An Enhanced Active Access-Point Configuration Algorithm Using the Throughput Request Satisfaction Method for an Energy-Efficient Wireless Local-Area Network (2024)

1. Introduction

As the most popular Internet access method, IEEE 802.11 protocols in Wireless Local-Area Networks (WLANs) have been applied in various scenarios, such as the Internet of Things (IoT) and Wireless Sensor Networks, aswell as densely populated user areas like offices or schools, due to their versatility, convenience, andcost-effectiveness[1,2,3]. InWLANs, ahost connects wirelessly with an access point (AP), providing greater extensibility and flexibility compared to wired LANs[4].

As the number of users and devices grows, thecongestion on WLANs increases under the limited number of available channels. Consequently, theissue of dense WLAN environments has been raised to address the challenges of APs in supporting a large number of users. Toavoid performance degradation, thenetwork configuration of a WLAN, including the number and coverage of active APs, their channel assignments, locations, andtransmission power, should be properly optimized according to traffic demands[5,6].

Considering the need to reduce the cost of aging devices and power consumption, particularly in IoT application systems demanding long lifespans and low-cost deployments, anincreasing number of researchers have conducted studies on efficient energy-saving wireless network design methods[7]. These methods include energy-efficient resource allocation[8,9] and Media Access Control (MAC) protocol improvements[10]. Their goal is to extend the operational lifespans of IoT devices, reduce overall power usage, andensure cost-effective and sustainable networks overtime.

To address energy-saving issues and performance optimizations in dense network environments, we previously proposed the active AP configuration algorithm using dual interfaces[11]. This algorithm enables dynamic optimization of the network configuration by activating or deactivating AP devices while considering the AP setup optimization regarding the channel assignment and the host association. This study computes the total transmission capacity potentially available in the network. Then, it determines whether the minimum throughput constraint is satisfied on average andoptimizes the number of activating APs using a local search method.

However, when multiple hosts are associated with the same AP and are located at different distances from it, theissue of the throughput unfairness or insufficiency will arise due to the interference among them. Ahost enjoys higher received signal strength (RSS) when it is located closer to its AP compared to one situated farther away[12]. Therefore, thethroughput unfairness/insufficiency problem may appear among the hosts and, due to this advantage of RSS, the result will be a larger TCP congestion window size and a higher modulation and coding scheme (MCS) at the transmitting packets, which will create higherthroughput.

To solve this problem, we have studied the throughput request satisfaction method[13,14]. It calculates the channel occupancy time and the target throughput for each associated host from the measured single throughput and concurrent throughput for it. Thesingle throughput is measured when only one host is communicating with the AP. Theconcurrent throughput is measured when all the hosts are communicating with the APs. Bycontrolling the outgoing data rates at the AP using traffic shaping at the target throughput, thefair or requested throughput is achieved for eachhost.

In the previous active AP configuration algorithm, only the average throughput among the hosts associated with the same AP is satisfied. Ifa host is far from the AP, it may not achieve the required minimum throughput. Toovercome this deficiency, inthis paper, we enhance the enhanced active AP algorithm by incorporating the throughput request satisfaction method. This enhancement consists of the following steps:

Applying the previous active AP configuration algorithm to find the network configuration. Thesingle throughput and concurrent throughput for every host is estimated by the throughput estimation model[15].
Calculate the target throughput for the fair throughput to every host using the throughput request satisfaction method.
If this target throughput does not satisfy the minimum host throughput, thetentative minimum host throughput is increased by a constant, andthe active AP configuration is applied in step 1.

Our design of an energy-efficient WLAN fair throughput allocation algorithm can be achieved by exploring network symmetry and the fairness of resource allocation. This can improve network efficiency by optimizing resource utilization, reducing energy consumption, andensuring fair access among different devices. The contributions of this proposal for energy saving are summarized as follows:

The number of active APs consuming energy is minimized by the active AP configuration algorithm.
Under the adoption of dual interface devices for APs, our algorithm can both find the minimum number of active APs and allow any host to enjoy the minimum throughput.
The enhanced algorithm can achieve fair throughput allocation and satisfy the minimum throughput constraint among the hosts. Meanwhile, thenumber of active APs will not increase in most cases.

For evaluations, we verified the validity of the proposal through simulations using the WIMNET simulator[16] and through experiments using the testbed system where a Raspberry Pi 4B with dual interfaces was used for the AP. For every channel of the AP, channel bonding is used, since it basically provides higher throughput[17,18]. Inboth evaluations, four network topology cases were considered. Theresults from the simulations show that the minimum throughput constraint was satisfied in every case by the proposal where all the hosts associated with the same AP enjoy the same throughput. Then, theresults from the experiments show that it was satisfied in all cases. Thus, thevalidity and effectiveness of the proposal areconfirmed.

The remainder of this paper is structured as follows. Section 2 introduces the literature review. Section 3 introduces the preliminary work of this study. Section 4 proposes the enhanced active AP configuration algorithm using the throughput request satisfaction method for an energy-efficient WLAN. Section 5 evaluates the proposal through simulations and experiments. Finally, Section 6 concludes this paper with futurework.

2. Related Work in the Literature

In this section, we introduce related work in the literature. The studies are classified into throughput control/allocation issues and energy-saving WLAN design issues.

2.1. Throughput Control/Allocation

In[19], Mao addressed the problem of joint AP association and transmission time allocation in densely deployed multi-rate WLANs using the time-sharing MAC protocol. Theissue was framed as an NP-hard single non-zero programming (SNZP) optimization problem with a goal of achieving proportionally fair (PF) throughput. Toaddress this, theauthor introduced two innovative algorithms: SNZP relaxation (SNZPR) and iterative SNZPR (iSNZPR). Moreover, fordynamic network conditions, adistributed joint admission, AP association, andtransmission time allocation (DAAA) algorithm was developed. Theperformances of these algorithms were compared with existing algorithms through numerical analysis. In contrast, we use traffic shaping to balance the concurrent communicating throughput based on channel occupancy time for each host to achieve fair throughput allocation. Atthe same time, our algorithm can improve the host association for minimum activated APs andachieve an energy-efficientnetwork.

In[20], Kimet al.addressed the issue of per-station fairness in uplink WLANs by tackling imbalances in access and outage probabilities. They utilized an enhanced distributed coordination function (DCF) combined with a hybrid automatic repeat request (HARQ) protocol, specifically HARQ with Chase combining (HARQ-CC). They also proposed a new Markov chain model for performance analysis, providing closed-form expressions for system throughput, delay, andoutage probability. Their results demonstrated that the algorithm ensured near-perfect per-station fairness and improved overall system performance.In contrast, our proposal does not require modifications to the MAC scheme, making it easier to implement in real-world scenarios. We achieve fair allocation by controlling incoming and outgoing traffic through traffic shaping, setting the data rate to represent the channel occupancy time.

In[21], Chenetal.introduced a Target Wake Time (TWT) scheduling scheme to manage throughput in the IEEE 802.11ax protocol. This scheme addresses OFDMA-based multiuser transmissions by minimizing resource conflicts among sleeping stations during each beacon interval. Their work emphasizes strategies to avoid collisions and allocate throughput efficiently while saving power through an innovative broadcast TWT approach. This approach enables the AP to specify the Target Beacon Transmission Time (TBTT) for each station that requests TWT, thereby improving overall throughput. Theeffectiveness of the TWT scheme was assessed using simulations, withconclusions drawn from the results.In contrast, our method is applicable to any WLAN protocol situation, achieving fair throughput allocation. Forcertain devices, especially in IoT scenarios where only a few currently support the 802.11ax protocol, our approach is designed for practical applications and can be effectively implemented and rapidlydeployed.

In[22], Khorovetal.presented a centralized approach called SEBRA (SAND-Enabled Bitrate and Resource Allocation) designed to improve network-assisted video streaming over wireless networks. SEBRA functions on access points (APs) to effectively control the distribution of video bitrates among clients and the allocation of channel time. Theprimary goal of this algorithm is to optimize the duration of channel occupancy in line with the bitrate requirements of each client. This problem was formulated as an NP-hard issue, forwhich the authors employed heuristic algorithms to find optimal solutions regarding channel time allocation and resource management.In contrast, our approach can adapt to different requirements by adjusting the traffic type. It is applicable not only to high-speed traffic such as network video but also to low-latency, low-traffic IoTenvironments.

In[23], Yagietal.presented two novel control strategies that leverage frame aggregation in IEEE802.11n/ac to enhance throughput and fairness across multiple WLANs in high-density environments. These strategies involved the dynamic adjustment of transmission frequency and frame aggregation size to reduce error probability. Their effectiveness was validated through simulations conducted with the network simulator NS-3[24].In contrast, our approach does not necessitate changes to the MAC scheme, simplifying its implementation in practical applications. We ensure fair allocation by managing incoming and outgoing traffic via traffic shaping, where the data rate is used to indicate the channel occupancy time. Atthe same time, theexperiments have verified the effectiveness of ourproposal.

In[25], Obataetal.proposed a switching method for Media Access Control (MAC) to enhance throughput fairness between WLAN systems under adjacent channel interference. Themethod dynamically switched between CSMA/CA and semi-active contention window adaptation (SACA) based on measured throughput, utilizing the capture effect to improve performance. Simulations using NS-3 demonstrated the method’s effectiveness in maintaining fairness and throughput in densely deployed environments.In contrast, we ensure fair allocation by adjusting the channel occupancy time without needing to modify the MAC scheme, making it easier todeploy.

2.2. Energy-Saving WLANDesign

In[26], Konget al.proposed a technique for optimizing AP deployment using the multi-objective particle swarm optimization (MOPSO) algorithm. They began by evaluating the performance of a single AP through random geometry theory to determine the necessary number of APs for the WLAN based on user service demands. Next, theMOPSO algorithm was used to identify the optimal positions and transmit power levels for the APs. Finally, agreedy algorithm was implemented to remove any redundant APs.In contrast, our proposed algorithm generates an initial solution based on the greedy algorithm and optimizes host association through local search. This ensures that the throughput requirements of all hosts are met while minimizing the number of active APs. Additionally, thechannels configured for the APs are optimized to reduceinterference.

In[27], Umaret.alproposed a method for using phone user clustering (PUC) to group users based on proximity and channel conditions, optimizing resource allocation and minimizing interference. This method, combined with hybrid multiple access (H-MA) techniques that integrate non-orthogonal multiple access (NOMA) with orthogonal multiple access (OMA), aims to efficiently utilize radio spectrum and power. Unmanned aerial vehicles (UAVs) are incorporated to provide flexible and targeted coverage, further improving throughput and energy efficiency. This approach effectively balances resource allocation, reduces power consumption, andenhances overall network efficiency, making it a promising solution for future 6G networks. In contrast, our proposal focuses on indoor WLAN optimization, and we use dual-interface devices to reduce the activated APs to achieve an energy-efficientnetwork.

In[28], Blobeletal.proposed a method for achieving energy efficiency in WLANs by integrating wake-up receivers (WuRxs). This method modified the standard IEEE 802.11 protocol to include a wake-up signal, allowing devices to stay in low-power mode until needed, thus saving energy. Their approach was fully compatible with existing WLAN standards, enabling gradual deployment. Experimental results using a hardware prototype and simulations showed significant energy savings, low delays, andimproved performance compared to traditional duty-cycling techniques.In contrast, our algorithm optimizes AP activation and connection allocation in the current network, achieving the minimum number of APs while ensuring the minimum throughput for hosts. This method does not require complex protocol modifications and can be directly deployed in practicalapplications.

In[29], Aliet al.proposed the greenMAC protocol, which enhances WLAN energy efficiency using Q-learning, areinforcement learning technique. This protocol optimizes the energy-saving process by adjusting the power-saving mode (PSM) of WLAN devices based on channel congestion observations. Byutilizing Q-learning to evaluate channel collision probabilities, thegreenMAC protocol dynamically decides whether a device should enter sleep mode in order toreduce unnecessary energy consumption while maintaining network throughput. This method resulted in significant energy savings for WLANs, especially in high-density environments, withoutsacrificing performance.In contrast, our algorithm focuses on optimizing AP activation and connection allocation within the existing network. It aims to minimize the number of APs needed while guaranteeing the minimum required throughput for hosts. This approach avoids complex protocol modifications, allowing for straightforward deployment in real-worldscenarios.

In[30], Dongetal.proposed the ES-MPTCP algorithm to optimize energy consumption in WLANs using Multipath TCP (MPTCP). TheES-MPTCP algorithm balances the energy consumption and network throughput by dynamically selecting the optimal sub-flows based on current network conditions. This approach reduced the energy usage by $16.2 %$ and increased the throughput by $13.6 %$ , achieving higher energy efficiency compared to existing methods.In contrast, our algorithm utilizes dual-interface APs, offering two different frequency bands and providing more options for host allocation. This approach effectively reduces the number of active APs and minimizes interference in the network, thereby enhancing overall networkperformance.

In[31], Karmakaretal.presented a method to improve WLAN energy efficiency through the GreenAP framework. This method minimized energy consumption by optimizing the AP association and channel width selection, activating only the necessary APs andusing energy-efficient transmissions within active BSSs. Theapproach saved significant energy without compromising the network performance by dynamically managing the AP activation and channel bonding. In contrast, our algorithm also focuses on optimizing AP activation and channel allocation. Additionally, it ensures rational planning of throughput allocation for each host, enabling all hosts to enjoy fair throughput sizes while achieving energyefficiency.

In[32], Qiuetal.proposed an energy-efficient method for dense WiFi networks based on IEEE 802.11ax. This method achieved energy savings by jointly optimizing the AP placement and power-channel-resource unit (RU) assignments. Theobjectives were to minimize the number of APs, fulfill user throughput requirements, andensure AP fault tolerances. Theauthors utilized orthogonal frequency division multiple access (OFDMA) to divide the wireless spectrum into time-frequency resource units and designed a heuristic algorithm to find high-quality solutions within polynomial time complexity. Simulation results showed that their algorithm effectively reduced the number of APs and enhanced network performance[32].In contrast, our method does not require a specific communication protocol, making it widely applicable. Theprimary goal of our algorithm is to achieve an energy-efficient network by reducing the number of activated APs. Thealgorithm provides optimal AP activation and host connection schemes, andit incorporates a throughput fairness allocation method, allowing for straightforward deployment in practicalapplications.

3. PreliminaryWork

In this section, we discuss our preliminary work related to this study. In addition, we review our previous active AP configuration algorithm and the throughput request satisfaction method, andwe demonstrate an analysis of potential throughput insufficiency and fairness issues that may arise with hosts in the previousalgorithm.

3.1. Throughput EstimationModel

First, we introduce the throughput estimation model, which provides the foundation for throughput calculations in algorithm simulations. This model estimates the throughput between an AP and a host in a WLANnetwork.

3.1.1. Received Signal StrengthEstimation

In our study, we use the log-distance path-loss model to estimate the received signal strength at the destination node[33]. TheEuclidean distanced (in meters) for each link or the AP/host pair is determined using the following formula:

$d = \sqrt{{(A P_{x} - H_{x})}^{2} + {(A P_{y} - H_{y})}^{2}},$

(1)

where $A P_{x}$ and $A P_{y}$ represent the x and y coordinates of the access point, and $H_{x}$ and $H_{y}$ represent the x and y coordinates of the user host, respectively.

Then, theestimated received signal strength, denoted as $R s s$ (in $- d B m$ ), at the host is as follows:

$R s s = R s s_{1 m} - 10 α {log}_{10} d - \sum_{k} n_{k} W_{k} .$

(2)

In this paper, we define $R s s_{1 m}$ as the received signal strength from the access point (AP) to the host when they are one meter apart with no obstacles in between. Thepath loss exponent is represented by $α$ . Thevariable $n_{k}$ indicates the count of type k obstacles or walls along the path between the AP and the host, while $W_{k}$ denotes the signal attenuation in dBm for each obstacle type k (with a range from 1 to 6). It is important to note that a building can have multiple types of walls. Inthis study, we consider six different types of obstacles: $W_{1}$ for corridor walls, $W_{2}$ for partition walls, $W_{3}$ for intervening walls, $W_{4}$ for glass walls, $W_{5}$ for elevator walls, and $W_{6}$ for doors, asnoted in previous studies[11].

3.1.2. ThroughputEstimation

Based on the RSS calculation, we established a functional relationship between RSS and throughput using experimental data. This estimation can provide us with the single throughput in the subsequent calculation of the channel occupancy time. Through curve fitting, we derived the following sigmoid function equation:

$T h r . = \frac{a}{1 + e^{- (\frac{(120 + R s s) - b}{c})}},$

(3)

where $T h r .$ represents the estimated throughput (Mbps), and $R s s$ is the received signal strength ( $- d B m$ ) at the $H o s t_{j}$ position. Theparameters a, b, andc represent the constants obtained from the parameter fitting with real-world measurement results. Theparameter values for a, b, c, $α$ , and $W_{K}$ in the throughput estimation model will be optimized by the parameter optimization tool.

3.1.3. Throughput ReductionFactor

To account for the decrease in throughput caused by interference among hosts connected to the same AP, theconcept of a throughput reduction factor was introduced. This factor enhances the precision of the concurrent throughput estimation under simultaneous communication[34]. Theequation is as follows:

$T h r ._{c o n .} = T h r . \times s r f (m),$

(4)

where $T h r ._{c o n .}$ represents the concurrent throughput of the host $H o s t_{j}$ , $T h r .$ is the estimated single throughput between $A P_{i}$ and $H o s t_{j}$ , $s r f (m)$ is the throughput reduction factor, andm is the number of hosts associated with the AP. Additionally, $s r f (m)$ was empirically derived as the contention factor, which is given as follows:

$s r f (m) = (\frac{1}{m + \frac{0.1 (m - 1)}{4}}) \times 1 - (0.1 \times m - 1) .$

(5)

3.1.4. ParameterOptimization

The throughput estimation model relies on several parameters that significantly affect the accuracy of the estimation results. Tooptimize these parameters, we employ a parameter optimization tool that utilizes a local search method. This method combines a tabu table with a hill-climbing function to effectively prevent convergence to a local minimum[35].

To better demonstrate the improvements of our enhanced algorithm compared to previous studies, we utilized the same conditions as described in the previous paper. Consequently, theparameters of the throughput estimation model are consistent with those in Ref.[11]. Theexperimental scenarios and the parameters of the throughput estimation model will be introduced in Section 5.3.

3.2. Active AP ConfigurationAlgorithm

The active AP configuration algorithm finds the optimal selection of the active APs and their host associations. Theobjective of the algorithm is to minimize the number of active APs that ensure that the minimum host throughput constraint is satisfied. Tofurther reduce it, each AP is assumed to be equipped with dualinterfaces.

3.2.1. Formulation

The formulation of the previous AP activation optimization problem is given as follows[11]:

Inputs:
- APs’ information (position, quantities);
- Hosts’ information (position, quantities);
- Estimated single throughput for each $A P_{i}$ and $H o s t_{j}$ pair: $T p_{i j}$ ;
- Minimum throughput for the association: S;
- Number of orthogonal channels (OCs) for each interface: C;
- Minimum host throughput: G;
- Available total throughput: $B^{a}$ .
Outputs:
- A collection of active APs equipped with dual interfaces;
- A group of hosts connected to each interface at every active AP;
- The channel assigned to each interface at every active AP.
Objectives:
- $E_{1}$ denotes the count of active access points (APs) equipped with dual interfaces that must be minimized while adhering to the minimum host throughput constraint:
  
  $E_{1} = [a c t i v a t e d A P s ’ n u m b e r] .$
  
  (6)
- Adhering to the first objective, maximize the minimum average host throughput $E_{2}$ :
  
  $E_{2} = m i n_{j} [T h r ._{a v g}],$
  
  (7)
  
  where $T h r ._{a v g}$ represents the average host throughput for $A P_{j}$ that is given by:
  
  $T h r ._{a v g j} = \frac{1}{\sum_{k} \frac{1}{T h r ._{c o n .}}},$
  
  (8)
  
  where $T h r_{c o n .}$ represents the link speed between $n o d e_{j}$ and $n o d e_{k}$ ( $l i n k_{j k}$ ), calculated by Equation(5).
- Adhering to the two objectives, minimize the total interfered communication time $E_{3}$ for channel assignments:
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  $E_{3} = \sum_{i = 1}^{N} [\sum_{k \in I_{i}, c_{k} = c_{i}} T_{k}],$
  
  (9)
  
  where $T_{k}$ represents the total communication time of $A P_{i}$ , $I_{i}$ represents the interference from APs at $A P_{i}$ , and $c_{i}$ is the channel assigned to $A P_{i}$ .
Constraints:
- Minimum host throughput: Each host must achieve an average throughput of at least G when all hosts are communicating simultaneously.
- Total throughput: The combined throughput of all hosts must not exceed the available total throughput $B^{a}$ .
- Channel assignment: Every interface of an AP must be allocated a channel.

3.2.2. AlgorithmProcedure

The active AP configuration algorithm is divided into the following three steps, andthe pseudocode can be found in Appendix A:

First Step: In this initial phase, thealgorithm identifies the active APs equipped with dual interfaces and determines their host connections. Theobjective is to reduce $E_{1}$ while enhancing $E_{2}$ [36].
(1)
Preprocessing: The algorithm begins with the input of AP and host locations. AP locations are manually selected within the network, considering factors such as electrical power supply, coverage, anduser demands. Thethroughput for every possible AP/host pair is then estimated using the throughput estimation model outlined in Equation(3). Additionally, the802.11n interface of an AP is initially selected as the candidate interface for anyhost.
(2)
Initial Solution Generation: A greedy algorithm is used to calculate the initial solution $E_{1}$ [37].
(3)
Host Association Improvement:
Host Reassociation for Maximum Throughput: Reassign each host to the interface of the AP that provides the highest throughput, asdetermined by Equation(5), fromamong the available AP interfaces. Compute the cost function $E_{2}$ at this stage and set it as the best-found cost function, $E_{2}^{b e s t}$ .
Identify Lowest Throughput Interface: Find the interface of the AP that offers the lowest throughput to its host using Equation(7). Create a list of modifiable hosts associated with this interface that can connect to other AP interfaces.
Random Reassociation of Modifiable Hosts: Select one host at random from the modifiable hosts list and reassign it to a different active AP interface at random. Compute the new cost function $E_{2}^{n e w}$ .
Update Best Cost Function: If $E_{2}^{n e w}$ is greater than $E_{2}^{b e s t}$ , replace $E_{2}^{b e s t}$ with it and keep the new AP–host association. Ifnot, revert to the previous association and maintain $E_{2}^{b e s t}$ .
(4)
AP Selection Optimization: This phase aims to optimize the number of active dual-interface APs and the associations between APs and hosts. Thegoal is to reduce both $E_{1}$ and $E_{2}$ metrics further using the local search method as described in[38].
(5)
Link Speed Normalization: The fairness criterion is applied if the total expected bandwidth exceeds $B^{a}$ . Subsequently, thelink speed isnormalized.
(6)
Termination Check: For each active AP, ifeither of its two interfaces is found to be inactive, theinterface should be activated, followed by executing the host association improvement phase. Thealgorithm will move to the second phase if the minimum throughput requirement for the host is fulfilled. Ifthis requirement is not satisfied, thealgorithm will then proceed to the AP selection optimization phase.
Second Phase: In the second phase, achannel is assigned to each active AP interface to minimize $E_{3}$ .
(1)
Preprocessing: Illustrate the network’s interference and delay conditions using a graphical representation.
(2)
Interfered AP Set Generation: Identify the set of interfering AP interfaces for each AP interface.
(3)
Initial Solution Construction: Utilize a greedy algorithm to determine the initial solution.
(4)
Solution Enhancement via Simulated Annealing: Employ the probabilistic optimization method, Simulated Annealing (SA), toprogressively refine solutions. Inthis approach, SA is applied to optimize the channel assignment for each interface of every active AP, thereby improving network performance. TheSA process is conducted at a fixed temperature $T^{S A}$ for a predetermined number of iterations $R^{S A}$ , withboth $T^{S A}$ and $R^{S A}$ specified as algorithm parameters.
Third Phase: The third phase balances the loads across different channels to minimize $E_{3}$ .
(1)
Initialization: Set all AP flags to 0 (OFF). This flag is used to ensure that each AP is processed only once.
(2)
AP Selection: Choose an AP currently marked as OFF and reassign its connected host to a different AP that uses another channel.
(3)
Host Selection: From the chosen AP, select one connected host for the AP reassignment process.
(4)
Application of Change: Finally, assign the host to a new AP.

3.3. Throughput Request SatisfactionMethod

To address the issue of throughput unfairness and insufficiency among multiple hosts communicating simultaneously in a WLAN, thethroughput request satisfaction method has been studied[13,14]. This approach employs three different types of throughput:

Single Throughput: The single throughput $S_{i}$ is determined when the corresponding host is the sole device communicating with the AP. This essentially reflects the maximum throughput achievable by the host in the absence of interference from other WLAN hosts.
Concurrent Throughput: The concurrent throughput $C_{i}$ is assessed when all hosts are communicating with their respective APs simultaneously within the WLAN. This measurement indicates the actual throughput of the host when subject to interference from other WLAN hosts.
Target Throughput: The target throughput $t_{i}$ for each host is computed on the basis that the total channel occupancy time, orcycle length, remains constant, even when the concurrent throughput is substituted with the target throughput.

The single throughput and the concurrent throughput are derived from measurements. Then, the target throughput is obtained from them. Finally, thetarget throughput is set as the data rate in traffic shaping with the PIcontrol.

3.3.1. Channel OccupancyTime

To determine the appropriate target throughput for each host, thechannel occupancy time is calculated based on the measured single throughput and concurrentthroughput.

For the i-th host $H_{i}$ , thechannel occupancy time can be estimated by the ratio $\frac{C_{i}}{S_{i}}$ . When all hosts communicate simultaneously, each host’s channel occupancy time can be represented as $\frac{C_{2}}{S_{2}}$ , …, $\frac{C_{n}}{S_{n}}$ , andtheir sum will be a constant for the data transmission cycle. If $C_{i}$ is replaced with $t_{i}$ , thetotal remains constant. Therefore, we derive the following equation:

$\begin{matrix} \frac{C_{1}}{S_{1}} + \frac{C_{2}}{S_{2}} + \dots + \frac{C_{n}}{S_{n}} = \frac{t_{1}}{S_{1}} + \frac{t_{2}}{S_{2}} + \dots + \frac{t_{n}}{S_{n}}, \end{matrix}$

(10)

where $S_{i}$ represents the single throughput, $C_{i}$ represents the concurrent throughput, and $t_{i}$ is the target throughput wedemand.

3.3.2. Target Throughput for FairnessAllocation

In the fairness throughput allocation scenario, all the communicating hosts should be assigned the equal target throughput. Thus, thefairness target throughput $F_{i}$ for host $H_{i}$ satisfies: $F_{1} = F_{2} = F_{3} = \dots = F_{n}$ . Totransmit $F_{1}, F_{2}, F_{3}, \dots, F_{n}$ (Mbit) data through the $S_{1}, S_{2}, S_{3}, \dots, S_{n}$ link, thechannel occupancy time can be calculated as follows:

$\begin{matrix} \frac{C_{1}}{S_{1}} + \frac{C_{2}}{S_{2}} + \dots + \frac{C_{n}}{S_{n}} = \frac{F_{1}}{F_{1}} + \frac{F_{2}}{S_{2}} + \dots + \frac{F_{n}}{S_{n}}, \\ F_{1} = F_{2} = \dots = F_{n} = \frac{\sum_{i = 1}^{n} \frac{C_{i}}{S_{i}}}{\sum_{i = 1}^{n} \frac{1}{S_{i}}}, \end{matrix}$

where S represents the single throughput, C is the concurrent throughput, andF is the calculated fairness target throughput for eachhost.

3.3.3. TrafficShaping

To realize the control of actual throughput, we deployed the traffic shaping method. Traffic shaping manages network bandwidth through the scheduling, policing, shaping, andclassification of traffic. InLinux, this can be achieved using the tc command, which includes queuing discipline ( $q d i s c$ ), classes, andfilters[39].

We utilized the classful HTB (Hierarchical Token Bucket) qdisc to regulate traffic at a specified data rate, $d_{i}$ . TheHTB employs token buckets to distribute traffic across different classes, governed by two parameters: ceil and data rate. These parameters define the allocated and maximum bandwidth, respectively. Inthis study, we set both parameters to identical values to maintain the desired quality of service across various trafficclasses.

3.3.4. PI Controller of Rate and CeilParameters

In the field of traffic shaping, thetc command controlling the data rate parameter $d_{i}$ can only determine the maximum upper limit for a host’s traffic. However, it cannot always guarantee that the actual throughput satisfies the target throughput. Tothis end, thePI (Proportional-Integral) feedback control mechanism is utilized. Foreach time step m (60s in this paper), bycalculating the error space $t_{i} - R_{i} (m)$ between the measured actual throughput and the target, underthe proper adjustment of the proportional gain and the integral gain, thesize of the input data rate $d_{i}$ of the system is effectively selected, so that the actual throughput is as close as possible to the target. The equation is as follows:

$d_{i} (m) = d_{i} (m - 1) + K_{P} \times (R_{i} (m - 1) - R_{i} (m)) + K_{I} \times (t_{i} - R_{i} (m)),$

where $R_{i} (m)$ represents the actual throughput result at each time step m, and $K_{P}$ and $K_{I}$ represent the parameters of P-control gain and I-control gain, respectively. Inthis paper, $K_{P} = 0.3$ and $K_{I} = 0.7$ are used, which have been experimentally adjusted in real-world situations where they can quickly and accurately control $d_{i}$ to meet the desiredtarget.

3.4. Limitations of the Active AP ConfigurationAlgorithm

In the previous active AP configuration algorithm, only the average throughput among the hosts associated with the same AP can satisfy the minimum host throughput constraint. Ifthere is a host located far from the AP, this host may not satisfy this constraint, since the throughput difference from other hosts located near the AP can belarge.

This problem must be solved in this paper by introducing the throughput request satisfaction method to these hosts. Withthis method, thetarget throughput is introduced to them. Ifit does not satisfy the given initial minimum host throughput G for the constraint (5 Mbps in evaluations of this paper), theactive AP configuration is reconstructed by applying the algorithm with the increased tentative minimum host throughput that is introduced to increase the number of active APs. Then, thetarget throughput is recalculated and checked in the enhanced active AP configuration algorithm in this paper, which will be presented in the nextsection.

4. Enhanced Active AP ConfigurationAlgorithm

In this section, we present the enhanced active AP configuration algorithm by introducing the throughput request satisfaction method. Each AP is equipped with dual interfaces for minimizing activeAPs.

4.1. Enhanced Active AP Configuration AlgorithmProcedure

Figure 1 illustrates the flowchart of the proposed enhanced active AP configuration algorithm. It outlines the application process of the proposed algorithm for fairness host throughput in an energy-efficient WLANenvironment. And the Appendix B shows the pseudocode of our enhanced algorithm.

Set the network field layout, including the locations of APs and hosts, as well asthe walls or obstacles, andinitialize the tentative minimum host throughput $G = 5$ Mbps in the problem.
Apply the AP active configuration algorithm to the network field layout to find the active AP configuration including the active APs, their channels, andassociated hosts with the tentative minimum host throughput G.
Apply the throughput request satisfaction method to the obtained active AP configuration to calculate the fair target throughput for thehosts.
(1)
Calculate the single throughput $S_{i}$ for each AP–host pair using the throughput estimation model.
(2)
Calculate the concurrent throughput $C_{i}$ from the single throughput with the throughput reduction factor.
(3)
Calculate the fair target throughput from them.
(4)
Terminate the procedure if the target throughput is equal to or larger than G. Otherwise, go to Step (5).
(5)
Increase G by the throughput constraint update in the following subsection and go to Step 2.
Apply traffic shaping to the hosts at the AP to control the throughput at the target throughput, while adjusting the data rate parameter $d_{i}$ by the PI control, andmeasure the actual throughput of all the hosts.

4.2. Throughput ConstraintUpdate

If the hosts’ association and activated APs given by the active AP configuration cannot satisfy the current minimum host throughput constraint, inorder to increase the number of activated APs, thetentative minimum host throughput $G_{n e w}$ is calculated with the following equation:

$G_{n e w} = G + Δ G,$

(11)

where $Δ G$ represents the given throughput increase unit (1 Mbps in this paper).

5. Evaluation

In this section, we evaluate the proposal through simulations using the WIMNET simulator[16] and experiments using the testbedsystem.

5.1. EvaluationSetup

Here, we introduce the setup for the simulation environment and experimentalenvironment.

5.1.1. Simulation

The WIMNET simulator is employed in this paper for simulation purposes. It was designed to assess the performance of large-scale wireless Internet access mesh networks on a standard PC within a reasonable CPU time. Inthis study, it has been used to simulate various WLAN configurations, including different topologies, channel models, andinterference conditions. Table 1 and Table 2 outline the hardware and software specifications utilized in thesimulations.

5.1.2. ExperimentalSetup

Table 3 shows the hardware and software configurations of the testbed system. Raspberry Pi 4B is used for each AP by running hostapd[40]. Theembedded wireless NIC is utilized for interface 1, with the 2.4 GHz 802.11n protocol of dual interfaces, while the Archer T4U wireless NIC[41] adapter is used for interface 2, with the 5 GHz 802.11ac protocol. The40 MHz bonded channel is used at both interfaces. Linux-based laptop PCs are used for the client hosts and theserver. And we used the software iperf[42] to test the throughput.

The testbed system using Raspberry Pi APs with single interfaces was previously implemented and used in our studies[11,36]. Inthis testbed system, Archer T4U is adopted at the AP to enable dual-interface functions, asillustrated in Figure 2.

5.2. Network Fields and Cases for DeviceLocations

Figure 3 shows the four cases of network topologies in two network fields for experiments, namely, Engineering Building #2 and the Graduate School of Natural Sciences Building at Okayama University, Japan. Ineach case, five dual-interface APs and ten hosts are placed at various locations considering the signal coverage in the field. Thehosts are randomly placed to investigate various host positions in real-worldscenarios.

5.3. Throughput Estimation ModelSetup

To estimate the single throughput, theconcurrent throughput, andthe fairness target throughput, aPython program for the throughput estimation model was implemented. Table 4 shows the parameter values of the model that were optimized for the network fields in Figure 3.

5.4. Results andDiscussions

Here, we first discuss simulation results using the WIMNET simulator in the four cases. Based on these simulation results, we conducted experiments to verify the effectiveness of our proposal in real-worldapplications.

5.4.1. Case1

First, we discuss simulation results in Case 1. Thegiven initial minimum host throughputG is set to 5 Mbps. Theactivated APs and the host associations are given by the enhanced active AP configuration algorithm before applying the throughput constraint update as follows:

$A P_{2_1}$ : $H_{2}$ , $H_{5}$ , $H_{7}$ ;
$A P_{2_2}$ : $H_{1}$ , $H_{3}$ , $H_{4}$ , $H_{6}$ , $H_{8}$ , $H_{9}$ , $H_{10}$ ,

where $A P_{2}$ represents $A P_{2}$ in the location map, and $_1$ and $_2$ represent the interface for 2.4 GHz and the interface for 5 GHz, respectively. Table 5 shows the simulationresults.

In this table, S represents the single throughput and C is the concurrent throughput that are obtained by the previous algorithm, while F represents the fair target throughput found by applying the fair throughput request satisfaction method. Unfortunately, inTable 5, thefair target throughput calculation for the seven hosts associated with $A P_{2_2}$ does not satisfy G (=5 Mbps). Then, thethroughput constraint update is applied tosatisfy the fairness throughput allocation by increasing it to $G_{n e w}$ . Theactivated APs and the host associations are given by the algorithm as follows:

$G_{n e w}$ : 6 Mbps;
$A P_{2_1}$ : $H_{2}$ , $H_{3}$ , $H_{5}$ , $H_{7}$ ;
$A P_{2_2}$ : $H_{1}$ , $H_{4}$ , $H_{6}$ , $H_{8}$ , $H_{9}$ , $H_{10}$ .

Table 6 shows the estimated throughput results. This time, any calculated fair target throughput result satisfies the current $G_{n e w}$ (6 Mbps).

Subsequently, thefinal host associations and activated APs were input into our experiment. InFigure 4, thered column represents the concurrent throughput result obtained using the previous algorithm. Althoughit can reduce the number of activated APs and save energy, it fails to provide the throughput $G_{n e w}$ (6 Mbps) in real-world applications for some hosts ( $H_{2}, H_{6}, H_{7}, H_{9}, H_{10}$ ). Bycomparing the data presented in Figure 4, it is evident that, following our proposal, each host achieved an actual throughput exceeding $G_{n e w}$ , andthe fairness among hosts is significantlyenhanced.

5.4.2. Case2

Second, we discuss results in Case 2. Forsimulation, theactivated APs and the host associations are given by the algorithm before the throughput constraint update as follows, where Table 7 shows the simulation results:

$A P_{5_1}$ : $H_{2}$ , $H_{7}$ , $H_{8}$ , $H_{9}$ ;
$A P_{5_2}$ : $H_{1}$ , $H_{3}$ , $H_{4}$ , $H_{5}$ , $H_{6}$ , $H_{10}$ .

In Table 7, thefair target throughput results for the four hosts associated with $A P_{2_1}$ do not satisfy the initial G (5 Mbps). Althoughthe average throughput can achieve 5Mbps, theresult of the fairness throughput allocation shows that the hosts connected to $A P_{2_{1}}$ suffer from insufficientthroughput.

Then, thethroughput constraint update is repeatedly applied, and the target throughput $G_{n e w}$ = 12 Mbps can be satisfied after gradual increases. Table 8 shows the improved estimated throughput results where any fair target throughput result satisfies the minimum throughput constraint. Theactivated APs and the host associations are given by the algorithm as follows:

$G_{n e w}$ : 12 Mbps;
$A P_{3_1}$ : $H_{9}$ ;
$A P_{3_2}$ : $H_{4}$ , $H_{5}$ , $H_{8}$ ;
$A P_{4_1}$ : $H_{3}$ , $H_{7}$ ;
$A P_{4_2}$ : $H_{1}$ , $H_{2}$ , $H_{6}$ , $H_{10}$ .

For the updated minimum throughput constraint $G_{n e w} =$ 12 Mbps, thesimulation result verify that all hosts can enjoy more than this constraint; meanwhile, afterthe experiment using our proposal, theactual throughput shown in Figure 5 has been balanced with fairer allocation and can achieve the updated $G_{n e w}$ .

5.4.3. Case3

Third, we discussed simulation and experiment results in Case 3. Theactivated APs and the host associations are given by the algorithm before the throughput constraint update as follows, where Table 9 shows the simulation results:

$A P_{2_1}$ : $H_{8}$ , $H_{9}$ ;
$A P_{2_2}$ : $H_{1}$ , $H_{2}$ , $H_{3}$ , $H_{4}$ , $H_{5}$ , $H_{6}$ , $H_{7}$ , $H_{10}$ .

In Table 9, thefair target throughput results for the eight hosts associated with $A P_{2_2}$ do not satisfy the initial G. Then, thethroughput constraint update is applied, where $G_{n e w}$ = 6 Mbps can satisfy G after it is gradually increased. Theactivated APs and the host associations are given by the algorithm as follows:

$G_{n e w}$ : 6 Mbps;
$A P_{2_1}$ : $H_{3}$ , $H_{5}$ , $H_{8}$ , $H_{9}$ ;
$A P_{2_2}$ : $H_{1}$ , $H_{2}$ , $H_{4}$ , $H_{6}$ , $H_{7}$ , $H_{10}$ .

Table 10 shows the estimated throughput results where any fair target throughput result satisfies G. Theexperiment results are shown in Figure 6.

In Figure 6, it can be observed that there is a significant difference in concurrent throughput with the previous algorithm. This discrepancy is due to the variations in RSS caused by the distance between the host and the AP, aswell as environmental interferences that can impact the actual values. Withour algorithm, it is evident that the new experimental results have significantly improved this issue. Each host can now meet the minimum throughputconstraint.

5.4.4. Case4

Fourth, we discuss the results in Case 4. Theactivated APs and the host associations are given by the algorithm before the throughput constraint update as follows, where Table 11 shows the simulation results:

$A P_{3_1}$ : $H_{1}$ , $H_{7}$ ;
$A P_{3_2}$ : $H_{2}$ , $H_{3}$ , $H_{4}$ , $H_{5}$ , $H_{6}$ , $H_{8}$ , $H_{9}$ , $H_{10}$ .

In Table 11, thefair target throughput results for the eight hosts associated with $A P_{3_2}$ do not satisfy G. Then, thethroughput constraint update is repeatedly applied, where $G_{n e w} = 8$ Mbps can satisfy G after it is gradually increased. Theactivated APs and the host associations are given by the algorithm as follows:

$G_{n e w}$ : 8 Mbps;
$A P_{3_1}$ : $H_{3}$ , $H_{5}$ ;
$A P_{3_2}$ : $H_{2}$ , $H_{4}$ ;
$A P_{4_1}$ : $H_{1}$ , $H_{7}$ ;
$A P_{4_2}$ : $H_{6}$ , $H_{8}$ , $H_{9}$ , $H_{10}$ .

Table 12 shows the estimated throughput results where any fair target throughput result satisfies G. Figure 7 shows the effectiveness of our proposal in a real-worldexperiment.

5.4.5. FairnessComparison

The simulation and experiment results show that every host satisfied the minimum host throughput after applying the throughput constraint update of the enhanced active AP configuration algorithm. These results confirm the validity and effectiveness of the proposal. Figure 8 compares the throughput distribution between the previous algorithm and the enhanced algorithm across fourcases.

In Case 1, theactivated access point (AP) remains the same as before, withonly one active AP in the scenario. Themedian throughput results, shown in Figure 8a, highlight an increase in efficiency after implementing our improved active AP configuration algorithm. Thedata points in the box plot are densely clustered around the median and display an approximately symmetrical distribution, indicating minimal skewness. This pattern illustrates the algorithm’s effectiveness in consistently and fairly distributing guaranteedthroughput.

In Case 2, asshown in Figure 8b, our enhanced algorithm results in higher throughput performance. Asmentioned in Section 5.4.2, thenumber of activated access points in the network only increases by one compared to the previous algorithm case. This adjustment still achieves significant energy savings compared to scenarios without any optimization measures. Additionally, our algorithm demonstrates a narrower range between the highest and lowest values, indicating reduced variability. Themajority of the data points are closely clustered, supporting the goal of fair resourceallocation.

In Case 3, asshown in Figure 8c, althoughthe maximum network throughput experiences certain limitations, thebox plot demonstrates that the throughput control method in our algorithm effectively regulates the actual traffic for each host, achieving a fairer distribution. This method ensures that even the minimum throughput in the actual test network meets the desired throughput constraints, thereby addressing the potential issue of the host’s insufficient throughput in practical applications, which was a concern with the previousmethod.

In Case 4, thesituation is similar to Case 2. Although the number of activated APs is increased to ensure that individual hosts can achieve throughput greater than the constraints, theincrease is limited to just one AP. This reduces the overall consumption of APs in the network compared to when this measure is not applied. Additionally, byexamining the data distribution, aswell as the maximum, minimum, andmedian values in Figure 8c, it is evident that fairness has improved compared to the results obtained with the previousalgorithm.

The discussion above fully demonstrates that our proposed algorithm, by adopting the throughput request satisfaction method, reduces the throughput variations among hosts. It not only maintains an average throughput comparable to the previous algorithm but also achieves a fairer distribution, preventing some hosts from having excessively high throughput while others have insufficientthroughput.

6. Conclusions

In this paper, we presented the enhanced active AP configuration algorithm by incorporating the throughput request satisfaction method to control the actual throughput at the fair target throughput for every host by applying traffic shaping at the AP. This is an extension of the previous active AP configuration algorithm that addresses the issue of part of the host suffering from insufficient and unfair concurrentthroughput.

To address this issue, we deployed dual-interface device support for higher access capacity and reduced the number of APs; in addition, thethroughput control phase provided the actual throughput of each host. It calculates the target throughput from the single and concurrent throughput of each host. Ifit does not satisfy the required throughput, thetentative minimum throughput is increased by the throughput constraint update, andthe active AP configuration and the target throughput arerecalculated.

For evaluations, infour topology cases with five APs and 10 hosts, we conducted simulations using the WIMNET simulator and experiments using the testbed system with Raspberry Pi 4B for APs. Theresults show that the proposal always achieved the required minimum throughput in simulations and in experiments and, at the same time, thenumber of activated APs has obviously been reduced to only one or two. Thus, thevalidity and effectiveness of our proposal were confirmed. In future work, we will further enhance the algorithm by considering the transmission power control at the AP andevaluate it using different protocols such as 802.11ax in various networkscenarios.

Author Contributions

Conceptualization, B.W. and N.F.; methodology, B.W.; software, B.W.; data curation, B.W., D.K., X.W. and T.S.; writing—original draft preparation, B.W.; writing—review and editing, N.F. and Y.-C.F.; validation, B.W., D.K., X.W. and T.S.; supervision, N.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no externalfunding.

Data Availability Statement

Data are contained within the article.

Acknowledgments

The authors thank the reviewers for their thorough reading and helpfulcomments.

Conflicts of Interest

The authors declare no conflicts ofinterest.

Appendix A

Algorithm A1: Previous Active AP ConfigurationAlgorithm

An Enhanced Active Access-Point Configuration Algorithm Using the Throughput Request Satisfaction Method for an Energy-Efficient Wireless Local-Area Network (1)

Appendix B

Algorithm A2: Enhanced Active AP Configuration Algorithm for FairThroughput

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Figure 1. Flow of enhanced active AP configuration algorithm.

Figure 2. Topology of the testbed system.

Figure 3. Device locations in network fields. The red triangle in the figure indicates the location of the AP (Access Point), while the blue circle denotes the host location. Case 1 and Case 2 refer to locations in the Engineering Building #2 at Okayama University, and Case 3 and Case 4 refer to the Graduate School of Natural Sciences Building at Okayama University.

Figure 4. Experimental results for Case 1.

Figure 5. Experimental results for Case 2.

Figure 6. Experimental results for Case 3.

Figure 7. Experimental results for Case 4.

Figure 8. Throughput distributions for the previous and enhanced algorithms.

Table 1. PCenvironment.

WIMNET Simulator PC	Configuration
CPU	Intel Corei7
Memory	8 GB
OS	Ubuntu LTS14.04

Table 2. Simulation parameters in the WIMNETsimulator.

Parameter	Value
packet size	1500bytes
max. transmission rate	150 Mbit/s
propagation model	log distance path lossmodel
rate adaptation algorithm	link speed estimationmodel
carrier sense threshold	85dBm
transmission power	19dBm
collision threshold	10
RTS/CTS	yes

Table 3. Hardware and software of the testbedsystem.

Host PC
type	1.ToshibaDynabookR731/B
	2.ToshibaDynabookR734/K
	3.FujitsuLifebookS761/C
OS	Linux Ubuntu 14.04 LTS (kernel 3.13.0-57)
CPU	1.Intel Core i5-2520M @2.5 GHz
	2.Intel Core i5-4300M @2.6 GHz
	3.Intel Core i5-2520M @2.5 GHz
RAM	4 GB DDR3-1333 MHz
software	iperf 2.0.5
Server PC
type	Fujitsu Lifebook S761/C
CPU	Intel Core i5-2520M @2.5 GHz
RAM	4 GB DDR3 1333 MHz
OS	Linux Ubuntu 14.04 LTS (kernel 3.13.0-57)
software	iperf 2.0.5
Access Point
type	Raspberry Pi 4B
OS	Linux (Raspbian)
CPU	Broadcom BCM2711 @1.5 GHz
RAM	8 GB LPDDR4-3200 SDRAM
NIC	BCM4345/6
external NIC	Archer T4U V3.0 AC1300
software	hostapd v2.10

Table 4. Parameters for the throughput estimation model.

Parameter	Field (a) Engineering Building #2		Field (b) Graduate School Building
Parameter	802.11n	802.11ac	802.11n	802.11ac
$P_{1}$	−28.9	−31.0	−28.5	−30.5
$α$	2.2	2.15	1.7	2.0
$W_{1}$	7.21	2.1	6.5	2.3
$W_{2}$	6.9	8.5	4.2	6.4
$W_{3}$	3.4	3.7	3.1	1.8
$W_{4}$	4.7	1.8	1.5	4.2
$W_{5}$	2.11	7.0	2.0	4.3
$W_{6}$	2.5	1.5	2.0	5.3
a	63.5	133	65.0	134.5
b	62.0	58.0	62.0	58.5
c	6.78	6.30	6.78	6.25

Table 5. Simulation results before throughput constraint update in Case 1.

Throughput (Mbps)	${AP}_{2_1}$			${AP}_{2_2}$
Throughput (Mbps)	H₂	H₅	H₇	H₁	H₃	H₄	H₆	H₈	H₉	H₁₀
S	38.28	55.26	30.46	88.77	128.2	127.2	99.94	71.94	112.9	53.34
C	10.04	14.49	7.99	4.97	7.17	7.12	5.59	4.02	6.32	2.98
F	10.21	10.21	10.21	4.99	4.99	4.99	4.99	4.99	4.99	4.99

S represents the single throughput, C represents the concurrent throughput, andF represents the fair target throughput. The data highlighted in red indicates results that fail to meet the current throughput constraints after the throughput fairness calculation.

Table 6. Simulation results after the throughput constraint update in Case 1.

Throughput (Mbps)	${AP}_{2_1}$			${AP}_{2_2}$
Throughput (Mbps)	H₂	H₃	H₅	H₇	H₁	H₄	H₆	H₈	H₉	H₁₀
S	38.28	55.26	55.9	30.46	88.77	127.2	99.94	71.94	112.9	53.34
C	6.58	9.6	9.49	5.23	7.25	10.39	8.16	5.87	9.22	4.35
F	7.24	7.24	7.24	7.24	6.93	6.93	6.93	6.93	6.93	6.93

Table 7. Simulation results before the throughput constraint update in Case 2.

Throughput (Mbps)	${AP}_{2_1}$			${AP}_{2_2}$
Throughput (Mbps)	H₂	H₇	H₈	H₉	H₁	H₃	H₄	H₅	H₆	H₁₀
S	8.44	27.08	14.9	56.0	88.77	127.2	99.94	71.94	112.9	53.34
C	6.58	9.6	9.49	5.23	7.25	10.39	8.16	5.87	9.22	4.35
F	2.86	2.86	2.86	2.86	7.15	7.15	7.15	7.15	7.15	7.15

The data highlighted in red indicates results that fail to meet the current throughput constraints after the throughput fairness calculation.

Table 8. Simulation results after the throughput constraint update in Case 2.

Throughput (Mbps)	${AP}_{3_1}$	${AP}_{3_2}$			${AP}_{4_1}$		${AP}_{4_2}$
Throughput (Mbps)	H₉	H₄	H₅	H₈	H₃	H₇	H₁	H₂	H₆	H₁₀
S	21.26	70.5	102.1	95.72	33.88	48.38	87.59	93.09	124.9	114.1
C	21.26	18.49	26.79	25.11	15.06	21.5	15.05	15.99	21.46	19.61
F	21.26	22.86	22.86	22.86	17.71	17.71	17.65	17.65	17.65	17.65

Table 9. Simulation results before the throughput constraint update in Case 3.

Throughput (Mbps)	${AP}_{2_1}$		${AP}_{2_2}$
Throughput (Mbps)	H₈	H₉	H₁	H₂	H₃	H₄	H₅	H₆	H₇	H₁₀
S	43.9	27.83	56.32	66.16	123.54	114.2	124.8	84.34	81.02	65.79
C	19.51	12.37	2.07	2.43	4.53	4.19	4.58	3.1	2.97	2.41
F	15.14	15.14	3.02	3.02	3.02	3.02	3.02	3.02	3.02	3.02

The data highlighted in red indicates results that fail to meet the current throughput constraints after the throughput fairness calculation.

Table 10. Simulation results after the throughput constraint update in Case 3.

Throughput (Mbps)	${AP}_{2_1}$				${AP}_{2_2}$
Throughput (Mbps)	H₃	H₅	H₈	H₉	H₁	H₂	H₄	H₆	H₇	H₁₀
S	59.41	59.9	43.9	27.83	56.32	66.16	114.19	84.34	81.02	65.79
C	10.21	10.21	10.11	4.78	4.6	5.4	9.32	6.88	6.61	5.37
F	7.45	7.45	7.45	7.45	6.04	6.04	6.04	6.04	6.04	6.04

Table 11. Simulation results before the throughput constraint update in Case 4.

Throughput (Mbps)	${AP}_{3_1}$		${AP}_{3_2}$
Throughput (Mbps)	H₁	H₇	H₂	H₃	H₄	H₅	H₆	H₈	H₉	H₁₀
S	30.17	59.51	25.22	72.66	70.86	118.0	125.7	100.9	24.27	62.7
C	13.41	26.45	0.93	2.67	2.60	4.33	4.61	3.71	0.89	2.30
F	17.8	17.8	1.95	1.95	1.95	1.95	1.95	1.95	1.95	1.95

The data highlighted in red indicates results that fail to meet the current throughput constraints after the throughput fairness calculation.

Table 12. Simulation results after the throughput constraint update in Case 4.

Throughput (Mbps)	${AP}_{3_1}$		${AP}_{3_2}$		${AP}_{4_1}$		${AP}_{4_2}$
Throughput (Mbps)	H₃	H₅	H₂	H₄	H₁	H₇	H₆	H₈	H₉	H₁₀
S	44.48	58.46	25.22	70.86	37.77	43.26	98.77	129.3	105.5	101.03
C	19.77	25.98	11.21	31.49	16.79	19.23	16.97	22.22	18.13	17.35
F	22.45	22.45	16.53	16.53	17.93	17.93	18.46	18.46	18.46	18.46

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