The rest of the manuscript is given as follows. In section 2, related work is presented, system model and problem formulation and proposed work i.e., AVOAVNF, are discussed in Section 3 and Section 4. Further, in Section 5, we discuss the simulation results. Finally, the conclusion is given in Section 6.

2. Literature Review

This section provides a summary of the present computational application situations that necessitate the use of edge computing platforms, in addition to a discussion of the essential elements that assist edge computing in providing SFC and VNF services. The service chain refers to the requirement that the request from the end user must be performed by numerous services that are dependent on one another. The management of service chain positioning receives a new facet with the addition of inter-service interdependence. For example, the end-to-end latency of a user request throughout the service chain ought to incorporate the communication latency that exists between the contingent services and the movement of traffic. It may be possible to loosen some restrictions to facilitate the development of solutions that are better suited to handle the complications of service chain positioning (Shahjalal et al., 2022; Wang et al., 2017).

Wang et al. (2019) focused on the positioning of service chains in MEC in order to evenly distribute the activity across the nodes. The writers modelled each service network as its own graph, with each vertex and line corresponding to a different service or communication route. The subsequent distribution challenge is an NP-hard one, and the research came up with two potential solutions. The first solution took an offline approach to position a single service chain, while the second solution took an online strategy to position numerous service chains, each of which is represented by a tree in the illustration. The first solution concentrated on the optimal positioning of a single service chain (Bahreini et al., 2020).

Yang et al. (2016) proposed an optimization problem of VNF placement in a MEC environment. The goal of this problem was to decrease the communication and network latency while also finding the optimum arrangements of VNFs. When the peripheral nodes that were housing the virtual network functions achieved their capacity limits, a dynamic resource distribution technique was used to adjust the present VNF deployments to address the time-varying workload. This technique may be able to forecast the upcoming workload of the system and determine which peripheral nodes will exceed their capabilities. One of the possible outcomes that could occur in this context is that the existing edge server will not be able to cope with and perform the anticipated workload because it will not meet the latency requirement. As a result, a new edge server ought to house VNF in order to perform the activity within the allotted amount of latency. Utilizing the online adaptive greedy heuristic algorithm is one way that this could be accomplished. The new node’s position can be determined with the help of this proposed technique, which also distributes the workload across the new service-hosting nodes (Wang et al., 2021).

Gao et al. (2022) proposed that a single SFC could be built of many virtual network functions (VNF). An SFC is, in point of fact, defined as an ordered list of VNFs that are able to deliver a service when current is directed through them. An SFC may be created by deploying the necessary VNFs and embedding virtual connections. This is done while taking into consideration the QoS criteria that are most suited for an SFC. Yang et al. (2019) proposed a NFV paradigm which reimagines traditionally cumbersome hardware middleboxes as groups of lightweight. As a result, NFV offers latency-sensitive services that are flexible as well as low-cost in the deployment of VNF instances on FCCN components. The overall goal of an SFC request is to send data across the FCCN using the path with the least impact on latency, bandwidth, and processing power of the VNFs. However, when dealing with complex services, the SFC placement problem is extremely challenging to solve because it is an NP-hard problem. The source terminal sends flow data to the network in the form of a sequence of VNFs in response to an SFC request from a user. This is done so that traffic moves in an orderly fashion via the VNFs and to its final destination terminal (Kouah et al.,2018; Qu et al., 2022).

Magoula et al. (2021) proposed an innovative SFC deployment architecture that works on top of the well-established network function virtualization infrastructure (NFVI) and seeks to minimize the end-to-end delay of all requested latency-critical services (such as IIoT). The proposed framework is built on top of a genetic algorithm (GA), which has been augmented with a number of context-aware improvements in the interest of further delaying the process as little as possible. In addition, each of the aforementioned studies proposed either model-based heuristics and metaheuristics or mathematical programming approaches. These approaches were intended for specific network structures and application situations. Regardless of how effective they are, scenario-customized solutions are notoriously challenging to implement in a realistic setting with other kinds of networks and applications. In recent years, a number of studies have been carried out with the intention of deploying service chains by utilizing various machinable learning techniques, such as optimization techniques (Luizelli et al., 2017; Sahoo et al., 2022; Khoshkholghi et al., 2020) These model-free approaches intend to produce data-driven solutions with the capability of being variably applied to various application and network situations (Pham et al., 2017).

Zhang et al. (2022) proposed an OSIR algorithm in mobile edge computing to reduce costs and improve the efficiency of the model and provide a solution for the deployment of SFCs that makes use of previously deployed instances. This is limitation of OSIR algorithm is VNF not sharing the network as well as not calculating the latency value over the networks.

Akhtar et al. (2021) proposed a binary integer program (BIP) model in an edge network environment for managing virtual service lines over the edge network; the solution improves virtual capacity compared to a "middlebox" approach using BIP algorithm. As the Wire network accepts fewer flows, the middlebox case fails to benefit from mm Wave links in edge network. Hazra et al. (2021) proposed a DRL based strategy in industrial edge network. The DRL-based strategy handles as many service requests as feasible using the set of available resource-constrained auxiliary servers.

Liang et al. (2022) proposed the PHS and AUB algorithm in edge-Open Jackson Networks to minimize general SFC deployment delay in open Jackson-based edge-core networks. It is not considered for minimizing the network overhead and fault tolerance. Munusamy et al. (2021) proposed the RSBD and SVM algorithms in IoT based edge network. Hall’s theorem effectively sends sorted financial data to edge servers with minimum delay and power and improved the analysis using SVM algorithm. There has been limitation in the prediction analysis and minimizing network overhead. Shahjalal et al. (2022) proposed a BGWO algorithm in 5G hybrid cloud and a nearly optimum solution was obtained in polynomial time using an AI-based BGWO VNF distribution strategy. The rollout of VNFs is a MOLP problem. Therefore, there are two competing objectives in the VNF placement problem: reducing service delay while keeping costs down. Artificial intelligence (AI) enables intelligent management of computational and network resources; therefore, it may be used to solve this kind of issue.

To the best of our understanding, the majority of the established initiatives only consider the processing and communication latency measures as metrics to take into consideration. Several studies have been conducted to address delay, throughput, and latency metrics in order to propose a delay-aware solution for service function chain (SFC) placement. These studies employed various techniques such as commercial algorithms, heuristics, and metaheuristics, as documented in the references (Zahedi et al., 2022; Yang et al., 2010). The present study introduces an AVOA methodology that considers the delay metrics mentioned above. The objective of this approach is to offer an optimal resolution to the challenge of optimizing SFC placement while being mindful of delays and avoiding the issue of being confined to local optima. The problem is formulated by considering the significance of selecting the most favourable transmission and propagation delay-conscious route for every SFC to attain the objective of minimizing the total link delay of the path. Furthermore, our model, which is based on AVOA, integrates supplementary enhancements, including location-sensitive augmented functionalities, aimed at diminishing the overall SFC delay and boosting throughput, thereby reducing the computational time required for the AVOA algorithm to execute its computations. In the end, a dynamic early stopping criterion is applied on the AVOA model in order to improve upon the static one that is used in the traditional version of AVOA in order to achieve quicker convergence.

3. System Model and Problem Formulation

We take into account a system where NFV is used to distribute SFCs to a physical network and where VNFs and virtual connections between VNFs share the available processing and transmission resources. Reduce system-wide SFC delay as much as possible

3.1. SFCs and Physical Network Scheme

In the physical network, there are a total of S_n physical servers, and the collection of physical servers can be denoted by the notation S_p={S₁,S₂,…..S_n}. The collection of physical communication channels is denoted by the notation Ch_n, where ∁_n={Ch₁,Ch₂,…..Ch_n}. There is a total of Ch_n physical communication channels connecting the computers that make up S_p. The physical network is denoted by the notation G=(S_p,∁_n). It has a computational capability of f_n for every physical server that it has, up to a maximum of S_n servers. The hardware computers come with varying numbers of CPUs, RAM, and other components. Different types of virtual network functions (VNFs) are best handled by specific categories of physical computers. A bandwidth, measured in bw bits per second, is assigned to each individual communication channel, denoted by c∈∁_n.

In SFCs, M indicates the total amount of SFCs that customers have requested. To indicate the collection of SFCs, we use the notation M = {1,2,…..M}. There is a source server designated by the notation s_m ∈ S_p and a destination server designated by the notation d_m ∈ S_p that correspond to each and every SFC m ∈ M. A connection needs to be made between SFC m and a path that goes from s_m to d_m. Each SFC m ∈ M is made up of a predetermined quantity of VNFs in the correct sequence. To designate the collection of VNFs in SFC m, we make use of the notation VN_m = {vn_m,1,vn_m,2,…..vn_m,Vm}. V_mis the total amount of VNFs contained within m number of SFC, and V_m,i represents the name of the ith VNF contained within SFC. In addition, we use the symbol VN_m to denote the whole set of VNFs found in every SFC. For each SFC, there is a set of virtual connections that link the source server (notated s_m), the VNFs, and the destination server (notated d_m). For ease of reference, we refer to the virtual connection between the ith and (i + 1)^th) VNFs inside SFC m as link_m,i. link_m,0 represents the virtual connection between the source server s_m and the virtual network VN_m,1, and link_m,Vm represents the virtual connection between VN_m,Vm and s_m. In addition, the set of virtual links shared by all SFCs is marked by the notation L_m, and the set of virtual links of a single SFC is indicated by the notation L_m, which may be expressed as L_m = {link_m,i Vi∈ {0,1,2,….V_m}}.

The workloads with sizes W_vnm,i,i ∈ {V₀,V₁,…..V_m}, and the sizes of data D_linkm,i,i ∈ {V₀,V₁,…..V_m} (in bits), respectively, must be handled by vn_m,i,i∈{_V0,V₁,…..V_m}, and transferred by link_m,i,i ∈ {V₀,V₁,…..V_m}. In particular, the i^th VNF vn_m,i desires to send the interim information that it can, about D_linkm,i potential to (i + 1)^th for SFC m ∈ M and i ∈ {V₀,V₁,…..V_m-1} after vn_m,i has completed its task of workloads W_vnm,i, VNF vn_m,i+1. After vn_m,i+1 has been given the intermediary data that was produced by vn_m,i, it begins the processing of its task, which has a capacity of W_vnm,i+1. Additionally, the source server s_m is required to send some starting data of size D_linkm,0 to the destination server vn_m,i via link_m,0 at the beginning of the process, and the destination server d_m is required to receive some output data of size D_linkm,Vm from the source server vn_m,Vm at the end of the process.

The suitability of placing a virtual network function (VNF) on a specific physical server can be evaluated based on the characteristics of the server, such as the number of RAM and CPUs. This evaluation is represented by the variable $$U_{vn}^n\in \left\{0,1\right\}$$. The placement decision is made for each VNF vn∈VN and physical server n∈S_n, with the goal of achieving fitness for purpose. The suitability of deploying vn on server n is directly proportional to the magnitude of $$U_{vn}^n$$.

3.2. SFC Deployment

There exist two options for the deployment of a service function chain (SFC). The initial step involves the selection of a route for the SFC, while the subsequent step pertains to the placement decision of the SFC’s virtual network functions (VNFs) onto physical servers situated along the chosen route.

The routing paths, connecting every pair of edge servers, are restricted and comparatively minimal. In accordance with previous studies (J Pei et al., 2019; Y Zhang et al., 2022; S Deng et al., 2020), we make the assumption that R_m represents the quantity of potential routes for each SFC m within the set M. All of the routes exhibit a line topology. R_m is the group of all possible routes that may be taken from m to M of the SFC and it is represented as {1, 2, ….R_m}. The value of the variable r_m, which is part of the R_m structure, provides an indication of the routing choice made by SFC, i.e., m∈M. In addition, the routing choices made by all service function chains (SFCs) are denoted by r = {r_m}m∈[M]. Let the number of physical servers that are present in route r_m of SFC m be denoted by the variable I_m,rm. For the purpose of representing the i^th physical server that is part of SFC m route r_m, the notation n_m,rm,i is used. In addition, the group of servers that are part of SFC m’s route r_m is indicated by the notation M_m,rm, and which can be expressed as $${\left\{n_{m,rm,i}\right\}}_{i=1}^{Im,rm}$$. Given that SFC m initiates at S_m and terminates at d_m, it follows that n_m,rm,0 and n_m,rm,Im,rm.

The placement choice for the i^th VNF in each SFC, i.e., m ∈ M is denoted by the variable p_m,i. Each SFC, m ∈ M undergoes this procedure. The i^th virtual network function (VNF) of SFC m is deployed on the (p│m,i)^th physical server under route r_m of SFC m. Since there are I_m,rm servers in route r_m of SFC m, we have p_m,i∈P_m,rm ≅ [I_m,rm]. Placement selection for all VNFs in SFC of m is denoted by the notation $${\overline{P}}_m\cong {\left\{p_{m,i}\right\}}_{i\in vm}$$). If $$i>\overline{i}$$., there is a bound on the set of all possible states p_m,ii ∈ [v_m] such that p_m,i≥p_m,i. This is because VNFs in an SFC follow a certain hierarchy. The set of all conceivable $${\overline{P}}_m$$ under route r_m is denoted by P_m (r_m), and for every value of r_m, this set is denoted by $${\overline{P}}_m\in P_m\left(r_m\right).$$. For a given combination of routes r_m and m number of SFC, the physical channels linking the (p│m,i)^th and (p│m,i + 1)^th physical servers are mapped to the link_m. The ∁_link is used to refer to the underlying physical channels that link_m is mapped. For instance, in route r_m of SFC m, the first three physical servers will be connected through two separate physical channels if p_m,1 is equal to one and p_m,2 is equal to three. The slot labeled ∁_link is freed up when the two VNFs linked by link₁ are unoccupied on the same physical server.

The act of deploying a system involves the amalgamation of both the choice of path and the placement selection. The placement selection of SFC m is denoted as s_m = (r_m,p_m). Furthermore, the placement selection of all SFCs is denoted by s =(s₁,s₂,….,s_m). Let S represent the set comprising all feasible s. The set of virtual network functions (VNFs) placed on a physical server n, where n belongs to the set of physical servers S_n, is denoted as K_n (s) for a given deployment selection s. It is to be noted that K_n (s) is a subset of the set of all VNFs [VN]. Likewise, the notation K_c (s) is employed to represent the collection of virtual connections which are allocated to the physical channel c, wherever c belongs to ∁_n and K_c (s) is a subset of L. Furthermore, the set of c that link is mapped to under placement selection s is denoted as ∁_n (s).

Example: Given a value of m within the set M and a value of r_m within the set R_m, it is possible to determine the optimum placement selection for m number of SFC by creating a graph. To find the shortest route from the source node X_0,1 to the destination node Y_Vm,Im,rm. Assuming I_m,rm = 4 and V_m = 4 for a given m within the set M and r_m within the set R_m, optimum placement selection p_m minimizes the SFC cost that can be determined by utilizing the graph depicted in Fig. 2. The purple route depicted in Fig. 2 denotes the allocation of the initial VNF to the second physical server along the r_m route, while the second and final VNFs are assigned to the ultimate physical server. The utilization of the lime route depicted in Fig. 2 involves the allocation of the initial, secondary, and final VNFs to the primary, secondary, and tertiary physical servers of the r_m route, respectively. The optimal path between the coordinates X_0,1 and X_3,3 is the shortest path, commonly referred to as the best path.

3.3. Energy Model

The energy model requires to consider the power needed for peripheral node transmission and VNF computation. When sending or receiving data between peripheral nodes, we accounted for the transmission latency alongside the electricity required. In equation (1), we represent the energy expended by communicating between two nodes as vn_i,vn_j∈ VN, where vn_ij is the power expended in this communication and p_delay (link_i,j ) is the transmission delay between these nodes.

$E_c=v{n}_{ij}\ast p_{\text{delay}}\left({\mathrm{link}}_{i,j}\right) (1)$

In equation (2), E_idl is the energy consumed by a vn at time t when it is in its idle vstate, E_max is the energy consumed by a vn when it is in its complete state, and u_n (t)is the usage of a vn at time t.

$E_{\text{idl}}(t)=E_{\text{idl}}+(E_{\text{max}}-E_{\text{idl}})\ast u_n(t) (2)$

Hence, the computational energy utilized in vn∈VN at t of binary variable at instance set to 1 is denoted by B_n, as given by equation (3).

$E_p=\sum _{v{n}_{i,j}\in I_{vn}}\sum _{e_{i,j}\in N}{E}_{idl}(t)\ast B_n,\mathrm{\forall }vn\in VN (3)$

Equation (4) calculates the energy usage for virtual link by the vn propagation delay p_delay (link_i,j) at time t.

$E_t=\sum _{v{n}_{i,j}\in I_{vn}}\sum _{e_{i,j}\in N}{p}_{\text{delay}}\left({\mathrm{link}}_{i,j}\right)\ast E_{{\text{link}}_{i,j}}\ast X_{{\text{link}}_{i,j}}^{v{n}_{i,j}},\mathrm{\forall }vn\in VN (4)$

3.4. Cost of the Network

We represent the expense of each SFC as the total of the processing delays that all of its VNFs experience as well as the communication delays that all of its virtual connections experience. The overall cost of the system can be calculated by adding up the prices of each SFC in the system. The workload size is w_vn that is used for VNF vn∈VN. If vn is determined to be vn∈K_n (s) for a particular SFC deployment selection s, then the quantity of processing capability that is allotted to v is equivalent to $$f_n{r}_{vn}^m$$, and the feasibility of executing VNF vn on server m is $$U_{vn}^m$$. The latency computation in VNF vn, which is represented by Delay_vn, is modeled as follows:

${\mathrm{Delay}}_{vn}=w_{vn}\ast \left(\frac{1}{U_{vn}^m{f}_n{r}_{vn}^m}\right) (5)$

Under this configuration, Delay_vn from equation (1) is equal to the processing delay of putting VNF vn with the workload capacity of w_vn on server m with a computational ability of $$f_n{r}_{vn}^m$$ and $$U_{vn}^m$$ is set to [0,1] of VNF vn and server m.

Delay in virtual connections; it is necessary to send data with a capacity of D_link through each virtual connection link∈L. The latency of link in physical channel c is ${\mathrm{Delay}}_{\text{link}}^c$ if and only if link∈K_n (s), in which case the bandwidth assigned to link is $$b{w}_c{r}_{vn}^m$$, as given in equation (5).

${\mathrm{Delay}}_{\text{link}}^c=\frac{D_{\text{link}}}{b{w}_c{r}_{vn}^m} (6)$

It is possible for a single virtual link to be mapped to several neighboring physical channels. The overall delay of link is determined by adding the latencies of each of the physical channels to which it is mapped. Therefore, the overall latency in virtual connection link, which we refer to as Delay_link, is calculated as follows:

${\text{Delay}}_{\text{link}}=\sum _{c\in C_n(s)}\frac{D_{\text{link}}}{b{w}_c{r}_{vn}^m} (7)$

The overall delay of an SFC m, which is indicated by the notation Y_m (s,R_a,R_b ) is equal to the aggregate of the latencies of all of its VNFs and virtual connections in the given equation (7)

$Y_m(s,R_a,R_b)=\sum _{vn\in V{N}_m}\sum _{vn\in K_n(s)}{w}_{vn}\ast \left(\frac{1}{U_{vn}^m{f}_n{r}_{vn}^m}\right)+\sum _{link\in L_m}\sum _{c\in C_{nlink}(s)}\frac{D_{\text{link}}}{b{w}_c{r}_{vn}^m} (8)$

The overall fitness of the network, which is represented by the notation Y(s,R_a,R_b ), is equal to the aggregate of the latencies of each of its SFCs in the given equation (8).

$\begin{array}{c}Y(s,R_a,R_b)=\sum _{m\in M}{Y}_m(s,R_a,R_b)\\ \sum _{m\in M}\sum _{vn\in V{N}_m}\sum _{vn\in K_n(s)}{w}_{vn}\ast \left(\frac{1}{U_{vn}^m{f}_n{r}_{vn}^m}\right)+\sum _{m\in M}\sum _{link\in L_m}\sum _{c\in C_{nlink}(s)}\frac{D_{link}}{b{w}_c{r}_{vn}^m}\end{array} (9)$

Finally, equation (9) defines the objective function to reduce the latency of the network, energy consumption, and VNF data transfer from edge nodes to their outbound lines. The energy consumption calculation incorporates the processing and propagation delays, thus rendering their exclusion from the analysis.

$\mathrm{minimize}[Y(s,R_a,R_b)+E_{\text{idl}}(t)+E_p+E_t] (10)$

4. The Proposed AVOAVNF

The AVOA metaheuristic method was first presented by Abdollahzadeh et al. (2021). Since that time, it has been implemented in a variety of real-world engineering applications. To build the AVOA, simulations and models were used that were based on the feeding behaviors and daily routines of African vultures. The following considerations are taken into account in order to carry out the simulation that is known as AVOA. This simulation recreates the life patterns and foraging strategies of African vultures, and it is carried out by using the following elements.