
The probability that a system or component will complete a specified task under specified time conditions, measured by reliabilityRt. The probability that a system will work properly within the 0,t time interval under the condition of normal operation at time 0 is generally considered [34]. The reliability is as follows:
(1)Rt=PX>t.
In the traditional system, there are two types of measures to improve reliability: (1) improve the reliability of the components in the system through redundancy and (2) improve the reliability of the components themselves through testing, replacement [35], etc.


### 2.2. Total Energy Consumption of the IoT Monitoring Center

Assume the total number of IoT monitoring center servers isN, the power of the server when it is operating normally is Pwork, the frequency of execution is C, the percentage of idle servers is u (that is, the number of idle servers/the total number of servers N), the power consumption when the server is idle is Pidle, the normal service duration of the server is t1, and the idle service duration is t2. Ignoring the energy consumption when a task is transmitted through the network, the total energy consumption of the IoT monitoring center is Etotal:
(2)Etotal=PworkNC1−ut1+PidleNut2.In Equation (2), Pwork, N, C, t1, t2, and Pidle are constants, so the total energy consumption of the IoT monitoring center Etotal is only related to the percentage of idle server nodes u. When the server is idle, the power is 50% to 60% of that when the server is fully loaded. Therefore, by increasing the percentage of idle server nodes u in the IoT monitoring center, the number of working servers in the IoT monitoring center can be minimized, and the total energy consumption of the IoT monitoring center Etotal can be minimized [36].


## 2.1. Reliability

Definition 1 (reliability).
The probability that a system or component will complete a specified task under specified time conditions, measured by reliabilityRt. The probability that a system will work properly within the 0,t time interval under the condition of normal operation at time 0 is generally considered [34]. The reliability is as follows:
(1)Rt=PX>t.
In the traditional system, there are two types of measures to improve reliability: (1) improve the reliability of the components in the system through redundancy and (2) improve the reliability of the components themselves through testing, replacement [35], etc.


## 2.2. Total Energy Consumption of the IoT Monitoring Center

Assume the total number of IoT monitoring center servers isN, the power of the server when it is operating normally is Pwork, the frequency of execution is C, the percentage of idle servers is u (that is, the number of idle servers/the total number of servers N), the power consumption when the server is idle is Pidle, the normal service duration of the server is t1, and the idle service duration is t2. Ignoring the energy consumption when a task is transmitted through the network, the total energy consumption of the IoT monitoring center is Etotal:
(2)Etotal=PworkNC1−ut1+PidleNut2.In Equation (2), Pwork, N, C, t1, t2, and Pidle are constants, so the total energy consumption of the IoT monitoring center Etotal is only related to the percentage of idle server nodes u. When the server is idle, the power is 50% to 60% of that when the server is fully loaded. Therefore, by increasing the percentage of idle server nodes u in the IoT monitoring center, the number of working servers in the IoT monitoring center can be minimized, and the total energy consumption of the IoT monitoring center Etotal can be minimized [36].


## 3. Reliability of User Services and Its Model

### 3.1. Reliability of User Services

Definition 2 (reliability of user services).
The probability that the IoT monitoring system will be able to continuously provide services to application layer users in the form of web services for a specific period of time, focusing on analyzing the continuity of normal operation of user services.


### 3.2. Reliability Modeling of User Services Based on a Markov Model

Users have different reliability requirements for various services, and the number of redundant virtual machines that need to be deployed is also different. The following is a reliability model based on a Markov model for user services at the application layer, and the following assumptions are made:(1)
The virtual machine corresponding to the user service is repairable(2)
The virtual machine life corresponding to the user service is independently distributed and follows the exponential distribution of the parameterλ(3)
The distribution of repair time after virtual machine failure corresponding to the user service follows the exponential distribution of the parameterμ(4)
The reliability requirement of the user corresponding to theith service is Ri(5)
To ensure that the reliability of the user’sith service meets Ri, the number of virtual machines that need to be redundantly deployed is liThe constructed virtual machine state transition diagram corresponding to a user service based on the Markov model is shown in Figure2. The Markov process has a state set 0,1,2,⋯,li−1,li, where 0,1,2,⋯,li−1 are transients, indicating that the virtual machine corresponding to the user service has 0,1,2,⋯,li−1 failed states. State li is the absorbing state, indicating that the corresponding li virtual machines have failed, and at this time, the user’s service is invalid. Suppose that the initial probability of the Markov process is π,πli, where π=π0,π1,⋯,πli−1 is met, and πe+πli=1 is satisfied.Figure 2
State transition diagram of the virtual machine corresponding to a user service.To solve the reliability of user services, we first need to solve the steady-state probability distribution of the continuous-time Markov chain (CTMC). According to the virtual machine failure rateλ and repair rate μ corresponding to the user service in the CTMC model, the probability density matrix can be obtained as follows:
(3)Q=qi,j0≤i,j≤li.The elementsqi,j of the matrix can be obtained by solving the following equations:
(4)qi,i+1=li−iλ,i=0,1,⋯,li−1,qi,i−1=iμ,i=1,2,⋯,li−1,qi,i=−li−iλ+iμ,i=1,2,⋯,li−1.qi,j=0,others.MatrixQ can be written in the following chunked form:
(5)Q=Tt00,where T is a matrix of li×li,Tij≥0i≠j,i,j=1,⋯,li−1, indicating the transfer rate from transient state i to transient state j; t is the matrix of li×1, indicating the transfer rate from transient state i to the absorption state, where Te+t=0; and 0 is the matrix of 1×li. The probability corresponding to each macro state in the matrix Q constitutes a steady-state probability vector ππ0,π1,⋯,πli−1. The initial state of the CTMC is π1,0,⋯,0, indicating that the virtual machine corresponding to the user service is working normally, and there is no virtual machine failure. τ is used to indicate the time when the user service first enters the absorption state li, thenτ~PHπ,T.Theorem 1.
Assumingτ~PHπ,T, the cumulative distribution of the steady-state probability distribution π of the continuous-time Markov process [37] is as follows:
(6)Prτ≤s=1−πexpT∗se,where s≥0 and e represents a column vector of dimension li×1 with all elements 1.The proof of Theorem1 is omitted, and the detailed process can be found in reference [37].Lemma 1.
Assume that the reliability of the user’sith service is Ri, and the condition Rs=1−πexpT∗se≥Ri is met for the first time; that is, li is the minimum number of virtual machines that should be deployed.According to Lemma1, it can be determined whether the current user service meets the reliability requirements, and the specific process can be implemented using Algorithm 1.Algorithm 1: Minimum number of redundant VMS to meet customer service reliability requirements.
INPUT:λ,μ,Ri,sOUTPUT:li1.li=1;2.   Calculate the matrixTaccording to Equation (4);3.Rs=1−πexpT∗se;4.   whileRs<Ri5.li=li+1;6.     Calculate the matrixT according to Equation (4);7.Rs=1−πexpT∗se;8.   end while9.   returnli.


## 3.1. Reliability of User Services

Definition 2 (reliability of user services).
The probability that the IoT monitoring system will be able to continuously provide services to application layer users in the form of web services for a specific period of time, focusing on analyzing the continuity of normal operation of user services.


## 3.2. Reliability Modeling of User Services Based on a Markov Model

Users have different reliability requirements for various services, and the number of redundant virtual machines that need to be deployed is also different. The following is a reliability model based on a Markov model for user services at the application layer, and the following assumptions are made:(1)
The virtual machine corresponding to the user service is repairable(2)
The virtual machine life corresponding to the user service is independently distributed and follows the exponential distribution of the parameterλ(3)
The distribution of repair time after virtual machine failure corresponding to the user service follows the exponential distribution of the parameterμ(4)
The reliability requirement of the user corresponding to theith service is Ri(5)
To ensure that the reliability of the user’sith service meets Ri, the number of virtual machines that need to be redundantly deployed is liThe constructed virtual machine state transition diagram corresponding to a user service based on the Markov model is shown in Figure2. The Markov process has a state set 0,1,2,⋯,li−1,li, where 0,1,2,⋯,li−1 are transients, indicating that the virtual machine corresponding to the user service has 0,1,2,⋯,li−1 failed states. State li is the absorbing state, indicating that the corresponding li virtual machines have failed, and at this time, the user’s service is invalid. Suppose that the initial probability of the Markov process is π,πli, where π=π0,π1,⋯,πli−1 is met, and πe+πli=1 is satisfied.Figure 2
State transition diagram of the virtual machine corresponding to a user service.To solve the reliability of user services, we first need to solve the steady-state probability distribution of the continuous-time Markov chain (CTMC). According to the virtual machine failure rateλ and repair rate μ corresponding to the user service in the CTMC model, the probability density matrix can be obtained as follows:
(3)Q=qi,j0≤i,j≤li.The elementsqi,j of the matrix can be obtained by solving the following equations:
(4)qi,i+1=li−iλ,i=0,1,⋯,li−1,qi,i−1=iμ,i=1,2,⋯,li−1,qi,i=−li−iλ+iμ,i=1,2,⋯,li−1.qi,j=0,others.MatrixQ can be written in the following chunked form:
(5)Q=Tt00,where T is a matrix of li×li,Tij≥0i≠j,i,j=1,⋯,li−1, indicating the transfer rate from transient state i to transient state j; t is the matrix of li×1, indicating the transfer rate from transient state i to the absorption state, where Te+t=0; and 0 is the matrix of 1×li. The probability corresponding to each macro state in the matrix Q constitutes a steady-state probability vector ππ0,π1,⋯,πli−1. The initial state of the CTMC is π1,0,⋯,0, indicating that the virtual machine corresponding to the user service is working normally, and there is no virtual machine failure. τ is used to indicate the time when the user service first enters the absorption state li, thenτ~PHπ,T.Theorem 1.
Assumingτ~PHπ,T, the cumulative distribution of the steady-state probability distribution π of the continuous-time Markov process [37] is as follows:
(6)Prτ≤s=1−πexpT∗se,where s≥0 and e represents a column vector of dimension li×1 with all elements 1.The proof of Theorem1 is omitted, and the detailed process can be found in reference [37].Lemma 1.
Assume that the reliability of the user’sith service is Ri, and the condition Rs=1−πexpT∗se≥Ri is met for the first time; that is, li is the minimum number of virtual machines that should be deployed.According to Lemma1, it can be determined whether the current user service meets the reliability requirements, and the specific process can be implemented using Algorithm 1.Algorithm 1: Minimum number of redundant VMS to meet customer service reliability requirements.
INPUT:λ,μ,Ri,sOUTPUT:li1.li=1;2.   Calculate the matrixTaccording to Equation (4);3.Rs=1−πexpT∗se;4.   whileRs<Ri5.li=li+1;6.     Calculate the matrixT according to Equation (4);7.Rs=1−πexpT∗se;8.   end while9.   returnli.


## 4. Energy Consumption Optimization Model of an IoT Monitoring Center Based on User Service Reliability

Assume that the user’s service set isF=F1,F2⋯,Fm; then, Fii∈1,m represents the user’s ith service, and li represents the number of virtual machines that need to be redundantly deployed in the IoT monitoring center under the requirements of ensuring service Fi reliability. The set of the IoT monitoring center’s servers is S=S1,S2⋯,Sn; then, Sjj∈1,n represents the jth server. Therefore, the deployment of virtual machines corresponding to user services to the server can be abstracted as 0-1 deployment problems. Assume that the deployment matrix is A, where the row vector represents the user service Fii∈1,m and the column vector represents the server Sjj∈1,n; then, A is an m×n matrix.
(7)A=a11a12⋯a1na21a22⋯a2n⋮⋮⋱⋮am1am2⋯amn.where aij indicates whether the virtual machine corresponding to user service Fi is deployed on server Sj,
(8)aij=1,whentheVMcorrespondingtoFiisdeployedonserverSj,0,else.When serverSj is selected (with a virtual machine deployed), it means that the server is in a working state, FSj=1; otherwise, FSj=0. The problem between the reliability of user services and the optimization of energy consumption of the IoT monitoring center can be described as follows:
(9)min∑j=1nFSj,s.t.(10)aij∈0,1,i=1,2,⋯,m;j=1,2,⋯,n(11)∑j=1naij=lii=1,2,⋯,m(12)∑i=1mFicpuaij≤Sjcpu(13)∑i=1mFimemaij≤Sjmem(14)∑i=1maij≤1j=1,2,⋯,n,where Sjcpu and Sjmem are the resource constraints of the CPU and memory of server Sj and Ficpu and Fimem are the resource requirements of the virtual machine corresponding to user service Fi for the server CPU and memory.The goal of this optimization problem is to minimize the number of servers in the working state of the IoT monitoring center. Equation (11) is expressed to meet the reliability of the application layer user service Fi, and the number of virtual machines to be deployed on the server is li. Equations (12) and (13) indicate the resource constraints that need to be met to avoid server overload. Equation (14) means that to avoid server failure, resulting in unreliable user services, the number of virtual machines corresponding to the deployment of the same service by up to the user is 1 on the same server.


## 5. Optimization Problem between the Reliability of User Service and Energy Consumption of an IoT Monitoring Center Based on the Max-Min Ant Colony Algorithm

This paper uses the improved max-min ant system to solve the multidimensional bin-packing problem. In this algorithm, each ant receives all items (a virtual machine corresponding to user services), randomly opens a box (a server of the monitoring center), and determines which item is loaded into the box at the next moment, depending on the path decision probability between the item-box sequence. Initially, everything is randomly selected, but with the “understanding” of the solution space and the searching of the entire ant colony, it becomes regular. The greater the concentration of pheromones and heuristic factor values between the item-box sequence, the greater the decision probability value and the greater the probability of selection; the global optimal solution is approximated gradually.


### 5.1. Path Decision Probability

The path decision probability refers to the probability that thekth ant will deploy the virtual machine corresponding to user service Fi to server Sj.
(15)Pijkt=τijtαηijtβ∑s∈Nkiτistαηistβ,whenj∈Nki,0,elsewhere τijt is the pheromone concentration on the virtual machine corresponding to user service Fi to be deployed on server Sj sequence, ηij is a heuristic factor, and α and β represent the relative importance of pheromones and desired factors, respectively.


### 5.2. Resource Normalization

There are two types of server and virtual machine resources: CPU resources and memory resources. Therefore, it is necessary to normalize all kinds of resources and obtain the corresponding resource vectors, and the specific processing methods are shown in Table1.Table 1
Normalization of various resources.
CategoryNormalization of CPU resourcesNormalization of memory resourcesVectorTotal resources of the server111,1Resources required by virtual machinesFicpu/SjcpuFimem/SjmemFicpu/Sjcpu,Fimem/SjmemResources that have been occupied on the serverbjcpu/Sjcpubjmem/Sjmembjcpu/Sjcpu,bjmem/Sjmem


### 5.3. Heuristic Factors

The objective function is to minimize the number of worker servers, that is, to maximize the utilization of server resources; then, the heuristic factor is as follows:(16)ηij=1Cj−bj+fi1.In Equation (16), cj indicates that the total capacity resource vector of the server is (1, 1), bj indicates the resource vector occupied by virtual machines deployed on the server bjcpu/Sjcpu,bjmem/Sjmem, and fi represents the resource vector of the virtual machine demand corresponding to user service Fi to be deployed Ficpu/Sjcpu,Fimem/Sjmem. Then, in Equation (15), the denominator represents the 1-norm of the remaining resource vector after the virtual machine corresponding to user service Fi is deployed. Smaller denominator values indicate higher server resource utilization and larger heuristic values.


### 5.4. Updates on Pheromones

(17)τij=1−ρτij+1FSbest,(18)FSbest=Min∑j=1nFSj.After all ants complete the virtual machine deployment corresponding to a user service, the pheromones on the path are updated, whereρ0<ρ<1 represents the evaporation coefficient of the virtual machine-server pheromone and 1−ρ represents the persistence coefficient of the pheromone. The max-min ant algorithm used in this article updates the pheromone pair only when the virtual machine-server sequence pair has the minimum value of the objective function value. In Equation (18), FSbest represents the objective function, which is the minimum number of servers that are in a working state after deployment. To avoid stagnation in the search, the value range of the pheromone trace quantity τij on each solution element is limited to the τmin,τmax interval. The maximum pheromone threshold is τmax=3, and the minimum pheromone threshold is τmin=τmax/g.


### 5.5. The Optimization Algorithm between the Reliability of User Service and the Energy Consumption of the IoT Monitoring Center Based on a Max-Min Ant System

Algorithm 2: The optimization algorithm between the reliability of user service and the energy consumption of an IoT monitoring center based on a max-min ant system.
INPUT: Initialize the number of virtual machinesm∗li, the number of servers n, parameter set of the max-min ant systemOUTPUT:Spbest (Optimal solution sequence for virtual machine deployment to servers)1. Initialize all virtual machine-server pairs with pheromoneτmax;2. ForT=1 to n Cycles3.  For allk∈1,nAnts4.SF=F;5.j=1;6.SA=aij=0i∈1,m,j∈1,n;7.   whileSF≠∅ do8.Nj=Fiaij==0&&bj+fi<=cj; //All undeployed services9.      ifNj≠∅ then10.Pijkt=τijαηijβ/∑s∈Njτisαηisβ;11.aij=1;12.SF=SF−Fi;13.bj=bj+fi;14.      else15.j=j+1;16.      end if17.  end while18. end for19. Comparek∈1,nAnts ants solutions SA, compute ∑j=1nFSA,FSbest=Min∑j=1nFSA ;20. ifFSbest<FSpbest then21.FSpbest=FSbest;22. end if23. for allFi,Sj∈FSbest do24.τij=1−ρτij+1/FSbest;25.     ifτij>τmax then26.τij=τmax;27.       end if28.     ifτij<τmin then29.τij=τmin;30.       end if31. end for32. end for33. ReturnSpbest


## 5.1. Path Decision Probability

The path decision probability refers to the probability that thekth ant will deploy the virtual machine corresponding to user service Fi to server Sj.
(15)Pijkt=τijtαηijtβ∑s∈Nkiτistαηistβ,whenj∈Nki,0,elsewhere τijt is the pheromone concentration on the virtual machine corresponding to user service Fi to be deployed on server Sj sequence, ηij is a heuristic factor, and α and β represent the relative importance of pheromones and desired factors, respectively.


## 5.2. Resource Normalization

There are two types of server and virtual machine resources: CPU resources and memory resources. Therefore, it is necessary to normalize all kinds of resources and obtain the corresponding resource vectors, and the specific processing methods are shown in Table1.Table 1
Normalization of various resources.
CategoryNormalization of CPU resourcesNormalization of memory resourcesVectorTotal resources of the server111,1Resources required by virtual machinesFicpu/SjcpuFimem/SjmemFicpu/Sjcpu,Fimem/SjmemResources that have been occupied on the serverbjcpu/Sjcpubjmem/Sjmembjcpu/Sjcpu,bjmem/Sjmem


## 5.3. Heuristic Factors

The objective function is to minimize the number of worker servers, that is, to maximize the utilization of server resources; then, the heuristic factor is as follows:(16)ηij=1Cj−bj+fi1.In Equation (16), cj indicates that the total capacity resource vector of the server is (1, 1), bj indicates the resource vector occupied by virtual machines deployed on the server bjcpu/Sjcpu,bjmem/Sjmem, and fi represents the resource vector of the virtual machine demand corresponding to user service Fi to be deployed Ficpu/Sjcpu,Fimem/Sjmem. Then, in Equation (15), the denominator represents the 1-norm of the remaining resource vector after the virtual machine corresponding to user service Fi is deployed. Smaller denominator values indicate higher server resource utilization and larger heuristic values.


## 5.4. Updates on Pheromones

(17)τij=1−ρτij+1FSbest,(18)FSbest=Min∑j=1nFSj.After all ants complete the virtual machine deployment corresponding to a user service, the pheromones on the path are updated, whereρ0<ρ<1 represents the evaporation coefficient of the virtual machine-server pheromone and 1−ρ represents the persistence coefficient of the pheromone. The max-min ant algorithm used in this article updates the pheromone pair only when the virtual machine-server sequence pair has the minimum value of the objective function value. In Equation (18), FSbest represents the objective function, which is the minimum number of servers that are in a working state after deployment. To avoid stagnation in the search, the value range of the pheromone trace quantity τij on each solution element is limited to the τmin,τmax interval. The maximum pheromone threshold is τmax=3, and the minimum pheromone threshold is τmin=τmax/g.


## 5.5. The Optimization Algorithm between the Reliability of User Service and the Energy Consumption of the IoT Monitoring Center Based on a Max-Min Ant System

Algorithm 2: The optimization algorithm between the reliability of user service and the energy consumption of an IoT monitoring center based on a max-min ant system.
INPUT: Initialize the number of virtual machinesm∗li, the number of servers n, parameter set of the max-min ant systemOUTPUT:Spbest (Optimal solution sequence for virtual machine deployment to servers)1. Initialize all virtual machine-server pairs with pheromoneτmax;2. ForT=1 to n Cycles3.  For allk∈1,nAnts4.SF=F;5.j=1;6.SA=aij=0i∈1,m,j∈1,n;7.   whileSF≠∅ do8.Nj=Fiaij==0&&bj+fi<=cj; //All undeployed services9.      ifNj≠∅ then10.Pijkt=τijαηijβ/∑s∈Njτisαηisβ;11.aij=1;12.SF=SF−Fi;13.bj=bj+fi;14.      else15.j=j+1;16.      end if17.  end while18. end for19. Comparek∈1,nAnts ants solutions SA, compute ∑j=1nFSA,FSbest=Min∑j=1nFSA ;20. ifFSbest<FSpbest then21.FSpbest=FSbest;22. end if23. for allFi,Sj∈FSbest do24.τij=1−ρτij+1/FSbest;25.     ifτij>τmax then26.τij=τmax;27.       end if28.     ifτij<τmin then29.τij=τmin;30.       end if31. end for32. end for33. ReturnSpbest


## 6. Experimental Results and Discussion

In this section, we present the evaluation results for the max-min ant colony algorithm in the user service reliability and the energy consumption optimization mechanism of the IoT monitoring center. We evaluate the proposed scheme in terms of the number of servers deployed and power consumption of the IoT monitoring centers.


### 6.1. Simulation Environment

We developed our own python-based simulation toolkit and used it to compare the max-min ant colony algorithm with the improved FFD algorithm. The simulation environment is described in this section. We simulated that the IoT monitoring center server is homogeneous, the CPU of the server is configured to 10,000 MIPS, and the memory is configured to 50 GB.The parameters of the max-min ant colony algorithm were derived empirically through numerous simulations and references [3, 38], and the final settings are shown in Table 2. Therefore, the numbers of cycles and ants were finally initialized to 10 and 5, respectively.Table 2
Parameters of the max-min ant colony algorithm.
αβρτmaxgnCyclesnAnts120.532105


### 6.2. Reliability of the User Services

The reliability of the user services is random; then, to ensure the reliability requirements, the number of virtual machines required for redundant deployment can be obtained using Formula (6).


### 6.3. Comparison of the Number of Servers Deployed

In the following experiments, we consider the number of user services at the application layer to be the same, the reliability requirements of the same user services are the same, and the reliability of each user service is 0.7 to 1. The virtual machine resources required by the same user services are the same, the memory configuration of the virtual machine is 4 GB to 16 GB, and the CPU configuration is 1000 MIPS to 3000 MIPS. We compare the number of servers deployed using the proposed max-min ant colony algorithm and the improved FFD algorithm [39]. The results are shown in Figure 3.Figure 3
The number of servers required by the IoT monitoring center.As expected, Figure3 shows that the number of servers required for the max-min ant colony algorithm is equal to or lower than the improved FFD algorithm. The max-min ant colony algorithm achieves nearly optimal results through improved resource utilization. Moreover, the evaluated greedy algorithm (the improved FFD) is highly centralized. The proposed max-min ant colony algorithm can be implemented in a distributed manner, thus making it more suitable for scalability and fault tolerance.


### 6.4. Power Consumption Comparison of the IoT Monitoring Center

To estimate the power consumption of the IoT monitoring center, we assume that the power consumption of the server is 150 W during normal operation. At the same time, considering that the number of user services at the application layer is 10 to 20, the interval between user service reliability requirements in this experiment takes a predefined time period in weeks. We compare the power consumption for the proposed max-min ant colony algorithm and the improved FFD algorithm. The results are shown in Figure4.Figure 4
Power consumption of an IoT monitoring center.Figure4 shows that when the number of user services is 10, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 900 W when the virtual machine corresponding to the service is running. In the case when the number of user services is 11, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 1950 W. In the case when the number of user services is 12, the power consumption of the max-min ant colony algorithm is 1650 W, and the power consumption of the improved FFD algorithm is 1950 W. In the case when the number of user services is 13, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 1950 W. In the case when the number of user services is 14, the power consumption of the max-min ant colony algorithm is 2550 W, and the power consumption of the improved FFD algorithm is 2850 W. In the case when the number of user services is 15, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 2400 W. In the case when the number of user services is 16, the power consumption of the max-min ant colony algorithm is 2400 W, and the power consumption of the improved FFD algorithm is 2700 W. In the case when the number of user services is 17, the power consumption of the max-min ant colony algorithm is 2700 W, and the power consumption of the improved FFD algorithm is 2850 W. In the case when the number of user services is 18, the power consumption of the max-min ant colony algorithm is 2700 W, and the power consumption of the improved FFD algorithm is 3000 W. In the case when the number of user services is 19, the power consumption of the max-min ant colony algorithm is 1800 W, and the power consumption of the improved FFD algorithm is 1950 W. Figure 4 shows that the max-min ant colony algorithm can reduce the power consumption of the IoT monitoring center to a certain extent, and the average reduced power consumption is 7.14%.


## 6.1. Simulation Environment

We developed our own python-based simulation toolkit and used it to compare the max-min ant colony algorithm with the improved FFD algorithm. The simulation environment is described in this section. We simulated that the IoT monitoring center server is homogeneous, the CPU of the server is configured to 10,000 MIPS, and the memory is configured to 50 GB.The parameters of the max-min ant colony algorithm were derived empirically through numerous simulations and references [3, 38], and the final settings are shown in Table 2. Therefore, the numbers of cycles and ants were finally initialized to 10 and 5, respectively.Table 2
Parameters of the max-min ant colony algorithm.
αβρτmaxgnCyclesnAnts120.532105


## 6.2. Reliability of the User Services

The reliability of the user services is random; then, to ensure the reliability requirements, the number of virtual machines required for redundant deployment can be obtained using Formula (6).


## 6.3. Comparison of the Number of Servers Deployed

In the following experiments, we consider the number of user services at the application layer to be the same, the reliability requirements of the same user services are the same, and the reliability of each user service is 0.7 to 1. The virtual machine resources required by the same user services are the same, the memory configuration of the virtual machine is 4 GB to 16 GB, and the CPU configuration is 1000 MIPS to 3000 MIPS. We compare the number of servers deployed using the proposed max-min ant colony algorithm and the improved FFD algorithm [39]. The results are shown in Figure 3.Figure 3
The number of servers required by the IoT monitoring center.As expected, Figure3 shows that the number of servers required for the max-min ant colony algorithm is equal to or lower than the improved FFD algorithm. The max-min ant colony algorithm achieves nearly optimal results through improved resource utilization. Moreover, the evaluated greedy algorithm (the improved FFD) is highly centralized. The proposed max-min ant colony algorithm can be implemented in a distributed manner, thus making it more suitable for scalability and fault tolerance.


## 6.4. Power Consumption Comparison of the IoT Monitoring Center

To estimate the power consumption of the IoT monitoring center, we assume that the power consumption of the server is 150 W during normal operation. At the same time, considering that the number of user services at the application layer is 10 to 20, the interval between user service reliability requirements in this experiment takes a predefined time period in weeks. We compare the power consumption for the proposed max-min ant colony algorithm and the improved FFD algorithm. The results are shown in Figure4.Figure 4
Power consumption of an IoT monitoring center.Figure4 shows that when the number of user services is 10, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 900 W when the virtual machine corresponding to the service is running. In the case when the number of user services is 11, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 1950 W. In the case when the number of user services is 12, the power consumption of the max-min ant colony algorithm is 1650 W, and the power consumption of the improved FFD algorithm is 1950 W. In the case when the number of user services is 13, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 1950 W. In the case when the number of user services is 14, the power consumption of the max-min ant colony algorithm is 2550 W, and the power consumption of the improved FFD algorithm is 2850 W. In the case when the number of user services is 15, the max-min ant colony algorithm and the improved FFD algorithm have the same power consumption of 2400 W. In the case when the number of user services is 16, the power consumption of the max-min ant colony algorithm is 2400 W, and the power consumption of the improved FFD algorithm is 2700 W. In the case when the number of user services is 17, the power consumption of the max-min ant colony algorithm is 2700 W, and the power consumption of the improved FFD algorithm is 2850 W. In the case when the number of user services is 18, the power consumption of the max-min ant colony algorithm is 2700 W, and the power consumption of the improved FFD algorithm is 3000 W. In the case when the number of user services is 19, the power consumption of the max-min ant colony algorithm is 1800 W, and the power consumption of the improved FFD algorithm is 1950 W. Figure 4 shows that the max-min ant colony algorithm can reduce the power consumption of the IoT monitoring center to a certain extent, and the average reduced power consumption is 7.14%.


## 7. Conclusion

In this study, an improved max-min ant colony algorithm is proposed to solve the optimization problems between user service reliability and the energy consumption of an IoT monitoring center. First, a reliability model of a user service based on Markov is constructed. Second, an optimization model for minimizing the energy consumption of an IoT monitoring center is proposed under the constraint of the application layer user service reliability index. Finally, the optimization problem is abstracted into a multidimensional bin-packing problem, and the improved max-min ant colony algorithm is used to solve the optimization problem. To verify the effectiveness of the max-min ant colony algorithm for the user service reliability and the energy consumption optimization mechanism of an IoT monitoring center, the max-min ant colony algorithm adopted in this paper is compared with the improved FFD algorithm for the number of servers required for deployment and the power consumption of IoT monitoring centers. When the number of user services at the application layer is the same, the reliability requirements of the same user services are the same, and the virtual machine resources required by the same user services are the same. The experimental results show that the improved max-min ant colony algorithm effectively reduces the number of servers to be deployed by an IoT monitoring center, thus reducing the power consumption of the IoT monitoring center to a certain extent, and the average power consumption reduction is 7.14%. However, the savings came at the cost of increased computation time. In future studies, we conclude that complementarity between the two approaches should be exploited to increase energy efficiency.



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*Source: 8178281-2023-02-13.xml*