Quantum-inspired improved African vultures optimization algorithm for efficient placement of IoT service in edge computing environment

Abstract

The emergence of 5G networks has led to development of Edge Computing (EC) environments, which offer improved support for applications that rely on the Internet of Things (IoT). However, Edge Nodes (ENs) have limited resources and heterogeneous IoT applications require changing resource requirements, making it difficult to integrate IoT services. During IoT service installation, ensuring QoS performance is also difficult. In this paper, Quantum-inspired Improved African Vultures Optimization Algorithm for Service Placement (QIAVOA-SP) is proposed for achieving efficient positioning of IoT service in EC environment. This QIAVOA-SP utilized the factors of computation load, delay, energy consumption and throughput during optimization such that necessitated service placement is achieved in EC. It formulated and evaluated the fitness function determined using parameters of load balancing, energy consumption, delay and throughput for optimal positioning of IoT services in EC scenario. It incorporated the concept of Quantum-inspired Improved African Vultures (QIAV) as search agents for representing the complex solutions that are essential for placing IoT services in an edge environment. It further used the technique of double hashing for decoding the QIAV, and further incorporated the Taguchi method for studying the parameters of impact. The simulation result of QIAVOA-SP approach confirmed 19.32% better load balancing, 18.98% reduced delay and 16.45% better energy consumption than baseline approaches used for investigation. The statistical analysis of this QIAVOA-SP approach conducted using Friedman test also confirmed its efficacy over the benchmarked approaches.

Introduction

Rapid advent of communication and information technologies resulted in wide deployment of Internet of Things (IoT) devices in diverse fields that includes healthcare systems, smart cities, industry 4.0 and smart agriculture, etc¹. Development of fifth Generation (5G) networks wide opened the possibility of utilizing the benefits of advanced IoT applications. Some of the application which utilizes the merits of advanced IoT include online gaming environment, Augmented Reality (AR), Virtual Reality (VR), video conferencing etc^{2, 3}. However, these applications necessitate high real-time data processing with maximized computation power. Moreover, the IoT devices unfortunately possess restricted energy, low memory and least computation power^{4, 5}. In this context, Edge Nodes (ENs) having comparatively a higher resource potentiality and higher computation power is deployed within the range which is closer to IoT devices and at network edge for the objective of satisfying and handling the progress of the demanding situations^{6, 7}. With this capability, the delay sensitive and computation intensive services can be offloaded for deploying the suitable services at the pertinent edge’s nodes. Hence, the IoT devices or the end users can be effectively provided by all Edge Servers (ESs) present in the implementation environment^{8, 9}. In specific, Edge Computing (EC) thus brings the cloud computing power much closer to network edge for improving services’ response time such that Quality of Services (QoS) and Quality of Experience (QoE) is eventually enhanced in the environment^{10, 11}. Moreover, the ENs comprise of different number of services that includes storage, bandwidth, memory, and computation unit. On the other hand, modern applications that utilized IoT devices require numerous resources in a heterogeneous manner¹². But deploying more amounts of application services efficiently over suitable ENs always remains a major challenge in EC environment by considering different limitations of resources with satisfied QoE and QoS requirements¹³.

Motivation

Service Placement Problem (SPP) represents the method of efficient positioning of IoT services to the ENs which is considered as a herculean challenge in EC systems. This service placement includes the steps that maps different servers to the suitable selected ENs by considering efficiency based on load balancing, delay, throughput and energy consumption¹⁴. This SPP problem is more complex as they necessitate potential algorithms that determine optimal service placement solutions owing to dynamic and heterogeneous characteristics of edge networks. Thus, novel and enhanced strategies of service placement are needed in EC environment for addressing the issues of SPP such that the objective that targets on better throughput with optimized load balance, delay and energy consumption is achieved¹⁵. But accommodating the complete set of comprehensive available IoT services in the ENs becomes highly challenging due to dynamic resource demands of IoT applications on one end, and restricted resource availability and heterogeneity of ENs from other end. Maximized system throughput is achieved in the implementation environment through the assignment of maximized number of services to ENs¹⁶. Hence, design and development of a potential strategy of service allocation is essential for guaranteeing maximized throughput. The ESs specifically incur a substantial quantity of energy for executing services which are assigned to them, and for communicating services with devices of IoT. Thus, energy consumption reduction with respect to the ENs is identified as another major concern during the design of the algorithms for attaining effective and efficient service placement¹⁷.

On the other hand, some of the IoT applications such as VR, online gaming etc., are delay sensitive. This delay sensitivity in these applications sometimes introduces an interruption which in turn results in QoS and QoE degradation. The delay incurred in these applications happen due to communication and computation of IoT services over ENs¹⁸. Moreover, the strategies of IoT service placement should possess the capability of delivering the required services with reduced amount of time for the purpose of guaranteeing maximized QoS and QoE in the edge network. Most of the IoT services ned to be assigned to the ENs which possesses a comparatively a higher computation power or the ENs that are in the closer proximity of the IoT nodes for minimizing the communication delay such that the delay can be significantly minimized in the EC environment¹⁹. But the utilization of this IoT service placement strategy may eventually increase the overhead in terms of overhead incurred by all the ENs resulting in degrading the system performance in terms of load balancing. In addition, underutilization of most of existing resources or imbalance overhead may introduce uneven energy consumption from perspectives of the ENs. The process of load balancing guarantees that none of the ENs is never overburdened by comparatively a higher number of service requests incoming to EC environment. This extra degree of services requests to ENs has the probability of introducing a high load of computation over each of the specified ENs²⁰. Thus, load balancing in the EC environment is determined one of the challenging problems which need to be handled with efficacy.

A diversified number of research works have been conducted for designing potential IoT service placement algorithm with respect to edge and fog computing network, but majority of them failed in handling the issues that are related to load balancing, energy consumption, delay, and throughput. Most of the existing IoT service placement mechanisms contributed for EC still possesses the challenge to hence the execution performance of the overall EC unit. This execution performance completely depends on power consumptions of edge consumption units, levels of load balancing and utilization of resources. It also needs to ensure preventing of leakage of privacy associated with IoT devices during service placement. Most of Swarm Intelligent (SI) metaheuristic optimization algorithms involved in placement of IoT service in EC are prone to major limitations of premature convergence, more number of parameters, poor solution diversity and imbalanced trade-off amid exploration and exploitation rate in Search Space (SS). A potential SI metaheuristic optimization-based IoT service placement approach that can prevent premature convergence, achieves better solution quality, guarantees superior solution diversity and confirms balanced deviation between the rate of exploration and exploitation becomes necessary. In specific, Quantum-based SI metaheuristic optimization algorithms-based IoT service placement approach are beneficial due to following reasons such as i) quantum algorithm contributed depending on quantum mechanics principles facilitates capabilities of potential parallel processing which is adaptable to diversified range of applications, the optimization methods when hybridized with quantum, mechanisms is determined to significantly handle the problem of NP-hard complexity with more efficacy and at a rapid exponential degree.

A motivating scenario

In the smart city environment, the IoT devices deployed over the network forms the major integral part which is completely responsible for provisioning an improved QoS. These IoT devices possess computing potentialities at the edges of the networks through a powerful and ideal paradigm named as EC. This EC paradigm facilitates most potential requirements to the features of large scale and distributed IoT network. In this context, the EC units play an indispensable role of hosting the IoT services in EC for execution. This hosting of IoT services in EC offers minimized latency with reduced bandwidth burden. At this juncture, achieving better resource utilization, balancing the load and minimizing the power consumption for improving overall execution performance of EC units is a herculean challenge. While placing IoT services, these parameters are required for guaranteeing required QoS in smart city environment²¹. In this situation, intelligent metaheuristic SI optimization algorithms based IoT service placement approaches are determined to be highly suitable for exploring optimization factors with different constraints imposed during optimization.

In addition, IoT SPP in edge networks represents a NP-hard problem. At this juncture, Quantum-inspired evolutionary algorithms which adopted the merits of quantum mechanism principles present a class of optimization algorithms those targets on maximizing the performance of the traditional evolutionary algorithms. This category of Quantum-inspired evolutionary algorithms possesses the capability of exploring a larger SS with maximized efficiency which helps in determining possible and better solution related to the problem of complex optimization. These algorithms also possess the capability of more rapid convergence. Moreover, Quantum-inspired African Vulture Optimization Algorithm²² has attracted wide attention for it’s potentially in solving complex optimization problems. The significance of QIAVOA towards the capability of solving different problems of optimization is kept in mind. It is employed in the proposed scheme for handling SPP in EC environment. Inclusion of QIAVOA facilitates optimal solution in SPP in polynomial time with rapid rate of convergence.

Advantages of QIAVOA

Advantages of adopted QIAVOA which is used for attaining potential service placement is listed as follows.

• (i)The inclusion of Quantum Computing (QC) into the classical AVOA algorithm helps the algorithm to exploit the quanta properties such that the population is converted into quantum population which aids in determining the optimal solution with respect to the objective function.
• (ii)It specifically used the merits of QDCE in the phase of initialization which helps in enhancing the process of exploration.
• (iii)It used QRD into the process of iteration such that the significant solutions can be determined for escaping from the local optima potential associated during the process of implementation.
• (iv)It used the merits of an elite mutation strategy for the objective of preventing the problem of local optima that aids in improving likelihood probability of reaching the best solution in SS by jumping out of local optimum.

Major contributions of the proposed work

The major contributions offered by proposed QIAVOA-SP scheme are presented as follows.

• (i)Proposed as an optimal IoT service placement strategy that incorporated the merits of QIAVOA for achieving maximized QoS performance in EC environment, and it is one of the few approaches that included QC into IoT service placement as far as our knowledge.
• (ii)Achieved IoT service placement using search agents (Quantum vultures) that helps in mapping and placing the IoT services into the available and resource intensive ESs for execution under the satisfaction of the user requirements and the factors considered during this optimization.
• (iii)Attained objective of generating optimal, valid and comprehensive solution of IoT service placement and used method of double hashing for guaranteeing uniform assignment of services to suitable ENs depending on decoding of quantum vultures.
• (iv)Guaranteed the process of IoT service placement over the ESs by determining their fitness value for execution depending on the important objectives that concentrates on minimizing load balancing, energy consumption and delay with maximized throughput.

The ensuing sections are organized as follows. "Related work" presents the complete survey of present IoT service placement in EC proposed over recent years with merits and limitations. "Quantum-inspired Improved African Vultures Optimization Algorithm (QIAVOA-SP)-based efficient placement of IoT service in EC environment" presents the detailed view of proposed QIAVOA-SP scheme-based IoT service placement with the system model, process of service placement with the role of QIAVOA which helped in achieving better optimization. Section 4 details on results and discussion of proposed QIAVOA-SP scheme with respect to the factors of load balance, data delay, throughput and energy consumption with different number of iterations and number of applications under number of services set to 25 and 50. Section 5 gives the conclusion with major contributions of the paper with future scope of improvement.

Related work

In this section, a comprehensive review of existing IoT services placement methodologies proposed for EC environment over latest years is offered with their merits and limitations.

Zhang et al.²³ proposed a methodology which combines ES and SP where placement of services considers present ES positioning, and request rates and prices of diverse services. It focuses on improving profit of ESs in terms of number of servers, relationship amid servers and Base Stations (BSs), and storage and computing capacities of every server. A 2-step method which includes clustering and non-linear programming is proposed. It is seen that propounded scheme offers improved outcomes when compared to standard methods. Ning et al.²⁴ have focussed on enhancing system utility of Pervasive EC (PEC) networks based on server storage capability along with service execution latency. The networks include numerous mobile users who move across servers seeking for resources. It supports dynamic SP by using Lyapunov optimization for decomposing long-term optimization problem into immediate problems. An average stochastic algorithm based on approximation is propounded to estimate the expected utility of the system. It also employs Markov approximation algorithm for determining SP configurations. To deal with storage capacity and execution delay of servers, Dynamic Storage-Stable Service placement (DASS) algorithm is proposed to improve system utility, balancing system stability as well as overhead. To overcome biased decisions, Sample Average Approximation (SAA) algorithm is used to estimate long-term amassed system utility. Time taken by the propounded algorithm is linear to quantity of users. It analyses performance for real trace-driven and synthetic scenarios. It is seen that proposed algorithm offers enhanced performance when compared to existing ones.

Mala et al.²⁵ have investigated load distribution along with positioning of IoT-based applications for reducing violations of Service Level Agreement (SLA) owing to resource limitations and conflicting objectives. A system model with several application replicas placed in various parts of network is designed for distributing load among replicas. A static scenario with sufficient information for SP and load distribution is provided. To deal with computational complexity, a meta-heuristic multi-objective Genetic Algorithm (GA) with initial population which is based on heuristic and random solutions for getting near-optimal solutions is proposed. SP and load distribution are expressed as Mixed-Integer Nonlinear Programming (MINLP) optimization problems for reducing SLA violations. It provides SP mapping with request distribution among nodes. MINLP is converted into Mixed-Integer LP (MILP) problem by using linear solver. The problem involving an objective can be applied to several conflicting objectives, giving priority to time-sensitive applications. The proposed mechanism outdoes other standard methods based on violation of response deadline and contradictory objectives like operational cost in addition to service availability. SP along with resource allocation is mainly complex based on stochastic task arrival, additional latency of migrating services and waiting time incurred by unprocessed tasks. Liu et al.²⁶ have used Deep Reinforcement Learning (DRL) and have proposed parameterized deep Q networks-based scheme for handling the issues of SP and resource allocation issues. The proposed scheme focuses on reducing total task latency in long term. Through simulations, convergence as well as performance of proposed scheme is assessed. This approach was proposed for handling the tasks that necessitates heterogeneous computation over the nodes of the edge network. It facilitated the option of placing each service to the ENs in advance. It used the merits of parameterized deep Q networks for achieving decisions related to computation resources allocation and joint service placement. This strategy targeted on the process of attaining reduced total latency incurred by the tasks in addition to time consumed for non-processing tasks waiting and service migration. It also handled resource allocation and SPPs with respect to computation by considering the tasks stochastic arrival rates.

Song et al.²⁷ have proposed computational offloading scheme for tasks involving multiple service. Task execution demands co-operation of several services, and every service is crucial. An evaluation metric is designed involving system cost. The proposed method focuses on finding decision to reduce the metric for solving Mobile EC (MEC) problem involving multi-services tasks. Multi-service Task Computing Offload Algorithm (MTCOA) is designed to get optimal solution. It is evident that the algorithm involves reduced computing offloading cost, offering increased resource utilization in contrast to the benchmarked schemes AI-based use Deep Neural Network (DNN) models which are huge in size offer increased accuracy. These models involve more amount of energy. Premsankar and Ghaddar²⁸ proposed seep neural network (DNN)-based energy-efficient positioning models through the design of a multi-period optimization problem. It places services and orders requests by focussing on reduction of overall energy consumed along with latency. It offers a heuristic which considers the influence of positioning services across time periods. Quality is assessed by comparing the solution with problem’s lower bound got by solving Lagrange relaxation of problem. The proposed scheme involves reduced energy and latency by packing services on reduced number of ENs. It was identified from simulation results that the adopted heuristic approaches exhibited better performance in terms of reduced energy utilization over a minimal ENs count. This approach sustained latency of requests to be satisfied with the use of a pre-determined threshold which is same for all the time periods. This DNN model store and transmit the services effectively with the view to reduce energy utilization degree.

In addition, Bey et al.²⁹ have proposed Quantum-inspired particle swarm optimization for efficient IoT service placement (QIPSO-SP) algorithm for EC-based environment. It involves a fitness function which focuses on improving throughput, and reducing the amount of energy consumed, delay and computation load. It uses QIPSO to represent IoT SP which handles assignment of services to ENs and employs double hashing for decoding the particles. It aids in concurrent representation of several states and solutions. It generates population based on particles to ensure uniform service assignment by using hash function. It represents final solution using decoded particles to aid in optimal SP. The proposed scheme involves less energy, delay, and load balancing with improved throughput when compared to benchmarked mechanisms taken for study. Moreover, Zhang et al.³⁰ have proposed a trusted placement scheme for controllers using deployment cost as well as link failure probability. Link failure probability-based reliability model as well as propagation delay model is built. Controller positioning approach involving reduced network cost is designed using controller layout scheme that depends on density-peak clustering. Mobile-based service adaptive positioning scheme is propounded to handle the issues related to prolonged user-observed delays with increased migration costs owing to restrictions of server resources as well as coverage areas as well as dynamic motion of user. Probability Density Function-based mobility model involving sojourn time and user mobility-based service deployment overhead model are built. Quantum Ant Colony algorithm is used for supporting adaptive SP. The propounded controller placement scheme focuses on deployment cost, propagation delay as well as controller reliability. It offers acceptable quantity of controllers with their locations and optimises QoE of users.

In addition, Table 1 presents the consolidation summary table of the related work that are related to the existing IoT services placement methodologies proposed for EC environment.

Table 1.

Consolidation summary table of the existing related to the existing IoT services placement methodologies contributed for EC.

Authors	Mechanism adopted	Merits	Limitations
Zhang et al.23	A Two-step method using clustering and non-linear programming (TSCNLP)	It focuses on improving profit of ESs based on number of servers, relationship amid servers and Base Stations (BSs), and storage and computing capacities of every server.	The response time incurred during service placement still needs reasonable improvement
Ning et al.24	Dynamic SP by using Lyapunov optimization (DSPLOA)	It employed Markov approximation algorithm for determining SP configurations which deals with execution delay and storage capacity of servers, DASS algorithm	This dynamic service placement approach was not able to handle the balance amid local and global search during optimization.
Mala et al.25	Meta-heuristic multi-objective GA-based service placement (GAMMOASP)	It was proposed based on heuristic and random solutions for getting near-ideal solutions that is proposed for SP and load distribution depending on the concept of MINLP optimization problems which in turn reduces SLA violations	It even though handled the issue of SLA violations but it can’t handle load balancing to the expected level.
Liu et al.26	DRL and parameterized deep Q networks-based service placement scheme (DRLDQSP)	It focuses on reducing total task latency in long term with maximized convergence	The problem of convergence needs further improvement with maximized throughput and data delay under different number of applications.
Song et al.27	Multi-service Task Computing Offload Algorithm (MTCOA)	The proposed method focuses on finding decision to reduce the metric for solving Mobile EC (MEC) problem involving multi-services tasks. MTCOA is designed to get optimal solution.	The computation cosy incurred by this MTCOA needs significant reduction in the computing offloading cost with improved increased resource utilization
Premsankar and Ghaddar28	Deep neural network (DNN)-based energy-efficient positioning models ()	It was proposed through the design of a multi-period optimization problem. It places services and orders requests by focussing on reduction of overall energy consumed along with latency.	It mainly adopted heuristic which considered the influence of positioning services across time periods into account
Bey et al.29	Quantum-inspired particle swarm optimization for efficient IoT service placement (QIPSO-SP) algorithm	It involves a fitness function which focuses on improving throughput, and reducing the amount of energy consumed, delay and computation load by adopting QIPSO to represent IoT SP which handles assignment of services to ENs and employs double-hashing for decoding the particles.	The factors used for optimization need to be comprehensively improved since it preventing to include all impactful parameters of fitness function into account.
Zhang et al.30	Quantum Ant Colony algorithm-based service placement model	This service placement scheme focuses on deployment cost, propagation delay as well as controller reliability with minimized number of controllers with their locations targeted on optimizing QoE of users	The factors of QoS and QoE still has the scope of improvement in the EC environment.

Extract of the literature

Major limitations of existing works on IoT service placement contributed to literature over recent years are listed as follows.

• (i)Majority of the existing service placement methods failed in considering the factors of load balance, throughput, energy consumptions and data delay comprehensively which results minimized performance of the ESs in EC environment.
• (ii)Only a few numbers of Quantum-inspired Evolutionary algorithms-based IoT service placement approaches were proposed in EC environment to the best of my knowledge even though they are potential for dealing with complex optimization problem.
• (iii)The existing Quantum-inspired Evolutionary algorithms-based IoT service placement approaches still possessed the limitations of unbalanced trade-off amid exploration and exploitation during placement of services to ENs.

Quantum-inspired improved African vultures optimization algorithm (QIAVOA-SP)-based efficient placement of IoT service in EC environment

In this section, system model used for implementing proposed QIAVOA-SP-based efficient placement of IoT service is initially presented. Then the Quantum-inspired Improved African Vultures Optimization Algorithm (QIAVOA-SP)-based Service Placement is demonstrated. In addition, the primitives of AVOA and QIAVOA used for achieving IoT service placement in EC is presented.

System model

The system model used for implementing proposed QIAVOA-SP-based Service Placement comprises of different IoT devices and end user equipment’s. These IoT devices of the system model are considered to support real-time applications. Let us assume that there are ‘’ number of applications as specified in Eq. (1)

1

Then each application ‘’ is determined to include a group of services as highlighted in Eq. (2)

2

Further EUD need to run an application at a time, and each services need to be positioned on suitable EN such that services may be offered to EUDs on demand. Each service includes certain resource requirement represented as,

3

Where,

- Processing power of edge user devices in terms of CPU cycle.

- Demanded Quantity of memory.

- Demanded Storage space.

- Demanded network bandwidth.

- Maximum Deadline defined for computing as well as communicating ‘’ to EUD.

Moreover, ‘’ involves a response time ‘’ which should not exceed ‘’ to sustain QoS and maximized performance, and set of ENs in the implementation environment is represented using Eq. (4)

4

Then each individual EN involves a particular quantity of resources represented as,

5

Where,

- Available Processing power (CPU).

- Available quantity of memory.

- Available storage space.

- Available network bandwidth in ‘’ EN.

In addition, Fig. 1 presents complete view of system model adopted for implementing the proposed QIAVOA-SP-based efficient IoT service placement.

Fig. 1.

System model used for implementing the proposed QIAVOA-SP-based efficient IoT service placement.

Model for service placement

In this service placement model, ‘’ is considered as a binary indicator used to determine whether a service is positioned on ‘’ EN as specified in Eq. (6)

6

Further, system throughput represents the quantity of services positioned on EN determined as shown below.

7

In addition, Service acceptance ratio is computed as shown in Eq. (8).

8

Model for determining energy consumption

The total energy consumed () by ENs include computation and communication energy. Computation energy involves static along with dynamic energy, where static energy denotes the amount of energy consumed by an active EN which is not involved in any task. The dynamic energy is the amount of energy involved when an EN performs tasks for offering services based on EUD’s demand. Then the static energy () of ‘’ EN is determined depending on Eq. (9)

9

Where,

- Fixed amount of energy consumed when EN is idle.

In this context, the dynamic energy consumed () by ‘’ EN is determined using Eq. (10)

10

Where,

- Unit computation energy involved per CPU cycle in ‘’ EN.

Hence, total computation energy () is given by Eq. (11):

11

At this juncture, the communication energy () is the amount of energy consumed in ENs when offering services to EUDs. Total communication energy () is the total energy consumed by all ENs () determined as shown below.

12

Where,

- Rate of data transfer rate of ‘’ EN.

- Unit communication energy consumed by EN.

Hence, total energy () is sum of computation as well as communication energy.

13

Model for determining delay

Delay incurred in offering services to EUDs includes computation as well as communication delays. Computation delay represents total time needed for executing services requested by EUDs. Hence, total computation delay () is computed as presented in Eq. (14):

14

Where,

The communication delay () represents the time needed by ‘’ EN to offer demanded service to EUD.

Total communication delay is determined as shown in Eq. (15):

15

where,

- Communication delay of ‘’ EN, and it depends on kind of service demanded by EUD.

Finally, total system delay () is computed as sum of computation as well as communication delays.

16

Model for balancing loads

To get an ideal load balance (), average resources used by ENs should be known initially¹⁴. While placing services, resource utilization refers to number of services positioned in ENs. The positioned services may involve resources which are available in ENs (Eq. 4). Resource utilization () of ‘’ EN is shown in Eq. (17):

17

Average resource utilization () of ENs is given by Eq. (18).

18

In addition, ‘’ of model is computed using Standard Deviation (SD) of resource utilization as shown below.

19

‘’, when identical amount of services are positioned in ENs. Reduced value of ‘’ infers improved balancing. Therefore, load balancing becomes optimal when ‘’ approaches 0.

Formulation of problem

For given quantity of EUDs, every EUD involves a set of applications. Each application includes a group of services. The services are to be effectively positioned in existing ENs, so that the throughput is maximised, and energy, delay and load balance are reduced by offering services to EUDs.

Problem is formulated mathematically as shown below.

Maximize throughput

20

21

22

23

Subject to

24

25

26

27

28

29

Constraint (24) indicates that ‘’ should have a value of ‘0’ or ‘1’, while constraint (25) shows that total CPU employed for services must not be greater than total amount of available resources. Likewise, constraints (26) to (28) show that total memory, disk space as well as bandwidth of services must not exceed that of the system. Constraint (29) shows that response time of every service must not exceed the predefined deadline of every service.

Quantum-inspired improved African vultures optimization algorithm (QIAVOA-SP)-based service placement

The different steps included in the implementation of the proposed QIAVOA-SP)-based Service Placement is presented as follows.

QP representation and swarm generation

QP represents service assignment to an EN. A system involves ‘’ applications, and every application has ‘’ services and ‘’ ENs. The QP’s dimension is considered as,

30

31

Where,

- Number of bits essential for representing number ().

Swarm which is the quantum population includes arbitrarily produced ‘’ quantum vultures. In specific, the quantum system involving ‘’ qubits is used for representing ‘’ states with particular probabilities. A quantum vulture with dimension () represents ‘’ solutions for SPP. More amounts of solutions may be identified for a smaller population or swarm.

State observation

The qubit state that produces a binary vulture from respective quantum vulture is determined.

Decoding

In this stage, the perceived binary string of dimension, is split into ‘’ sets of binary string of length ‘’. They are decoded to respective decimal values. Every string denotes the decimal value corresponding to EN number.

are used for addressing service allocation to an EN in range. Nevertheless, ‘’ bits may produce decimal number outside range . Hence, double-hashing is employed for mapping the range.

Double hashing

An improved double-hashing method is used for mapping decoded decimal number within the limit. It is implemented only when decoded numbers are more than ‘’, as implementing double-hashing on the numbers increases the computation load. If suppose , then the least number of qubits necessary for representing 10 s using 4 qubits is determined as 15. In specific, double hashing is utilized only when the value of decoding is greater than 10. Hence, value generated is uniformly assigned with values of 1 to 10 for addressing the allocation of a specific service to an ideal ENs. On the other hand, if the system comprises of four applications, and each individual application in turn comprises of six services. Then the number of bits used for allocating the existing ENs in the system is estimated to be 4. The dimension of artificial vulture (search agent) is 96.

Algorithm 1.

Double hashing.

In specific, double hashing is used for decoding when the hash tables with open addressing since it facilitates an efficient and more robust method of addressing the issue of collision on par with simple methods of probing. It specifically uses a second hash function for identifying the step size when addressing the problem of collisions. This use of second has function in double hashing results in minimized clustering and more even keys distribution.

Fitness function

Fitness function focuses on maximising throughput (), reducing the amount of energy consumed (), delay () and load balance (). Fitness function is obtained based on the following objectives.

32

33

34

35

Weighted sum technique is used for designing fitness function¹⁵.

36

Where,

- Weight such that .

For every solution, the conforming objective values () are determined. Quantum vulture which has maximum fitness is taken as solution for SP.

QP updating

This QP updating phase is responsible for confirming whether a specific IoT service can be positioned in the available ES by satisfying the factors that should be optimized in EC scenario. In this phase, the Quantum angular vector of QP is generated for accomplishing the task of placing the IoT services over the ESs for execution. This phase first determines the updated angular vector ‘’ and QP ‘’ through the computation of ‘’. Then new QP ‘’ is identified and decoded to determine decoded vulture , through which fitness value is computed using the decoded search solution . In every iteration, there is improvement in the fitness of newly produced solution. Finally, the local Best (LB) and Global Best (GB) solutions are updated iteratively until the termination condition is satisfied.

In this section Algorithm 2 presents the steps included in achieving IoT service placement in ESs based on objectives of maximizing throughput and reducing the amount of energy consumed, delay and load balancing.

Algorithm 2.

QIAVOA-SP.

Figure 2 shows the flowchart of proposed QIAVOA-SP)-based Service Placement scheme.

Fig. 2.

Flowchart of the proposed QIAVOA-SP)-based service placement.

In the forthcoming section, the primitives of AVOA and QIAVOA are presented for understanding its steps and significance attributed by them during the process of IoT service placement.

African vultures optimization algorithm (AVOA)

AVOA, a meta-heuristic algorithm¹⁶ simulates the foraging behaviour of AV. Ensuing model is used for simulating the foraging behaviour of AV.

Phase 1: grouping of population

Initialize vulture population, compute fitness of every vulture, group vultures based on fitness. First group includes the best value, second set of vultures includes the following best value, and the rest are included in next collection. Vultures are grouped as shown in Eq. (35):

37

Where,

‘’ is found using roulette wheel.

‘’ and ‘’ - Random values in the range [0, 1].

The sum of ‘’ and ‘’ is 1.

38

Where,

- Probability of choosing the vulture.

If ‘’ has a value closer to 1 and ‘’ has a value close to 0, convergence is faster. On the contrary, it improves AVOA’s diversity.

Phase 2: vultures’ hunger rate

Vultures fly longer distances seeking for food. They become aggressive when hungry and circle around stronger vultures in pursuit of food. Equation (39) shows their hunger rate.

39

Where,

- Current iteration.

- Maximum number of iterations.

- Random value in [0, 1].

- Random value in [− 1, 1].

When , it means that vulture is hungry, and when , it means vulture is full.

40

Where,

t - Random variable in .

ῲ - Probability that algorithm performs exploitation.

Phase 3: exploration

There are 2 separate exploration patterns. ‘’ represents the exploration behavior seen in a vulture, . The behavior of vultures in this phase is simulated as shown below.

41

Where,

- Vulture’s location.

, - Random numbers in .

, - Upper, lower bounds of solution.

‘’ represents gap between a vulture and an optimal one.

42

Where,

C - Random number in range .

Phase 4: first phase of exploitation

Vulture enters first exploitation stage when . To determine whether they fight for food or take rotational flight, ‘’ which is random in range [0, 1] is defined. When , vulture strives for food. When ‘’, vulture starts rotating in flight. This behavior is shown in the following Eq. 

43

Where,

and - Random values in range .

‘’ and ‘’ are computed as shown below.

44

45

Where,

and - Random numbers in range .

Phase 5: second phase of exploitation

The vulture moves into this phase when . To determine whether vultures aggregate or attack, ‘’ is defined in preliminary exploitation stage. When , they carry out aggregation. When , vulture attacks. This behaviour is shown below.

46

47

48

Where,

- Random value in the range .

Lévy flight¹⁷ is determined as shown below.

49

50

51

Where,

- Number set to 1.5.

and - Random values in range .

As the algorithm is easy to use and offers improved optimization performance with simple settings of parameters, it is used in practical applications, and outcomes are typically competitive. Nevertheless, algorithm prematurely converges to local optimum¹⁸. The algorithm adds following 3 enhancement approaches to AVOA to handle the issues: (i) Quantum Double-Chain Encoding (QDCE) (ii) Quantum Rotating Gate (QRG) and (iii) Elite Mutation (EM) approach.

Quantum-inspired AVOA with an elite mutation strategy (QEMAVOA)

In QEMAVOA, QC is included in AVOA, thus improving performance by exploiting quanta’s properties. The population is converted into quantum population of vultures and changezb in population is used for determining optimum solution of objective function. Cui et al.³¹ have augmented Differential Evolution (DE) by incorporating QDCE and QRG schemes that enables it to efficiently handle large optimization problems. QDCE along with QRG from QC are introduced into AVOA. A detailed description of QDCE and QRG schemes is given below.

QDCE

Quantum Bit (QB) is the smallest unit of data stored in devices involved in QC. Dissimilar to a standard storage unit (bit), it may be a grouping of ‘0’ and ‘1’ states. QB is defined as shown below.

52

Where,

and - Probability amplitudes of ‘’ and ‘’ states.

QB is given by,

53

The concept of Quantum Encoding (QE) is included and location of a Quantum Vulture (QV) is presented in the following Eq. 

54

Where,

- Location of ‘’ vulture.

- Number of vultures.

- Problem dimensionality.

Every QV covers 2 positions in solution space with every location signifying a solution with 2 locations.

55

56

To get individuals which determine fitness, quantum location of vulture is mapped to solution space. It is assumed that solution space is .

Transformation of location is shown below.

57

58

Following the analysis, initialisation of solution of real number coding is converted to that of initialization of QDCE. Solution initialization of QE involves the ensuing steps.

Step 1: Establishment of angle matrix

Population includes ‘’ vultures with dimension of ‘’. Probability amplitudes are produced from angle matrices, and they are employed for representing state of QBs. For initialising quantum, angle matrix ‘’ with angles in the range must be produced. The production formula is given in Eq. (57).

59

Where,

and - Minimum and maximum angles.

- Randomly produced numbers in range .

Angle matrix is given by,

60

Step 2: Establishment of quantum population

‘’ represents quantum population with ‘’ QVs, each involving 2 locations in SS.

61

Step 3: Transformation of solution space

Candidate solutions filling constraints are got by mapping population into solution space.

QRG.

In QC, variation in relative stage of quanta is attained using quantum operators. Exploration as well as mining capacity is balanced by adapting rotation angle of QRG. In QE-MAVOA, QRG is given by,

62

Where,

- Rotation angle.

By modifying quantum gate, QBs are updated using QRG as shown below.

63

In QE-MAVOA, rather than using a fixed rotation angle, rotation angle is dynamically determined by using PSO algorithm. The rotation angle is modified using PSO as shown below.

64

Where,

and - Random number in range .

and - Learning factors which are predefined.

- ‘’ dimension angle conforming to optimal vulture.

- ‘’ dimension angle conforming to former optimal vulture of ‘’ vulture.

EM approach

EM is included to overcome the demerits of AVOA which inclines to local optimum. Optimal vulture explores for an ideal location in its neighbourhoods and substitutes the original location with another in case it is better. This raises probability of attaining best solution and enhances algorithm’s ability to move from local optimum. Elite variation approach is given by,

65

‘Mutation ()’ performs random choice of 2–3 dimensions with complete ranking. Appropriate dimensions of ideal vulture location are exchanged based on outcomes of complete ranking.

In case a dimension is beyond bounds, new values are arbitrarily produced, followed by retaining of individual with best adaptation as new ideal vulture. In addition, Algorithm 3 presents the QEMAVOA adopted for IoT service placement in EC.

Figure 3 gives a complete view of QEMAVOA used for achieving IoT service placement in EC environment.

Fig. 3.

Complete view of the QEMAVOA used for achieving IoT service placement.

Algorithm 3.

QEMAVOA used for IoT service placement.

Simulation results and discussion

Performance of proposed QIAVOA-SP and the benchmarked schemes is analysed using synthetic dataset and resource demand specified in Table 2. The parameters considered for simulation along with the assigned values is presented in Table 3. The complete set of simulation experiments are conducted using Python 3.9 programming language with the support of libraries that includes SciPy, Matplotlib and NumPy. The experiments are conducted in a system with the configuration of an Intel Core i7-7820HQ processor which is execution over 2.9 GHz and 8 GB of RAM. These comprehensive simulations and evaluations are conducted over a 64-bit Ubuntu 20.04 LTS operating system. Simulations are executed with 50 number of generations as the fixed limit for each algorithm.

Table 2.

Service configuration used for implementing the proposed QIAVOA-SP scheme.

Parameter	Value	Explanation
CPU requirement of the service	(10, 1000000)	[10 Hz to 1 MHz]
Total memory requirement of the service	(10, 104857600)	[10 B to 100 MB]
Delay incurred during the execution of each service	(10, 300)	[10 ms to 300 ms]
Bandwidth requirement of the service	(10, 10485760)	[10 BPS to 10 MBPS]
Response time facilitated by the service	(10, 524288000)	[10 B to 500 MB]

Table 3.

Service configuration used for implementing the proposed QIAVOA-SP scheme.

Methodology used	Size of the population	Number of iterations
DRLDQN-SP	50	50–250
DASS	50	50–250
MTCO-SP	50	50–250
QIPSO-SP	50	50–250
Proposed QIAVOA-SP	50	50–250

The configurations considered for evaluating proposed QIAVOA-SP and baseline approaches are the same for providing a non-bias performance investigation process. The algorithms are run for 50–250 iterations, and the results are averaged, and the plots are demonstrated for highlighting the efficacy of proposed scheme over benchmarked approaches used for evaluation. Moreover, the size of the population adopted for proposed QIAVOA-SP and baseline schemes is also equal to 50. Moreover, the process of IoT service placement over ESs is non-pre-emptive, such that each IoT service possesses a priority over the other subsequent tasks in the EC environment.

The quantum-inspired approach is used with justification even when the size of the population is 50 and the number of iterations ranges between 50 and 250 since it plays a vital role in obtaining a balance between exploration and exploitation during complex search process. Even when the count of iterations is relatively lower, the aspect of quantum increases the probability of introducing quantum leap during the process of determining better solutions. In specific, quantum-based optimization algorithms utilizes the merits of QC such as entanglement and superposition such that it explores the solution space in a more significant manner. On the other hand, quantum-inspired algorithms incorporate the capability of exploring the SS with maximized diversity such that potential solutions are identified in the promising regions. It used quantum leap for speeding up the process of faster convergence such that optimal solutions is determined in the SS with a relatively lesser number of iterations. The inclusion of quantum strategy assists in the process of establishing a better balance between the process of exploring diversity solutions and exploiting potential areas of the SS. In the problems of complex optimization, quantum-based methods are beneficial as it explores diverse regions and converge rapidly. These approaches even under limited number of iterations still facilitate a potential merit in identifying a better solution compared to the traditional algorithms. In specific, Quantum-inspired AVOA algorithm enhances the search capabilities of the classical AVOA since the quantum rotating data aids in establishing the balance between the phases of exploitation and diversification which results in determining better solutions. It is more beneficial since the solutions are determined in the complex SS even with limited computational resources such as 50 iterations.

Performance of proposed QIAVOA-SP scheme is compared with benchmarked QIPSO-SP, QIPSO-SP, MTCO-SP, DASS and DRLDQN-SP based on load balance, data delay, energy consumptions and throughput (service acceptance rate) with different number of applications (number of services in every application set to 25 and 50) and number of iterations.

Performance of the proposed QIAVOA-SP scheme using load balance

Performance of proposed QIAVOA-SP scheme is compared with the benchmarked approaches based on load balance with different number of generations and number of applications respectively. Initially the performance of the proposed QIAVOA-SP scheme and the benchmarked approaches estimated based on load balance with number of Iterations is presented in Table 4; Fig. 4.

Table 4.

Performance of the proposed QIAVOA-SP scheme using load balance with different number of Iterations.

Number of Iterations	Strategies used for comparison
	DRLDQN-SP	DASS	MTCO-SP	QIPSO-SP	Proposed QIAVOA-SP
50	0.8124	0.7654	0.6986	0.6239	0.6134
100	0.8076	0.7319	0.6754	0.6065	0.5818
150	0.7896	0.7188	0.6621	0.5565	0.5416
200	0.7562	0.6984	0.6458	0.5285	0.5112
250	0.7369	0.6872	0.6242	0.5156	0.5058

Fig. 4.

Proposed QIAVOA-SP- Load balance with number of Iterations.

In specific Fig. 4 demonstrates the results of QIAVOA-SP scheme and the benchmarked QIPSO-SP, QIPSO-SP, MTCO-SP, DASS and DRLDQN-SP approaches with different number of iterations. This experimentation is conducted with 50 number of applications in which each of the applications comprises of 25 services. The results obtained confirmed that the proposed QIAVOA-SP scheme independent to the number of iterations performs well since it adopted better exploration and exploitation capability of QIAVOA in the SS during service placement. The proposed QIAVOA-SP scheme well handled the parameters of IoT services placement in a more excellent manner such that load is balanced in the network. This clearly confirms that the proposed QIAVOA-SP scheme distributes the load of computation among all the existing ENs. Thus, the proposed QIAVOA-SP scheme achieved optimal load balance of 13.28%, 16.78%, 18.92% and 21.35% better than the benchmarked schemes taken for investigation.

Figures 5 and 6 present the results of QIAVOA-SP scheme and the benchmarked QIPSO-SP, QIPSO-SP, MTCO-SP, DASS and DRLDQN-SP approaches with different number of applications. When the number of applications increases in the EC environment, the load to be balanced also respectively increases. But the proposed QIAVOA-SP scheme independent to the number of applications and services possessed by each application works well by preventing minimized rate of convergence and maximized diversity in the SS.

Fig. 5.

Proposed QIAVOA-SP- Load balance with number of applications with the number of services set to 25.

Fig. 6.

Proposed QIAVOA-SP- Load balance with number of applications with the number of services set to 50.

This proposed strategy also handled the number of applications and services remarkably by adaptively adopting an improved rate of exploration which always contributed towards better candidate solutions in the implementation environment. Hence the proposed QIAVOA-SP scheme with different number of applications (services count set to 25) achieved optimal load balance of 11.86%, 13.21%, 15.98% and 17.69%, better than the benchmarked approaches used for investigation. Moreover, the proposed QIAVOA-SP scheme with different number of applications (services count set to 50) also achieved optimal load balance of 12.86%, 15.49%, 17.68% and 19.62%, better than the benchmarked approaches used for investigation.

Performance of the proposed QIAVOA-SP scheme using data delay

In this section, the performance of the proposed QIAVOA-SP scheme is compared with the benchmarked QIPSO-SP, QIPSO-SP, MTCO-SP, DASS and DRLDQN-SP approaches are evaluated based on data delay with different number of generations and number of applications respectively. Initially the performance of proposed QIAVOA-SP and the benchmarked schemes estimated based on data delay with number of Iterations is presented in Table 5; Fig. 7.

Table 5.

Performance of the proposed QIAVOA-SP scheme using load balance with different number of Iterations.

Number of iterations	Strategies used for comparison (data delay (milliseconds)
	DRLDQN-SP	DASS	MTCO-SP	QIPSO-SP	Proposed QIAVOA-SP
50	44842.236	43071.241	36826.224	34076.223	32116.151
100	42971.742	39690.562	34966.231	27774.232	30189.516
150	38892.671	35396.226	32037.234	30056.232	27184.582
200	36782.982	35159.231	31128.114	28214.221	24178.119
250	35981.564	33160.174	30546.284	27116.714	23157.134

Fig. 7.

Proposed QIAVOA-SP-Data delay with different number of iterations.

Figure 7 shows the outcomes of QIAVOA-SP and benchmarked schemes evaluated based on data delay with different number of iterations. This experimentation is also conducted with 50 applications in which each of the applications comprises of 25 services. The results proved that the proposed QIAVOA-SP scheme independent to the number of iterations confirmed reduced data delay since it adopted the minimizing objective function that concentred towards the reduction of data delay to the expected level during the assignment of services to the ENs associated with ESs. The rapid convergence rate facilitated by the proposed QIAVOA helped in attaining preventing unnecessary delay during the process of IoT service placement. This the data delay incurred by proposed scheme is identified to be comparatively minimized by 5.78%, 8.96%, 11.18% and 14.32% better than the benchmarked approaches taken for study.

Then Figs. 8 and 9 depicts the data delay incurred by proposed QIAVOA-SP and benchmarked schemes with different number of applications respectively. In this context, the proposed capability of QIAVOA-SP which aids in obtaining the necessitated services at a rapid pace compared to the other strategies helped in ideal assignment of services to the ES nodes. This tendency of the proposed approach helped in reducing the data delay to the expected level.

Fig. 9.

Proposed QIAVOA-SP- Data delay with number of applications under the number of services set to 50.

Fig. 10.

Proposed QIAVOA-SP- Energy consumptions with number of applications under the number of services set to 25.

Fig. 8.

Proposed QIAVOA-SP- Data delay with number of applications under the number of services set to 25.

This proposed strategy also handled the number of applications and services remarkably by adaptively adopting an improved rate of exploration which always contributed towards better candidate solutions in implementation environment. Hence, proposed QIAVOA-SP scheme with varying number of applications (services count set to 25) considerably reduced the data delay by 12.68%, 14.92%, 17.65% and 19.31% better than standard schemes taken for study. Instead, QIAVOA-SP scheme with different number of applications (services count set to 50) also reduced the data delay to the significant level of 11.32%, 14.19%, 16.58% and 18.51% better than benchmarked approaches used for investigation.

Performance of the proposed QIAVOA-SP scheme using energy consumptions

Performance of proposed QIAVOA-SP scheme is compared with benchmarked QIPSO-SP, QIPSO-SP, MTCO-SP, DASS and DRLDQN-SP approaches are evaluated based on energy consumptions with different number of generations and number of applications respectively. Initially the performance of the proposed QIAVOA-SP scheme and the benchmarked approaches estimated based on energy consumptions with number of Iterations is presented in Table 5.

From Table 6, it is identified that lower energy values are utilized during employment of proposed QIAVOA-SP scheme. This energy consumption (kWh) represents the amount of energy incurred during the process of computing the communication and computation of the services assigned to available ESs. It is identifying that each of the strategy reduces the energy consumption of the system even under increasing number of iterations. But the proposed QIAVOA-SP scheme is even more capable in delivering better results in terms of energy consumption with increase in the number of iterations.

Table 6.

Performance of the proposed QIAVOA-SP scheme using energy consumptions with different number of Iterations.

Number of Iterations	Strategies Used for Comparison (Energy consumptions)
	DRLDQN-SP	DASS	MTCO-SP	QIPSO-SP	Proposed QIAVOA-SP
50	4.316	4.316	4.316	4.316	4.316
100	4.219	4.219	4.219	4.219	4.219
150	4.194	4.194	4.194	4.194	4.194
200	4.118	4.118	4.118	4.118	4.118
250	4.094	4.094	4.094	4.094	4.094

Furthermore, Figs. 10 and 11 present the energy consumption spent by proposed and benchmarked approaches with different number of applications respectively. Thus, the proposed QIAVOA-SP scheme with different number of applications (services count set to 25) remarkably minimized the energy consumptions by 13.28%, 15.31%, 18.94% and 20.28%, better than the benchmarked approaches used for investigation. On the other hand, the proposed QIAVOA-SP scheme with different number of applications (services count set to 50) also minimized the consumption of energy to required level by 12.42%, 15.68%, 18.62% and 21.42% better than benchmarked approaches taken for investigation.

Fig. 11.

Proposed QIAVOA-SP- Energy consumptions with number of applications under the number of services set to 50.

Performance of the proposed QIAVOA-SP scheme using throughput

In this section, experimental results of proposed QIAVOA-SP and baseline approaches conducted using throughput are presented with different number of generations. In this evaluation, throughput represents the ratio between cumulative number of services placed over ENs to total services count present in an application. From the simulation result presented in Fig. 12, it is identified that proposed QIAVOA-SP and benchmarked schemes deliver comparatively an equal degree of throughput. This comparative degree of service acceptance rate or throughput is achieved by the proposed and benchmarked approaches since they adopted optimized setting of influential parameters during the implementation process. It is confirmed that all the methodologies used for service placement independent on the number of iterations as per the optimal degree of factors considered during the process of simulation, However, the adoption of optimal parametric values during the implementation process may not deliver potential possible solution in all the cases of real time environment.

Fig. 12.

Proposed QIAVOA-SP- Throughput with number of generations.

Then, an investigation without considering the optimal values of influential parameters is considered with different number of applications which comprises of services count set to 25 and 50, respectively. Figures 13 and 14 present the throughput (service acceptance rate) achieved by the proposed QIAVOA-SP scheme and the baseline approaches with number of applications varies from 20 to 100. Moreover, this investigation is conducted with each application comprising of 25 and 50 services respectively. In both the scenarios of implementation, the proposed QIAVOA-SP scheme delivered best optimized throughput compared to baseline schemes with different number of applications taken for investigation. The proposed QIAVOA-SP scheme balanced trade-off between local and global search such proper and significant placement of IoT services over the ESs is achieved in the implementation environment. Thus, the proposed QIAVOA-SP scheme with different number of applications (services count set to 25) achieved better throughput by 13.21%, 15.49%, 17.94% and 19.32%, better than the benchmarked approaches used for investigation. Moreover, QIAVOA-SP scheme with different number of applications (services count set to 50) also achieved better throughput of 10.76%, 13.29%, 15.68% and 17.85%, better than the benchmarked schemes taken for investigation.

Fig. 13.

Proposed QIAVOA-SP- Throughput with different number of applications and services set to 25.

Fig. 14.

Proposed QIAVOA-SP- Throughput with different number of applications and services set to 50.

The efficiency of QIAVOA-SP in achieving an optimal placement of IoT service in EC environment is listed as follows, (i) QC included into optimization algorithm which improves the search potential in the SS, (ii) its capability in balancing trade-off between the rate of exploration and exploitation with probability of solutions being struck into local point of optimality, (iii) the tendency of AVOA in preventing premature convergence and poor solution diversity.

Taguchi method for studying the parameters of impact

In this proposed methodology, Taguchi method is utilized for examining the influence of different factors of impact and their related levels depending in the objectives considered for implementation. In specific, the factors considered for attaining service placement in the EC system include throughput, load balance, delay and energy consumption. The impact of throughput is explored for examining its role in attaining service placement in edge system. Then the parameters such as number of ENs, applications count, count of services in each application and the capacity of disk associated with each ENs.

Based on the above Table 7, an orthogonal array is selected for exploring the impact of the above four factors over throughput which need to be achieved during the implementation of the proposed methodology. This orthogonal array with sixteen values are presented as follows.

Table 7.

Levels of control factors.

Control factors	Control factors’ level
	1	2	3	4
Capacity of disk associated with each ENs ()	1.25	2.50	3.75	5.00
Count of services in each application ()	10	15	20	25
Applications count ()	40	60	80	100
Number of ENs ()	5	10	15	20

Then the signal to noise ratio after the process of level settings adjustment through Table 8 is determined for identifying the experimental output quality. In specific, the method of Taguchi is used for exploring the quality properties such as high, moderate and lower of.

Table 8.

Orthogonal array with sixteen values associated throughput impact analysis.

Experiment
1	1.25	10	40	5
2	2.50	15	60	5
3	3.75	20	80	5
4	5.00	25	100	5
5	1.25	10	40	10
6	2.50	15	60	10
7	3.75	20	80	10
8	5.00	25	100	10
9	1.25	10	40	15
10	2.50	15	60	15
11	3.75	20	80	15
12	5.00	25	100	15
13	1.25	10	40	20
14	2.50	15	60	20
15	3.75	20	80	20
16	5.00	25	100	20

. The value of is used for representing the maximizing objective like throughput. This signal to noise ratio () is determined based on Eq. (66) and the results are presented in Eq. Table 9.

66

Table 9.

Throughput and its related .

Experiment	Throughput
1	0.737	− 2.650
2	0.863	− 1.279
3	0.274	− 11.244
4	0.421	− 1.360
5	0.855	− 1.360
6	0.855	− 1.360
7	0.659	− 3.622
8	0.661	− 3.595
9	0.838	− 1.535
10	0.846	− 1.452
11	0.838	− 1.535
12	0.846	− 1.452
13	0.839	− 1.524
14	0.843	− 1.483
15	0.843	− 1.483
16	0.839	− 1.524

From Tables 10 and 11 presents the Factorial Impacts of for throughput and the Contribution Ratio of different control factors for throughput. These results clearly proved that Number of ENs () contributes towards better throughput during the application of the proposed QIAVOA-SP used for achieving optimal placement of IoT service in EC environment.

Table 10.

Factorial impacts of for throughput.

	Levels	Control Factors
for throughput	1	− 3.895	− 4.464	− 4.471	− 1.518
	2	− 2.975	− 3.528	− 3.528	− 1.586
	3	− 2.303	− 1.768	− 1.768	− 2.684
	4	− 1.994	− 1.496	− 1.496	− 5.882
Maximum -Minimum		1.901	2.968	2.975	4.364
Rank		4	3	2	1

Table 11.

Contribution ratio of different control factors for throughput.

Factors
Contribution ratio	0.1557	0.2431	0.2436	0.3574

Performance of proposed QIAVOA-SP scheme using execution time under two scenarios of implementation (number of applications under services of 25 and 50)

In this section, the proposed QIAVOA-SP scheme and the benchmarked approaches are compared based on Execution Time with different applications and services set to 25 and 50, respectively (Scenario-1 and Scenario-2). These experiments are conducted for comparing the proposed QIAVOA-SP scheme with the IoT service placement approaches reviewed in the literature to determined how the proposed strategy performs well in terms of execution time with different number of applications. From Fig. 15, it is identified that the proposed QIAVOA-SP scheme independent to the applications performed well since it used the method of double hashing such that it helps in mapping the applications to the ENs available in the EC scenario. It also used the Taguchi method to identify which parameters contribute to the factors of impact during the process of IoT service placement in EC environment.

Fig. 15.

Proposed QIAVOA-SP- Execution Time with different applications and services set to 25.

Similarly the pattern visualized in Fig. 16, confirmed that the proposed QIAVOA-SP scheme with different applications and service set to 50 involve reduced execution time compared to the baseline approaches. This pattern is mainly realized since it used a decoding strategy which mapped a specified service of an application to specified edge resources such that execution is significantly minimized in the network. It prevented the waiting of the applications executing on the ES through the enforcement of constraints that contribute towards minimized makespan. At the same time, the baseline approaches fall short in terms of time to completion of the tasks associated with the application.

Fig. 16.

Proposed QIAVOA-SP- Execution Time with different applications and services set to 50.

Scalability analysis of the proposed QIAVOA-SP scheme using convergence time under different ENs

In this section, the scalability of the proposed QIAVOA-SP scheme is explored with respect to different number of ENs which is incrementally changed from 4 to 20. This scenario for emulating the scenario of EC is achieved for the purpose of including additional number of edges nodes for satisfying the increasing demands of service. This scalability analysis is evaluated with respect to different number of ENs using time of convergence on par with the benchmarked approaches. Figure 17 consistently confirmed better scalability for sustaining minimized and stable times of conference over all the tested configurations. In specific, the proposed QIAVOA-SP scheme minimized the convergence time from 34 s to 106 s. On the other hand, the benchmarked approaches utilized a comparatively higher convergence rate they were not able to balance the trade-off between the rate of exploration and exploitation in the SS. They faced struggle in maximizing the diversity of the solutions in the SS.

Fig. 17.

Proposed QIAVOA-SP- Convergence time with different number of ENs.

The above result confirmed that the proposed QIAVOA-SP scheme is effective in scaling with respect to the largest sizes of problem which makes it as a significant candidate for real-time service placement in the large scalable EC scenarios.

Conclusions

The proposed QIAVOA-SP achieved optimal placement of IoT service in EC environment by adopting the fitness factors of computation load, delay, energy consumption and throughput into account. It incorporated the concept of QIAV as search agents for representing the complex solutions that are essential for placing IoT services in an edge environment. The simulation results confirmed that the proposed QIAVOA-SP scheme with different number of applications (services count set to 25) remarkably minimized the energy consumptions by 13.28%, 15.31%, 18.94% and 20.28%, better than the benchmarked approaches used for investigation. Moreover, the proposed QIAVOA-SP scheme with different number of applications (services count set to 50) also achieved better throughput of 10.76%, 13.29%, 15.68% and 17.85%, better than the benchmarked approaches used for investigation. As the part of future scope of research, the examination towards the process of designing service placement algorithms which could operate in uncertain and dynamic environments can be studied. In addition, some of the recently proposed quantum-inspired multi-objective evolutionary algorithms is adopted for solving the problem of service placement addressed in the paper.

Author contributions

B.P.: Writing- Original Draft, Conceptualization, Methodology, Investigation, Software, Experiments, Data curation, Validation, Review & Editing. N.K: Conceptualization, Methodology, Data curation, Validation, Writing— Review & Editing. R.N.: Conceptualization, Methodology, Data curation, Validation, Writing— Review & Editing. N.D: Conceptualization, Methodology, Software, Data curation, Formal analysis, Investigation, Writing - Review & Editing.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.