Throughput and load balancing optimization in heterogeneous networks using Red-Tailed Hawk Algorithm

Abstract

In wireless communication networks, the growing need for data has presented significant issues in the last years. This will continue, with mobile consumers’ needs for Quality of Service (QoS) changing and their data use skyrocketing. The complexity of Heterogeneous Network (HetNet) situations and the sharp rise in traffic demand have significantly increased the issues. It is challenging to accommodate the various traffic needs of mobile users with traditional methods as they maintain network imbalances inside the HetNets by giving priority to maximum received power in the cell association process. In this work, a Red-Tailed Hawk (RTH) algorithm with a Cell Range Extension (CRE) approach is integrated to maximize the number of users whose downlink demands are fulfilled, rather than just focusing on improving downlink rates for individual users. The suggested approach formulates a fitness function with the goal of determining appropriate CRE bias values for individual Small Base Stations (SBSs) while taking into account the workload of BS as well as the Signal to Interference-plus-Noise Ratio (SINR) of user devices. The efficiency related to the suggested strategy is demonstrated by a comparison with conventional methods. The proposed methodology meets user throughput requirements while lowering network imbalances and call drop rates. Experimental findings demonstrate the betterment of the proposed model by 56.67% load balancing, 49.23% throughput, 91.49% call drop rate, 77.55% execution time, 92.68% delay, and 20.11% convergence than the existing methods.

Introduction

With the rapid advancement of wireless communication technology, 5G and beyond Heterogeneous Networks (HetNets) have emerged, offering unprecedented levels of connection as well as data transfer^1,2. But in order to fully utilize these networks, difficult problems like effective load balancing and user association should be solved³. CRE, a standardized method developed by the 3GPP, appears to be a viable way to achieve better user balance in a mobile network⁴. Precisely computing the bias values for every layer in the HetNet is necessary to overcome the difficulties associated with CRE deployment.

Many problems, such as worse user experience, unequal resource utilization, lower network capacity, and higher energy usage, can result from load imbalance^5,6. Within the context of mobile cellular networks, “load” has several meanings, frequently associated with the number of User Equipments (UEs) that are attached to a BS⁷. The BS’s traffic load linearly correlates with the count of associated UEs⁸. Load balancing becomes more important in 5G and beyond HetNets because of the wide diversity of services, devices, and applications these networks offer. As a result, load balancing is crucial when using HetNets⁹.

In a heterogeneous cellular network, integrating bio-inspired frameworks with network operating techniques offers a viable way to improve load balancing and user association^10,11. There’s a chance that some BSs will be overburdened or underutilized while trying to evenly spread the load across network levels¹². As such, the requirement is to accomplish load balance for every BS in addition to coordinated real-time network resource optimization¹³. This method does not require additional signaling methods and is in line with the smooth functioning of mobile networks^14,15. The heterogeneous network representing the CRE is depicted in Fig. 1.

Fig. 1

Heterogeneous network representing the CRE.

In heterogeneous networks, it is crucial to maximize the system’s throughput as well as balance the load on different networks. One of the mandatory features when many devices and technologies interface, is the coordination of data through put. Throughput optimization ensures that there is an increase in speed and reduction of delay and hence also enhances the satisfaction of every user. Most especially, when there are various types of networks are in use in an organization, the load balancing becomes inevitable in the of proper distribution of work load across active networks. As such, reliability and continuity always become assured while at the same time no node risks being prevented from becoming a bottleneck. It can be pointed out that in order to meet variable demands, networks can adapt to the situation and reroute the data traffic based on the current conditions. This makes utilization of the resources efficient and also caters for support of other users at the same instance. Efficient optimization methods also help in reducing operating costs, and at the same time, reduce the impact these costs have on the external environment through energy conservation. There will be an even growing need for throughput as well as load balance when proceeding to smart cities as well as IoTs. Moreover, implementing efficiencies in this category of networks has the advantage of expanding the application of the advanced methods and technology. Thus, by optimizing these parameters it ensures that the connected future we all envision creates reliable networks that can support today’s as well as tomorrow’s needs for all the users.

The paper contribution is given as.

• To integrate a RTH algorithm with a CRE approach to maximize the number of users whose downlink demands are fulfilled, rather than just focusing on improving downlink rates for individual users.

• To formulate a fitness function with the goal of determining appropriate CRE bias values for individual SBSs while taking into account the workload of BS as well as the SINR of user devices.

• To demonstrate how well the suggested approach meets user throughput requirements while lowering network imbalances and call drop rates.

The paper organization is as follows. Section 1 is the introduction of heterogeneous network. Section 2 is literature survey. Section 3 is proposed methodology with system model, WiFi channel model, problem formulation, channel and interference models, performance evaluation metrics, and RTH algorithm. Section 4 is results. Section 5 is conclusion.

Related work

For multi-tier cooperating frameworks, a novel real-time dynamic user (UE) association method was created that took into account traffic dynamics and users’ mobility while taking into account the total network load as well as the received SINR¹⁶. Through simulation, the novel algorithms were investigated and evaluated, and it was shown that they outperformed existing algorithms in terms of effectiveness.

For dependable relay coverage and user-to-user message delivery, a sizable fleet of UAVs was deployed¹⁷. Initially, a relay coverage method was proposed that continually maximized the ground users’ cell division as well as UAV positions to offer complete coverage to users. Second, a number of relay message passing techniques was examined among UAVs while accounting for user heterogeneity. To guarantee complete communication among UAVs, a relay selection approach was developed that optimized the relay link throughput. Lastly, how different relay forwarding techniques impacted the relay network’s efficacy was compared and examined. The experimental findings showed that the suggested relay coverage method may more effectively balance the UAV relay load.

The focus of load balancing in multi-UAV capable wireless networks was on UAVs providing Time Division Multiple Access (TDMA) service to ground UEs¹⁸. Spatial-temporal heterogeneous requests from UEs for data transfer must be completed promptly; this incomplete portion was known as an unfinished user request. The UAVs’ versatility was used to present a versatile and effective Multi-UAV-enabled Load Balancing (MULB) strategy that enhanced overall system effectiveness and improved QoS. The network optimization challenge was described as minimizing the maximum incomplete user request by concurrently optimizing UAV trajectory, user association, and time slot allocation, taking into account the load balancing impact.

In order to increase the throughput of 5G with the existing LTE Advanced Heterogeneous Networks (5GLHNs), this research suggested a system that used cell association approach and a load-balancing algorithm called Constriction Factor Particle Swarm Optimization (CFPSO)¹⁹. The efficacy related to the suggested CFPSO strategy was assessed by analyzing the allocation time, average throughput, convergence, and cumulative distribution function (cdf) associated with the UEs rate.

In order to provide QoS provisioning for 5G and next generation networks with throughput and load balancing, this study tackled the cell association difficulty²⁰. As users have different QoS requirements and BSs have different backhaul capacity, this situation was quite complex. According to simulation findings, the suggested load-aware-oriented approach accomplished better with respect to load-balancing and throughput than traditional cell association methods on the basis of RSRP as well as its variations.

Using a novel strategy on the basis of Q-learning, the research proposed a way to balance loads and link cells on the network for both H2H and M2M devices²¹. The two separate algorithms used by the system were both dependent on Q-learning. The effectiveness related to the suggested plan was evaluated by comparison using two methods. The suggested strategy’s findings indicated that there was a decreased chance of H2H and M2M device blockage. This approach was power-efficient since M2M devices’ uplink transmission power was decreased even in situations of heavy load.

To solve the issues with the traditional load balancers and boost throughput, an improved heterogeneous load balancing algorithm was created²². The Least Connection algorithms and Weighted Round Robin (WRR) were used as scheduling strategies to implement the devised load balancing algorithm. The test’s outcomes showed that the HDSE’s method performed better than other traditional load balancing algorithms.

Selective Handoff was used in the construction of the Hierarchical and Hybrid Cell Load Balancing (HHCLB) approach²³. Using this method, every cell’s UEs were sorted into clusters based on how close together they were. A cluster controller (CC) was present in every cluster, and its duties included assessing intra-cell load and rerouting a UE’s request for cell selection. The cell reselection procedure was carried out. Based on the findings of the simulation, it was demonstrated that load balancing might be performed by the CCs either explicitly when a UE requests cell reselection or proactively (implicitly) when the load was imbalanced.

A unique proactive load balancing method was proposed²⁴. In order to maximize quality of experience and minimize load, this system simultaneously learnt users’ movement. Conventional reactive techniques were contrasted with system level simulations conducted. A new proactive load balancing system was suggested that minimized cell loads and maximized downlink throughput by combining content demand information and user mobility. Through a Semi-Markov renewal procedure, this platform predicted user mobility patterns and used past content demand to provide proactive content caching.

This paper investigated a Reinforcement Learning (RL)-oriented approach for almost optimum effectiveness and a reasonable level of complexity in handling the downlink HLWN load balancing issue²⁵. Three distinct reward functions for reinforcement learning have been proposed; the first as well as second reward functions aimed to maximize user satisfaction and average network throughput, respectively. Table 1 explains the previous methods and their contributions.

Table 1 Existing methods and their contributions.

Problem statement

The increasing density of heterogeneity is a critical challenge for load balancing and, moreover, throughputs. This behavior is diverse thereby making it hard for usual network management practices to address customer requirements. The main problem is to provide resource sharing across several network types and keep low latencies while maximizing the throughput of the whole network in its using of cellular, Wi-Fi, and satellite networks. Due to the poor load balancing in some areas the network may receive multiple requests within a short span of time thereby slowing down the system and reducing its efficiency. Thus, traffic is often unbalanced in a network and its nodes will be either overloaded or vice versa. The optimization procedure is even more complicated by dynamic changes of traffic flow or user activity levels that can hardly be predicted and adjusted in real time as to resource distribution. In addition, low numbers of algorithms and methods dealing with various networks often result in increased energy and operating costs. It can be stated that solving of these problems remains to be a critical aspect, and it will help to enhance the user experience and maintain the stability of the network. Therefore, new solutions to improve throughputs when intended to ensure load balancing in different network architectures are desperately demanded in the present unsteady internal digital environment.

Proposed methodology

This section elaborates on the proposed method for load balancing in HetNet. This system comprises six modules, which are: (i) system model, (ii) WiFi channel Model, (iii) Problem formulation, (iv) Channel and Interference Models, (v) Performance evaluation metrics, and (vi) RTH algorithm.

System model

This section provides an illustration of the system model and formulates an optimization problem that is specifically designed to calculate unique CRE bias values that should be assigned to every SBS while taking the unique traffic patterns of users into account. A downlink HetNet architecture is considered with $\:L$ BS autonomous network tiers, in which $\:L$ can be any number between 1 and $\:l$. A typical UE in this configuration is located at network position$\:{S}^{3}$. According to the arrangement, user as well as BS locations are sampled using different distributions that are obtained from Homogeneous Poisson Point Processes (HPPP). This indicates that users’ and BSs’ places are selected at random in accordance with HPPP. In this case, the density associated with every $\:{l}^{th}$ layer is $\:{\lambda\:}_{l}$, and its BSs are produced at random by HPPP $\:\varphi\:\left({\lambda\:}_{l}\right)$ while user placement is achieved by HPPP $\:\varphi\:\left({\lambda\:}_{v}\right)$.

The total BS collection is expressed as $\:\varphi\:$, in which $\:\varphi\:=\left(\delta\:\cup\:\gamma\:\right)$. The MBS group is described by $\:\delta\:={N}_{1},{N}_{2},{N}_{3},\cdots\:,{N}_{n}$, and the SBS group is described by $\:\gamma\:={T}_{1},{T}_{2},{T}_{3},\cdots\:,{T}_{t}$. In this case, $\:1\le\:k\le\:c$ (in which $\:c=n+t$) is used to index $\:\varphi\:$. The collection of UEs is represented by the symbol $\:\pi\:={V}_{1},{V}_{2},{V}_{3},\cdots\:,{V}_{v}$, in which $\:1\le\:j\le\:v$. Furthermore, $\:\psi\:={\theta\:}_{1},{\theta\:}_{2},{\theta\:}_{3},\cdots\:,{\theta\:}_{t}$ denotes the collection of bias values linked to SBSs. Additionally, the $\:{j}^{th}$ user makes a request for a particular service class, which is described by the tuple $\:{\rho\:}_{j}=\left({\eta\:}_{j},{\tau\:}_{j}\right)$, in which $\:{\eta\:}_{j}$ and $\:{\tau\:}_{j}$ stand for the average throughput as well as compression factor, respectively. Therefore, the product of $\:\left({\eta\:}_{j}\cdot\:{\tau\:}_{j}\right)$ may be used to calculate the necessary data rate for the $\:{j}^{th}$ UE.

The received SINR has a direct association with Shannon’s theory, making it a crucial indication of the outage effectiveness and UE rate. The $\:{j}^{th}$ UE tends to associate with the $\:{k}^{th}$ BS according to the Max-SINR association criterion, in which $\:k=argmax\:\left({SINR}_{jk}\right)$ for every $\:k\in\:\varphi\:$. UEs tend to associate predominantly with MBSs in the context of a two-tier HetNet $\:\left(L=2\right)$ and the prevalent scenario that MBSs hold significantly more transmission power $\:\left({Q}_{1}\gg\:{Q}_{2}\right)$. UEs enjoy superior distribution within BSs when a CRE bias is added to every SBS’s SINR; this might boost every UE’s long-term rate. When the $\:{j}^{th}$ UE chooses an MBS $\:l\in\:\delta\:$ and moves towards the MBS tier (tier-1), the received SINR $\:\left(\zeta\:\right)$ satisfies criteria (1) and (2).

$$\:{\zeta\:}_{jl}>{\zeta\:}_{jk},\:\:\:\:\:\forall\:k\in\:\delta\:,\:\:\:\:\:l\ne\:k$$

(1)

$$\:{\zeta\:}_{jl}>{\zeta\:}_{jk}+{\theta\:}_{k},\:\:\:\:\:\forall\:k\in\:\gamma\:$$

(2)

Here, $\:{\theta\:}_{k}$ stands for the CRE bias that is applied to the SBS that is indexed as $\:k$. Additionally, when CRE is implemented, the $\:{j}^{th}$ UE chooses the $\:{m}^{th}$ SBS if the incoming SINR satisfies the requirements listed in Eqs. (3) and (4):

$$\:\left({\zeta\:}_{jm}+{\theta\:}_{m}\right)>{\zeta\:}_{jk},\:\:\:\:\:\forall\:k\in\:\delta\:$$

(3)

$$\:\left({\zeta\:}_{jm}+{\theta\:}_{m}\right)>\left({\zeta\:}_{jk}+{\theta\:}_{k}\right),\:\:\:\:\:\forall\:k\in\:\gamma\:,\:\:\:\:\:k\ne\:m$$

(4)

These BSs change their coverage area for downlink, which affects the count of users connected to them, by varying the suitable bias or Cell Specific Offset (CSO) values for the tiny BSs. The downlink SINR $\:\left({\zeta\:}_{jk}\right)$ may be expressed as follows when the $\:{k}^{th}$ BS is connected to the $\:{j}^{th}$ user:

$$\:{\zeta\:}_{jk}={Q}_{j}{H}_{jk}/\left(\sum\:_{l\in\:\varphi\:}{Q}_{l}{H}_{jl}+{Q}_{AWGN}\right)$$

(5)

The power transmitted by BS $\:t$ is denoted by $\:{Q}_{j}$ in Eq. (5), the Additive White Gaussian Noise power is $\:{Q}_{AWGN}$, and the gain related to the downlink channel for the link between BS $\:t$ and UE $\:v$ is $\:{H}_{jk}$. $\:{Q}_{j}$ represents the power transmitted by the interfering cells, while $\:{H}_{jk}$ represents their gain. $\:{H}_{jk}$ is said to have been averaged within the association period and overall physical resource blocks in the complete channel spectrum because cell selection is thought to be carried out on a longer time scale. This implies that rapid fading as well as frequency-selective fading are averaged out. As a result, even throughout the cell selection phase, $\:{H}_{jk}$ does not change, and the SINR for every sub-channel among BS $\:k$ and user $\:j$ is comparable. Consequently, the following formula may be used to determine the achievable per-channel downlink rate for the $\:{j}^{th}$ user connected to the $\:{k}^{th}$ BS:

$$\:{S}_{j}={e}_{m}\cdot\:\frac{{o}_{SC}\cdot\:{o}_{SYM}}{{U}_{Subframe}}$$

(6)

In this case, $\:{e}_{m}$ represents the bit-by-bit effectiveness per sub-carrier for every Orthogonal Frequency-Division Multiplexing (OFDM) signal at a specified threshold SINR. Usually, a number of variables, including the system specifications, intended QoS, and environmental considerations, are taken into account while selecting this threshold SINR. This effectiveness is obtained by using an MCS function, $\:\mu\:\left({\zeta\:}_{jk}\right)$ it is written as $\:{e}_{m}$. The feasible communication reliability and data rate over the sub-channel are determined by mapping the SINR values to certain coding and modulation strategies via the MCS function. The number of subcarriers per channel, the number of OFDM symbols per subframe, and the duration related to every subframe are represented by the variables $\:{o}_{SC}$, $\:{o}_{SYM}$, and $\:{U}_{Subframe}$, respectively. The total amount of resource blocks (RBs) obtained by the $\:{j}^{th}$ user from the $\:{k}^{th}$ BS may be expressed mathematically as follows when an equitable resource allocation technique is used and the RBs are divided equally within the connected users:

$$\:{o}_{{RB}_{j}}=\frac{{o}_{{RB}_{k}}}{{M}_{k}}$$

(7)

Here, $\:{M}_{k}$ is the entire user load connected to BS $\:k$, and $\:{o}_{{RB}_{k}}$ is the total count of RBs that are accessible in BS $\:k$. The balancing of loads between cells on the basis of system capacity is shown in Fig. 2.

Fig. 2

Balancing of loads between cells on the basis of system capacity.

WiFi channel model

When a user $\:\mu\:$ connects to WiFi AP $\:{\alpha\:}_{1}$, the SNR is provided by:

$$\:{SNR}_{\mu\:,{\alpha\:}_{1}}\left(g\right)=\frac{{\left|{H}_{\mu\:,{\alpha\:}_{1}}\right|}^{2}\left(g\right){Q}_{U}}{{O}_{WiFi}{C}_{WiFi}}$$

(8)

Here, $\:{Q}_{U}$ stands for transmitted power, $\:{O}_{WiFi}$ for the PSD of WiFi noise, and $\:{C}_{WiFi}$ for the WiFi AP’s bandwidth. $\:{H}_{\left(\mu\:,{\alpha\:}_{1}\right)}\left(g\right)$ describes WiFi channel gain. $\:{H}_{\left(\mu\:,{\alpha\:}_{1}\right)}\left(g\right)$, the WiFi channel gain, is determined by:

$$\:{H}_{\mu\:,{\alpha\:}_{1}}\left(g\right)=\sqrt{{10}^{\frac{-M\left(e\right)}{10}{i}_{s}}}$$

(9)

Here, $\:{i}_{s}$ represents the small-scale fading gain, which has an average power of 2.46 dB and follows an independent identical Rayleigh distribution, and $\:g$ represents the carrier frequency. The large-scale fading loss is represented by the $\:M\left(e\right)$, which is shown as:

$$\:M\left(e\right)=\left\{\begin{array}{l}\begin{array}{cc}{M}_{fs}\left(e\right)+{Y}_{sf},&\:e<{e}_{bp}\end{array}\\\:\begin{array}{cc}{M}_{fs}\left({e}_{bp}\right)+35\text{log}\left(\frac{e}{{e}_{bp}}\right)+{Y}_{sf},&\:e\ge\:{e}_{bp}\end{array}\end{array}\right.$$

(10)

Here, $\:e$ stands for the $\:\mu\:$ user’s distance from WiFi AP $\:{\alpha\:}_{1}$, $\:{M}_{fs}$ for the free space loss, $\:{e}_{bp}$ for the breakpoint distance, and $\:{Y}_{sf}$ for the shadowing loss. Due to the system model’s single WiFi AP, WiFi users won’t experience any interference. The following formula may be used to determine the possible data rate among WiFi AP $\:{\alpha\:}_{1}$ and user $\:\mu\:$:

$$\:{DR}_{\mu\:,{\alpha\:}_{1}}={C}_{WiFi}{log}_{2}\:\left(1+{SNR}_{\mu\:,{\alpha\:}_{1}}\right)$$

(11)

Problem formulation

Consider for the moment that the binary matrix represented by the letter $\:Y$ represents the link among the $\:{j}^{th}$ user and the $\:{k}^{th}$ BS. As a result, the following determines the factor $\:{y}_{jk}$‘s value:

$$\:{y}_{jk}=\left\{\begin{array}{l}\begin{array}{ll}1& \quad if\:the\:{j}^{th}\:user\:is\:connected\:to\:the\:{k}^{th}\:BS\end{array}\\\:\begin{array}{cc}0 & \quad\:else\end{array}\end{array}\right.$$

(12)

Furthermore, suppose that $\:Z$ represents an array made up of binary values that represent the user’s demand for downlink rate being satisfied. In particular, the element $\:{z}_{j}=1$ if the download requirements of the $\:{j}^{th}$ user are met, as shown by:

$$\:{z}_{j}=\left\{\begin{array}{l}\begin{array}{ll}1& \quad if\:the\:{k}^{th}\:use{r}^{{\prime\:}}sdownlink\:demand\:is\:fulfilled\end{array}\\\:\begin{array}{ll}0& \quad else\end{array}\end{array}\right.$$

(13)

Moreover, suppose $\:A$ represents an array with binary values in it. As seen beneath, the component $\:{a}_{k}$ indicates if the $\:{k}^{th}$ BS is connected to at least single user:

$$\:{a}_{k}=\left\{\begin{array}{l}\begin{array}{ll}1& \quad if\:the\:BS\:k\:is\:linked\:to\:atleast\:single\:user\end{array}\\\:\begin{array}{ll}0& \quad else\end{array}\end{array}\right.$$

(14)

Considering the decision factors as well as performance requirements, an optimization problem is formulated whose fitness function is as follows:

$$\:maximize\:\alpha\:\cdot\:\sum\:_{j\in\:\pi\:}{z}_{j}+\beta\:\cdot\:\sum\:_{k\in\:\varphi\:}{a}_{k}$$

(15)

Equation (15) seeks to maximize the number of UEs whose downlink requirements are met and the number of BSs connected to UEs in order to increase user satisfaction. It is expected that the count of BSs linked to UEs as well as the count of resource blocks used by those users would rise when element $\:{a}_{k}$ is maximized. The elements $\:\alpha\:$ and $\:\beta\:$ (i.e.$\:\:\alpha\:,\beta\:=1$) balance each other out in terms of how each element contributes to the fitness function. Furthermore, the predetermined values $\:\psi\:=\left\{{\theta\:}_{1},{\theta\:}_{2},{\theta\:}_{3},\cdots\:,{\theta\:}_{t}\right\}$ are linked to the maximization aim and have an immediate effect on the values obtained from $\:{z}_{j}$ and $\:{a}_{k}$. Moreover, the below limitations place limits on the fitness function:

$$\:\sum\:_{k\in\:\varphi\:}{y}_{jk}=1,\:\:\:\:\:\:\forall\:j\in\:\pi\:$$

(16)

$$\:\sum\:_{j\in\:\pi\:}{o}_{{RB}_{j}}\le\:{o}_{{RB}_{k}},\:\:\:\:\:\forall\:k\in\:\varphi\:$$

(17)

$$\:{o}_{{RB}_{j}}\ge\:{U}_{C},\:\:\:\:\:\forall\:j\in\:\pi\:$$

(18)

By guaranteeing that every user is connected to a single BS, Constraint (16) suggests that a Coordinated Multipoint Transmission (CoMP) be not considered. Constraint (17) ensures that the number of RBs used by the $\:{j}^{th}$ UE does not surpass the total number of RBs available at the $\:{k}^{th}$ BS. Finally, constraint (18) ensures the viability of the system by mandating that the resource blocks that a user receives above a minimum threshold (0.3) of $\:{U}_{C}$.

Channel and interference models

For both the Macro as well as Micro layers, the route loss exponent is regarded as $\:\alpha\:$. It is expected that BSs are working together and communicating statuses (i.e., accepting or granting UEs) to one another.

Taking $\:\left({Y}_{j},{Z}_{j}\right)$ and $\:\left({Y}_{k},{Z}_{k}\right)$ as the coordinates related to the two Macro BSs’ locations, the distances $\:{e}_{jk}$ represent the Euclidean distance among the two Macro BSs, which is as follows:

$$\:{e}_{jk}=\sqrt{\left({Y}_{j}^{2}-{Y}_{k}^{2}\right)+\left({Z}_{j}^{2}-{Z}_{k}^{2}\right)}$$

(19)

Additionally, the Euclidean distances $\:{e}_{jv}$, $\:{e}_{vw}$, $\:{e}_{qr}$, and $\:{e}_{jq}$ are computed using the similar method as in (19). Likewise, the Rayleigh fading gains are represented by $\:{i}_{jk}$, $\:{i}_{jv}$, $\:{i}_{qr}$, and $\:{i}_{jq}$. The following will happen when two Macro BSs, $\:j$ and $\:k$, interfere:

$$\:{J}_{jk}={Q}_{N}{\left({i}_{jk}\right)}^{2}{e}_{jk}^{-\alpha\:}$$

(20)

Likewise, interferences among a Macro BS $\:j$ at any provided cell and a Micro BS $\:q$ at the core of the similar cell $\:\left({J}_{jq}\right)$ as well as those among a Macro BS $\:j$ and a Micro BS $\:v$ at the edge of the next cell $\:\left({J}_{jv}\right)$ will be computed as in (20). The following will be the interference among two Micro BSs, $\:v$ and $\:w$, that are situated at the boundaries of two nearby cells:

$$\:{J}_{vw}={Q}_{n}{\left({i}_{vw}\right)}^{2}{e}_{vw}^{-\alpha\:}$$

(21)

Likewise, the calculation associated with the interference $\:\left({J}_{qr}\right)$ among two Micro BSs ($\:q$ and $\:r$) at the centre of a specific cell will follow the formula (21).

Performance evaluation metrics

The various performance metrics considered here are explained below.

Load balancing: Because diverse users have distinct needs, every user has unique messages that must be communicated. The count of users connected to $\:\left(R\right)$ and their average “packet in” message arrival rate $\:\left(D\right)$ are the primary factors when estimating the load. The load $\:{N}_{j}$ of node $\:{V}_{j}$ is described as follows after normalization because the order of magnitude of $\:R$ and $\:D$ are inconsistent.

$$\:{N}_{j}=b{R}_{j}+c{D}_{j}$$

(22)

Here, $\:b+c=1$ and $\:{R}_{j}=\sum\:_{k=1}^{Q}{y}_{j,k}$. They may be modified to meet the needs of the real-world situation. The load balance rate $\:\left(W\right)$ associated with the relay network is represented by variation based on the load and is given as

$$\:\left\{\begin{array}{l}\stackrel{-}{N}=\frac{1}{O}\sum\:_{j=1}^{O}{N}_{j}\\\:W=\frac{\sum\:_{j=1}^{O}{\left({N}_{j}-\stackrel{-}{N}\right)}^{2}}{O}\end{array}\right.$$

(23)

Here, $\:\stackrel{-}{N}$ is the load’s average value. The relay load is more balanced when the value of $\:W$ is less.

Throughput: The relay selection outcome has a big influence on the overall performance and transmission rate of the relay network. The suggested relay selection technique aims to maximize the relay connection throughput in order to identify a suitable relay node. The throughput of a relay connection designed as $\:{V}_{j}\to\:{V}_{s}\to\:{V}_{k}$ is expressed as follows.

$$\begin{aligned} {S}_{s}& =\frac{1}{2}min\left({S}_{js},{S}_{sk}\right) \\ & \quad \times\:\frac{C}{2}min\left\{{\text{log}}_{2}\left(1+\frac{{Q}_{j}^{\left(U\right)}\tau\:{\left|{i}_{js}\right|}^{2}}{\sum\:_{l=1,\:l\ne\:j}^{{G}_{s}}{\epsilon\:}_{ls}{\lambda\:}_{l}{Q}_{l}^{\left(U\right)}\tau\:{\left|{i}_{ls}\right|}^{2}+{O}_{0}}\right), {\text{log}}_{2}\left(1+\frac{{Q}_{s}^{\left(U\right)}\tau\:{\left|{i}_{sk}\right|}^{2}}{\sum\:_{l=1,\:l\ne\:s}^{{G}_{k}}{\epsilon\:}_{lk}{\lambda\:}_{l}{Q}_{l}^{\left(U\right)}\tau\:{\left|{i}_{lk}\right|}^{2}+{O}_{0}}\right)\right\}\end{aligned}$$

(24)

RTH-CRE algorithm

This article introduces the RTH algorithm for calculating every SBS’s unique CRE bias, also referred to as CSO. Finding distinct CSO values for the items that make up the group $\:\psi\:=\left\{{\theta\:}_{1},{\theta\:}_{2},{\theta\:}_{3},\cdots\:,{\theta\:}_{t}\right\}$ is the goal. The main idea behind using this RTH-based CRE method is to parallelize the search process over several running computing threads. This method makes use of a dynamic memory format that contains data on the computational agents’ prior activities’ success.

The RTH algorithm emulates the hunting style of the red-tailed hawk. The high flying stage mathematical method is represented by Eq. (25):

$$\:Y\left(u\right)={Y}_{best}+\left({Y}_{mean}-Y\left(u-1\right)\right)\cdot\:levy\left(Dim\right)\cdot\:UG\left(u\right)$$

(25)

Here, $\:{Y}_{best}$ denotes the optimal-attained location, $\:{Y}_{mean}$ denotes the location’s mean, and $\:Y\left(u\right)$ describes the red-tailed hawk location at iteration $\:u$. Equation (26) may be used to compute the levy flight distribution function $\:levy$, and Eq. (27) may be used to generate the transition factor function, which is represented by the symbol $\:UG\left(u\right)$.

$$\:\begin{array}{c}levy\left(Dim\right)=t\frac{\mu\:\cdot\:\sigma\:}{{\left|w\right|}^{\beta\:-1}}\\\:\sigma\:=\left(\frac{\Gamma \left(1+\beta\:\right)\cdot\:\text{sin}\left(\pi\:\beta\:/2\right)}{\Gamma \left(1+\beta/2\right)\cdot\:\beta\:\cdot\:{2}^{\left(1-\beta/2\right)}}\right)\end{array}$$

(26)

Here, $\:v$ and $\:w$ represents random values [0 to 1], $\:Dim$ represents the issue dimension, $\:\beta\:$ represents a constant (1.5), and $\:t$ represents a constant (0.01).

$$\:UG\left(u\right)=1+\text{sin}\left(2.5+\left(u/{U}_{max}\right)\right)$$

(27)

Here, $\:{U}_{max}$ stands for the maximum iteration count. The following represents an expression for this phase:

$$\:\begin{array}{c}Y\left(u\right)={Y}_{best}+\left(y\left(u\right)+z\left(u\right)\right)\cdot\:step\:size\left(u\right)\\\:step\:size\left(u\right)=Y\left(u\right)-{Y}_{mean}\end{array}$$

(28)

Here, $\:y$ and $\:z$ are direction coordinates, which are computed in the manner described below.

$$\:\left\{\begin{array}{c}y\left(u\right)=S\left(u\right)\cdot\:\text{sin}\left(\theta\:\left(u\right)\right)\\\:z\left(u\right)=S\left(u\right)\cdot\:\text{cos}\left(\theta\:\left(u\right)\right)\end{array}\right.\:\:\:\:\:\left\{\begin{array}{c}S\left(u\right)={S}_{0}\cdot\:\left(s-u/{U}_{max}\right)\cdot\:Rand\\\:\theta\:\left(u\right)=B\cdot\:\left(1-u/{U}_{max}\right)\cdot\:Rand\end{array}\left\{\begin{array}{c}y\left(u\right)=y\left(u\right) /max\left|y\left(u\right)\right|\\\:z\left(u\right)=z\left(u\right) /max\left|z\left(u\right)\right|\end{array}\right.\right.$$

(29)

Here, $\:{S}_{0}$ is the radius’s starting value. $\:B$ stands for the angel gain, $\:s$ for the control gain, and $\:Rand$ for a random gain [0–1]. These variables facilitate the hawk’s spiral motions as it circles the prey.

The hawk abruptly lowers itself to strike the victim from the optimal-attained posture during the low flying stage during the Stooping and Swooping stage. The following may be used to design this phase:

$$\:Y\left(u\right)=\alpha\:\left(u\right)\cdot\:{Y}_{best}+y\left(u\right)\cdot\:step\:size1\left(u\right)+z\left(u\right)\cdot\:step\:size2\left(u\right)$$

(30)

Every step size may be computed as below.

$$\:\begin{array}{c}step\:size1\left(u\right)=Y\left(u\right)-UG\left(u\right)\cdot\:{Y}_{mean}\\\:step\:size2\left(u\right)=H\left(u\right)\cdot\:Y\left(u\right)-UG\left(u\right)\cdot\:{Y}_{best}\end{array}$$

(31)

Here, $\:\alpha\:$ and $\:H$ stand for the acceleration and gravity components, and they may be defined as follows respectively:

$$\:\begin{array}{c}\alpha\:\left(u\right)={sin}^{2}\left(2.5-u/{U}_{max}\right)\\\:H\left(u\right)=2\cdot\:\left(1-u/{U}_{max}\right)\end{array}$$

(32)

Here, $\:H$ describes the gravity effect, which lowers to lessen the exploitation diversity when the hawk is very close to the prey, and $\:\alpha\:$ represents the hawk’s acceleration, which increases with an increase in t to boost the convergence speed. The pseudocode of RTH is shown in Algorithm 1 and the RTH-based CRE model for the proposed load balancing and throughput optimization of the heterogeneous network is portrayed in Fig. 3.

Fig. 3

RTH-based CRE model for the proposed load balancing and throughput optimization of the heterogeneous network.

Algorithm 1

RTH.

Results and analysis

Experimental setup

The proposed RTH-based CRE model for the throughput and load balancing optimization in heterogeneous networks was implemented in MATLAB and the findings were analyzed. The population size, iteration count, and number of users was considered to be 10, 100, and 1000.

Table 2 Simulation parameters.

Table 2 describes the simulation parameters for load balancing in HetNet.

The proposed RTH-based CRE model was compared with several state-of-the-art methods like MULB¹⁸, CFPSO¹⁹ and HHCLB²³ with consideration of analysis such as load balancing, throughput, call drop rate, execution time, delay, and convergence to demonstrate the betterment of the developed methodology. The effectiveness of every algorithm is assessed by calculating the various metrics for various users. The outcomes are examined to see how various approaches, which seek to increase throughput while guaranteeing equitable resource distribution throughout the diverse network, affect performance. The results are examined, showing how well every strategy works to maximize network effectiveness.

Load balancing analysis

As the count of users rises, the load balancing study of the heterogeneous network model reveals notable differences in performance across various techniques, as seen in Fig. 4; Table 3. Interestingly, the proposed RTH-based CRE technique has a maximum efficiency of 0.94 at 1000 users, outperforming all other methods. This implies that the RTH-based strategy is a good fit for deployment in heterogeneous networks as it excels at controlling load and optimizing resource allocation. The research underscores the need of carefully choosing a load balancing technique for diverse networks; among these, the proposed RTH-based CRE appears to provide the most potential in terms of effectiveness as well as scalability. The proposed RTH-based CRE model in terms of load balancing is 56.67%, 88%, 56.67%, and 10.59% better than the conventional methods.

Table 3 Load balancing analysis.

Fig. 4

Load balancing analysis.

Throughput analysis

As seen in Fig. 5; Table 4, the heterogeneous network model’s throughput analysis assesses how well various approaches function under various user loads. A crucial indicator of network performance is throughput, which is defined as the number of successful data transfers. This is particularly true in diverse contexts, in which user demands might vary greatly. Although MULB performs well when dealing with lesser user loads, it finds it difficult to keep up with increasing demands. The throughput of CFPSO becomes more difficult to maintain as user density rises. HHCLB shows a dependable ability to control throughput beneath a range of circumstances. Significant vulnerability is shown by WaOA-HetNet in high-demand situations. By comparison, the proposed RTH-based CRE technique has remarkable throughput performance. This technique regularly achieves the maximum throughput across the user range, proving how reliable and successful it is at allocating network resources. In terms of throughput performance, the Proposed RTH-based CRE technique leads the pack overall, demonstrating its applicability for heterogeneous networks, in which keeping transmission rates high is essential for overall network efficiency and user satisfaction. The proposed RTH-based CRE model with respect to throughput is 49.23%, 59.02%, 51.56%, and 67.24% advanced than the conventional methods.

Table 4 Throughput analysis.

Fig. 5

Throughput analysis.

Call drop rate analysis

A critical indicator of the dependability and level of service in telecom networks, especially in settings with fluctuating demand, represents the call drop rate. Both Table 5; Fig. 6 make it quite evident. Even with MULB’s enhancements beneath higher loads, there is still a significant drop rate, which suggests that there may be problems with the efficient use of network resources. Although CFPSO shows a reasonable capacity to manage higher user densities, there is still opportunity for development in terms of reducing call dropouts. HHCLB performs poorly beneath load, which makes it less appropriate for settings, in which call quality must be maintained. WaOA-HetNet’s inadequacies in high-demand scenarios is shown by its significant difficulty to sustain connections as user density grows. The suggested RTH-based CRE approach, in sharp contrast, performs better than the other approaches, guaranteeing heterogeneous networks and dependable communication services. The proposed RTH-based CRE model in terms of call drop rate is 91.49%, 91.30%, 84.62%, and 80% higher than the existing methods.

Table 5 Call drop rate analysis.

Fig. 6

Call drop rate analysis.

Execution time analysis

The responsiveness as well as effectiveness of network management solutions are directly impacted by execution time, which represents a crucial aspect, especially in situations with variable demands like those shown in Fig. 7; Table 6. When the count of users increases, the execution time for the MULB technique exhibits a worrisome rising trend. This notable rise raises the possibility that MULB may find it difficult to deploy resources effectively during periods of heavy traffic, which might cause delays that negatively impact user experience. While CFPSO continues to execute more quickly than MULB while user loads are small, the increase in execution time indicates a growing inefficiency when managing increased user demands, which may result in network performance bottlenecks. While it’s still not the best option for bigger networks, HHCLB could become more skilled at resource management as user density increases. WaOA-HetNet performs better and shows that it can tolerate higher loads with fewer severe penalties on execution time, making it a more dependable choice for heterogeneous networks. The best outcomes are shown by the proposed RTH-based CRE technique, indicating that it is an extremely effective resource manager. However, the proposed RTH-based CRE approach is unique in that it can retain reasonably low execution times. Because of its effectiveness in maintaining responsiveness in diverse networks, it is a good choice for implementation in situations where prompt resource allocation is necessary to satisfy users. For this reason, continuous optimization as well as assessment of these approaches are essential to improving network effectiveness in practical applications. The proposed RTH-based CRE model with respect to execution time is 77.55%, 70.27%, 42.11%, and 26.67% more than the traditional methods.

Table 6 Execution time analysis.

Fig. 7

Execution time analysis.

Delay analysis

The delay is an important performance parameter in network systems. For a seamless user experience, delay must be kept to a minimum, especially in applications that need real-time connectivity, like Table 7; Fig. 8. Among all user counts, the proposed RTH-based CRE technique had the lowest delays. This substantial decrease demonstrates its remarkable ability to effectively manage network resources, minimizing delay even as user demands increase. Although there exists a slight rise in delay for entire approaches as user loads increase, the proposed RTH-based CRE technique consistently achieves much shorter delay times than the other ways. This effectiveness makes the proposed RTH-based CRE an excellent choice for diverse network settings, especially for applications that need to transmit data in real-time. Continuous assessment as well as improvement of these techniques will be necessary to maximize efficiency and improve user experience in various networking situations. The proposed RTH-based CRE model in terms of delay is 92.68%, 87.5%, 90.63%, and 66.67% greater than the conventional methods.

Table 7 Delay analysis.

Fig. 8

Delay analysis.

Convergence analysis

Convergence analysis is essential in the setting of heterogeneous networks in order to assess the effectiveness and performance of different approaches under variable user loads, as shown in Fig. 9; Table 8. The effectiveness associated with every approach is measured by a statistic, which we can deduct from the decreasing trend as the count of users rises to be some sort of delay or network efficiency. The efficacy of the proposed RTH-based CRE approach has declined the greatest. This significant decrease points to benefits in managing resource distribution in a diverse setting. The proposed RTH-based CRE model with respect to convergence is 20.11%, 17.82%, 18.29%, and 16.37% superior to the existing methods.

Table 8 Convergence analysis.

Fig. 9

Convergence analysis.

Conclusion

This study integrated a CRE technique with an RTH algorithm to maximize the count of users whose downlink requests were satisfied, instead of concentrating just on enhancing downlink rates for specific users. In order to determine acceptable CRE bias levels for specific SBSs, the proposed technique formulated a fitness function that accounted for both the user device’s SINR and the workload of the BS. A comparison of the proposed solution with traditional approaches illustrated its efficiency. The simulation results showed how well the recommended strategy reduced call drop rates and network imbalances while satisfying user throughput needs. The results of the experiments showed that the suggested model outperformed the traditional approaches in terms of 56.67% load balancing, 49.23% throughput, 91.49% call drop rate, 77.55% execution time, 92.68% delay, and 20.11% convergence.