Performance evaluation of opportunistic schedulers based on fairness and throughput in new-generation mobile networks

This paper discusses radio resource management in the telecommunications industry that utilizes opportunistic scheduling approaches and methods. It proposes a new scheduler called IFMR (Improved Fairness of MaxRate) to extend the opportunistic approach with the proposition of a new scheduling solution that enables to significantly maximize the system throughput. Our goal is to ensure better results that maximize system throughput, ensure perfect fairness at three levels and maximize the number of satisfied users who have achieved their desired throughput. Similarly, the performance of the proposed algorithm is evaluated and compared with reference algorithms: round robin, MaxSNR and proportional fair (PF). The focus of this study is to evaluate and analyze the quality of service guaranteed to each network subscriber, considering the heterogeneous data traffic based on simulations. The algorithms presented in this paper are programmed and simulated using the MATLAB simulation software. The study aims to effectively analyze the impact of radio resource management algorithms and schedulers, including the round robin algorithm, MaxSNR and PF, among others, with the main objective of evaluating the performance of the schedulers used by telecommunication and cellphone network operators. The scheduling phase, which precedes resource allocation and assignment, is a critical aspect of the study. The impact of these schedulers on throughput and fairness will also be evaluated and analyzed based on specific criteria.


Introduction
Previous years have witnessed great developments in the field of communication and multimedia.The number of subcarriers in communication systems has increased, and the demand for higher rates persists.The challenge for the telecommunications sector is to ensure a fair sharing of radio resources and guarantee the best quality of service (QoS).Orthogonal frequency division multiple access (OFDMA) has emerged as the most auspicious physical layer technique for new-generation wireless networks, widely implemented in recent wireless systems such as 802.11a/g or 802.16 and clearly emerged for future broadband wireless multimedia networks.However, this access technique must be combined with algorithms to enhance the resource allocation process.These algorithms are called "schedulers."The scheduler, considered a key component in communication systems, is used to allocate resource units (RU) to all active users in a cell.The main goal of the scheduler is to optimize spectral efficiency to maximize the overall system throughput, ensure fairness and service differentiation between different users and guarantee the best QoS.Several mobile radio communication networks deploy opportunistic techniques for resource management, sharing and scheduling.Next-generation 4 G and 5 G networks are promising examples, and consequently, opportunistic networks have emerged.Several scheduling techniques with different levels of complexity are present in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].
Similarly, opportunistic scheduling techniques have been deployed in telecommunications networks in general and computer networks in particular to optimize and save energy [18][19][20].The growth of wireless technology has made opportunistic scheduling a widespread theme in recent research, as providing high system throughput without reducing fairness in allocation is becoming a challenging task.A suitable policy for resource allocation among users is of crucial importance.The main objective of this research paper is to analyze and implement opportunistic scheduling techniques on new-generation networks.We approached the problem by analyzing the performances and characteristics of the schedulers.Given the large number of proposed schedulers, the first problem is to compare and classify them.However, we later discovered that usual measurement systems are inadequate for judging correctly on the same level playing field.Several works have been carried out on scheduling in computer networks, and the same work has been applied to scheduling strategies in new-generation mobile networks.Indeed, these scheduling techniques are applied in computer and telecommunications networks to schedule resources before they are used by network users [21].
The technique of opportunistic scheduling has received significant attention in various fields, including cloud computing, computer networks and wireless communications.This approach involves dynamically allocating available resources based on the current system conditions, rather than following a predetermined schedule, thereby maximizing resource usage and enhancing system efficiency.Opportunistic scheduling offers an advantage in handling resource constraints and fluctuations.For example, in wireless networks, this technique is often used 1 3 Performance evaluation of opportunistic schedulers based… to increase system capacity by exploiting the spatial diversity of wireless channels, while in cloud computing, it can allocate computing resources dynamically, improving system efficiency and reducing energy consumption.Advancements in technology are driving the continuous evolution of opportunistic scheduling, with new algorithms and techniques being developed to improve its efficiency and effectiveness.As a result, opportunistic scheduling is expected to play an increasingly significant role in optimizing resource utilization and system performance.
In this paper, we proposed a new approach for scheduling called IFMR (Improved Fairness of MaxRate).We compared, studied and developed the impact of our proposal scheduling algorithm on throughput and fairness.To achieve these objectives and prove the effectiveness of our contribution, several basic scheduling algorithms have been considered and compared, including round robin (RR), MaxSNR and proportional fair (PF).

Schedulers' classification
Several research studies have been carried out to propose more effective schedulers.This range of schedulers makes it possible to significantly improve fairness.Figure 1 presents the different classes of schedulers.

Different levels of equity
There are several levels of equity, which can be considered in terms of access to resources, flow and degree of satisfaction.Here are some examples: • Level 1 Equity can be considered in terms of access to resources.This category of equity is based on the idea that all users will have the same number of resource units (RU) and that resources will be distributed evenly.• Level 2 Equity involves ensuring equivalent throughput for each user.Given the variation in radio conditions among different network users, it would be unfair to allocate the same amounts of resource units (RU) to all users, resulting in different throughputs.In conclusion, level 2 equity involves guaranteeing equivalent throughput for each user.• Level 3 Level 3 equity involves providing the same level of satisfaction among users.Indeed, offering the same throughput to two users with different needs (throughput, maximum delay, jitter, BER, etc.) and different radio conditions seems unfair and does not guarantee optimal equity.Level 3 equity therefore consists of ensuring the same level of satisfaction.

Fair schedulers
Numerous studies have been conducted to propose more effective schedulers, and this wide range of schedulers has significantly improved fairness.

Round robin algorithm (RR)
Round robin (RR) is one of the simplest and most commonly used schedulers [22,23].With RR, backlogged flows are served in sequence, one packet at a time.The RR algorithm allocates the same quantity of resource units (RUs) to all active users, one after the other.Each user in a cell has all the subcarriers during a time slot.This ensures that each user receives the same number of RUs and reaches the medium regularly, making the allocation strategy fair (the level 1 fairness hierarchy).However, RR has several weaknesses.The principle of the algorithm is illustrated in Fig. 2.
• The distance from the base station (BS):The distance from the base station affects the transmission capacity of a user.Users close to the base station have a different transmission capacity compared to those far from it due to path loss.Therefore, RR scheduling does not guarantee the same rate for all users, which violates the level 2 fairness hierarchy.• Service differentiation: Even if users are located at the same distance from the BS (base station), they may not obtain an equal throughput.This is due to the different QoS constraints that each user may have.

Fair queuing (FQ)
Fair queuing (FQ) [22,[24][25][26] allocates each active user K with a height of D/K for a possible link rate of D. FQ ensures the same throughput for each user, making it fairer than round robin.Therefore, it achieves the level 2 fairness hierarchy.However, FQ still neglects the user's needs, penalizing MSs that require higher throughput compared to others.As a result, QoS requirements are often not met, and the level 3 fairness hierarchy is not achieved.The principle of the algorithm is illustrated in Fig. 3.

Max-min fair (MMF)
The max-min fair allocation algorithm [27,28] assigns RUs in a repetitive manner such that the rate offered to each user increases gradually and identically.

3
Performance evaluation of opportunistic schedulers based… Once a user receives the rate they requested, no other RUs are assigned to them, and scheduling continues with other users.The execution of max-min fair ends when all users are satisfied or when all RUs are distributed.This allocation is similar to fair queuing and has the same characteristics, where MSs receive equal throughput.Consumers with lower needs are favored, as their desired flow is almost always provided, and they are frequently fully satisfied.However, other users with higher needs share the remaining resources fairly, which is often insufficient to satisfy them.Note that if all users have the same needs, RR scheduling would be equivalent to MMF.The principle of the algorithm is illustrated in Fig. 4. Some researchers believe that a quality of service (QoS) achieved through max-min fairness is satisfactory.However, we believe that this perspective, which was relevant in the early days of the internet, is now obsolete.With the increasing profitability of multimedia applications and the growing demand from the public and operators, it is no longer feasible to prioritize users with low demands at the expense of overall QoS.We believe this approach is unfair and ineffective in utilizing bandwidth.Granting users only a fraction of the bandwidth they requested typically results in subpar QoS.Additionally, the MMF approach is not opportunistic and only achieves level 2 fairness hierarchy out of the three levels described in Introduction.

Weighted round robin (WRR)
In WRR queuing [29,30], packets are first classified into different service classes and then allocated to a queue dedicated to that particular service class.Each of the queues is then serviced in a round-robin manner.This means that WRR is capable of serving all service classes, although not necessarily treating them equally.Additionally, WRR provides fairness among all queues.However, WRR is not opportunistic, and it only partially achieves level 3 fairness hierarchy.Performance evaluation of opportunistic schedulers based…

Deficit round robin (DRR)
Deficit round robin (DRR) [31] is a variant of weighted round robin (WRR) scheduling.In DRR, each flow is allocated a quantum (Qi) that is proportional to its weight.
DRR scans all non-empty queues in sequence.When a non-empty queue is selected, its deficit counter is incremented by the quantum value.The deficit counter value then represents the maximum amount of bytes that can be sent in that turn.If the deficit counter is greater than or equal to the size of the packet at the head of the queue, that packet can be sent, and the deficit counter value is decremented by the packet size.This process continues until either the queue is empty or the deficit counter value is insufficient, at which point the scheduler moves on to the next queue.If the queue is empty, the value of the deficit counter is reset to 0. By following this policy, DRR ensures that each flow receives a minimum rate, regardless of packet size.However, DRR is not opportunistic and only partially achieves level 3 fairness hierarchy.

Weighted fair queuing (WFQ)
Weighted fair queuing (WFQ) [32,33] is an enhanced version of the fair queuing (FQ) algorithm.This algorithm utilizes a weight system, which enables certain flows to be prioritized by granting them more bandwidth.This approach enables QoS control and, to some extent, service differentiation management.However, WFQ is not opportunistic and only partially achieves level 3 fairness hierarchy.

Fair and effective queueing (FEQ)
In [34], the authors presented a queue management system for various types of traffic on the WiMAX network.Bandwidth allocation is achieved in two phases.In the first phase, the WRR algorithm serves the queues.The system allocates bandwidth equal to minimum disastrous reserved (MRR) for each traffic type.MRR for each traffic type represents the weight of the corresponding file during phase 1.This policy supports traffic with less tolerance compared to those with fewer requirements.Thus, packets not served during phase 1 are placed in the earliest deadline first (EDF) system queue to be processed in phase 2. During the second phase, EDF is used.However, FEQ is not opportunistic and only partially achieves the level 3 fairness hierarchy.The principle of the algorithm is illustrated in Fig. 5.

Channel-aware QoS scheduling (CQ)
Another queue management system has been proposed in [35], which ensures the scheduling of rtPS (Real Time Polling Service), nrtPS (Non-Real Time Polling Service) and BE (Best Effort) traffic.Once a connection is accepted, packets are Performance evaluation of opportunistic schedulers based… classified according to their type and placed in the corresponding queue.The management of the three queues affected by the scheduling system is performed using the WFQ algorithm.In addition, when selecting a packet to be served, the system takes into account its virtual start service time ( S i ) and virtual finish service time ( F i ) values (see Fig. 6).The channel-aware QoS scheduling scheme, unfortunately, is not opportunistic.If we consider the three levels of fairness described in Introduction, it only partially achieves the level 3 fairness hierarchy.

Opportunistic schedulers
The algorithms mentioned below are unable to fully utilize the available bandwidth and offer a global system throughput that is far from the theoretical limits.Therefore, many studies have addressed this critical issue for current and future networks.They have concluded that an opportunistic approach is a paramount solution to achieve optimal allocation of radio resources [2,3,19,36].Based on this idea, two classes of algorithms have emerged: maximum signal-to-noise ratio (MaxSNR) and proportional fair (PF).These algorithms take advantage of frequency diversity and multiuser allocation to prioritize resources that have the most favorable transmission/reception conditions (i.e., the best signal/noise) and maximize the flow rates of OFDMA networks.However, it should be noted that the opportunistic approach used in these algorithms makes them non-fair, and they do not provide an equal share of resources to all users.

Maximum signal-to-noise ratio (MaxSNR)
Many high-performance schedulers are derived from MaxSNR [also known as maximum carrier-to-interference ratio (Max C/I)].With MaxSNR, priority is given to Taking advantage of multiuser and frequency diversity, MaxSNR scheduling constantly allocates the RU to the user with the best spectral efficiency by dynamically adjusting the modulation, allowing for an extremely efficient use of radio resources and getting closer to the Shannon capacity limit, thereby greatly increasing system throughput.However, this allocation strategy has a negative impact: Users close to the access point always have disproportionate priority over distant users, as they benefit from a lower path loss and therefore a greater SNR.Nearby MSs will often be, if not always, selected before remote MSs, which will be allocated only the remainder.
Maximizing flow rate via MaxSNR accentuates system unfairness.Figure 7 illustrates this phenomenon: In the green area, MSs get access to radio resources and (1) Performance evaluation of opportunistic schedulers based… have their needs met, but in the red zone, MSs are "penalized" and are given the residual bandwidth when the "priority" area is served.

Proportional fair (PF)
Proportional fair scheduling has been proposed as a way to incorporate a degree of fairness while still benefiting from the throughput maximization of MaxSNR.Due to its simplicity and excellent performance, much research has focused on this scheduler, both in the development of new algorithms based on PF and in the study of its characteristics and performance.The principle of PF is to allocate a time interval of subcarrier n to the user j who has the most favorable transmission conditions in relation to their average throughput: The mean value of m k,n is denoted as M k,n .With this allocation strategy, it is less likely for "bad" channels to be selected for each user.In contrast, proportional fair scheduling (PF) allocates an equal share of bandwidth to all mobile stations (MSs), similar to round robin, while achieving much higher throughput.Therefore, the same amount of resource units are allocated to all users regardless of their positions.The fairness provided by PF is at level 1, which is a significant improvement over MaxSNR.

Multimedia adaptive OFDM proportional fair (MAOPF)
The multimedia adaptive OFDM proportional fair (MAOPF) [46] offers an interesting evolution of PF by considering the data transmitted/received by each stream during the allocation process.The principle is to allocate bandwidth in proportion to each user's desired throughput.For each time interval, the subcarrier n is then allocated to the mobile j with the highest proportionality factor, which is defined as the ratio of the user's desired throughput to its current throughput: where R k refers to the desired throughput by user k.
The multimedia adaptive OFDM proportional fair (MAOPF) [46] is an extension of the proportional fair (PF) scheduling algorithm that takes into account the amount of data transmitted/received by each user in the allocation process.The principle of MAOPF is to allocate bandwidth between users in proportion to their desired throughput, taking into consideration their channel conditions.The subcarrier n is then allocated, for the time interval, to the user j with the highest value of w j,n , which is defined as the ratio of the desired throughput of user j to the mean value of the maximum number of bits that can be transmitted during a time interval of the subcarrier n for all users.This allows for a more efficient use of the available bandwidth and ensures that users with high-throughput demands are allocated more resources, while still maintaining a certain level of fairness.

Hybrid opportunistic algorithms
There are various methods that aim to strike a balance between conventional and opportunistic resource allocation while also ensuring fairness in the network.Two examples of such methods are proposed in [36,[39][40][41].These methods involve selecting a subset of users in an opportunistic manner based on their radio conditions and then allocating resources to this subgroup in a round robin fashion.However, preselecting subgroups of users results in a suboptimal allocation that does not maximize overall throughput, and the fairness gain is not significant.Nonetheless, opportunistic approaches and algorithms can be used to evaluate and implement routing protocols for wireless and next-generation networks [42].This research primarily investigates the opportunistic problem of resource unit allocation algorithms.The goal of the research is to achieve not only a maximum overall system throughput but also a high level of fairness in the allocation process.
The research conducted in this paper has focused on the opportunistic problem of resource unit (RU) allocation algorithms.Specifically, the main objective is not only to maximize the overall system throughput but also to ensure a high level of fairness in the allocation process.

State of the art
Opportunistic scheduling is a scheduling technique that is used to maximize the utilization of available resources and enhance the overall efficiency of the system.This strategy has gained significant attention in various fields, such as cloud computing, wireless communications and computer networks in recent times.The dynamic allocation of resources based on current system conditions is one of the critical benefits of opportunistic scheduling.This approach enables tasks to be scheduled according to the availability of resources at any given time, instead of following a predetermined schedule.This can result in substantial performance improvements, particularly when resources are scarce or fluctuate frequently.
In wireless networks, opportunistic scheduling is frequently employed to increase the overall system capacity by exploiting the spatial diversity of wireless channels.Multiple users can transmit simultaneously, which maximizes the throughput and reduces latency.Similarly, in cloud computing, opportunistic scheduling can be used to allocate computing resources dynamically, which can enhance system efficiency while minimizing energy consumption.The field of opportunistic scheduling is continuously evolving, with novel algorithms and methods being developed to increase its efficiency and effectiveness.As technology progresses, opportunistic scheduling is anticipated to play an increasingly crucial role in optimizing resource utilization and system performance.

Performance evaluation of opportunistic schedulers based…
The first part of our research paper aims to summarize the performance level of the best-known schedulers in terms of maximizing throughput, contributing to fairness and enabling service differentiation.Maximizing throughput is essential for accepting users into the network, while ensuring fairness and service differentiation is necessary to guarantee QoS.In Table 1, we present the analyzed algorithms classified into families based on their common characteristics.
In order to better evaluate the schedulers, the system throughput and the level 3 fairness hierarchy are scored from lowest to highest [36]: • For throughput, the lowest indicates that the scheduler do not ensure a throughput maximization and highest represents the maximum attainable objective which is desirable to reach, • For level 3 fairness hierarchy, lowest indicates that there is no service differentiation, important indicates that the scheduler ensures a service differentiation according to the context and highest indicates that the scheduler ensures an equal satisfaction among users regardless of the context.
In Table 2, we can appreciate the main characteristics shown by the most important schedulers analyzed.In this table, the main evaluation criterion is based on: • Channel conditions, • Buffer occupancy, • Throughput maximization • Fairness.

AWGN model
Initially, it is assumed that the channel used is of the additive white Gaussian noise (AWGN) type.The received signal is obtained by adding the transmitted signal and the AWGN.This noise model is the simplest way of modeling all the noises that disturb the signal during transmission.The overall noise is completely characterized by its variance, which is the sum of the variances of the different noises assumed to be Gaussian and independent.For making decisions, the decision variable Y is given by: where e corresponds to the useful signal and "n" is a noise variable following a Gaussian distribution with zero mean and 2 .Thus, the decision variable Y follows a normal distribution with a variance of 2 and a mean of m Y = e , depending on the emitted bit being either i = 0 or i = 1 .Figure 8 illustrates the channel modeling principle.

Resource block allocation deploying scheduling approach
In our research, we focused on resource allocation in the downward path of a single cell.Access points have packets to deliver to users located within their coverage area.We define a resource block (RB) as a grid of time-frequency resources.The system scheduler allocates each resource block according to its criteria to one of (4) Performance evaluation of opportunistic schedulers based… the mobiles belonging to the access point's coverage area.Hence, the scheduler has perfect knowledge of the link states.To do so, the access point estimates the attenuation experienced on each channel and for each mobile from measurements related to signal-to-noise ratio (SNR).Furthermore, we consider that transmissions on different RBs by different mobiles undergo independent link state variations over time.

Description of the model
In this research, we consider a downlink transmission of an OFDM multiuser system.We assume that the overall bandwidth B is divided into N orthogonal narrowband subcarriers.Each user measures the channel gain of each subcarrier and feeds back the channel status information to the base station (BS) via a separate return channel.
The simulation parameters are presented in Table 3.To analyze the resource block allocation process, we opted for numerical simulation based on the implementation of the most widely used schedulers in the literature, namely round robin (RR), MaxSNR and proportional fair (PF).

Simulation results
The algorithms presented in this paper have been programmed and simulated in MATLAB.According to the numerical simulation results, Fig. 9 shows that all users have the same channel response.
The RR algorithm assigns RBs to users one after the other in each timeslot (each color represents a user).The scheduler does not take advantage of multiuser diversity, In Fig. 10, the MaxSNR algorithm is considered as the scheduler responsible for the allocation of resource blocks.It is worth noting that MaxSNR does not maintain fairness policy, as it allocates RBs to users based on the flow requirements and the signalto-noise ratio (SNR).MaxSNR scheduler allocates RBs to users close to the base station, as long as these users have the best SNR.This algorithm will only serve distant mobiles once all nearby mobiles are fully served and inactive.As a result, it constantly benefits from only part of the multiuser diversity.When the users do not have the same channel response, one can observe the difference between MaxSNR and proportional fair (PF) in terms of resource allocation to users.As shown in Fig. 11, PF considers fairness, and there is no dominant user, unlike the case of user 6 in the MaxSNR scheduler.all flows and maintaining the same percentage of packets for different traffic loads, while paying particular attention to the differences in treatment between mobiles located at different distances from the base station (BS).

Model description
In the simulations, we consider an OFDM system operating on a carrier frequency of 2.4 GHz to evaluate fairness.We simulate different numbers of users and assume that all users have the same data to be transmitted.Each user is assigned a subcarrier in three different scenarios using three different algorithms: RR, PF and MaxSNR.Table 4 shows the simulation parameters related to the case study.

Experiment validation of scheduling algorithms
We can observe from the numerical simulation results, as shown in Fig. 12, that the classic round robin scheduler performs poorly and is incapable of providing the same quality of service (QoS) to different groups of mobile users.Fig. 12 Fairness assessment (Scenario A) 1 3 Performance evaluation of opportunistic schedulers based… Despite allocating resources evenly to mobile users, RR fails to consider that those who are located further from the access point experience lower spectral efficiency than those who are closer.This results in disparities in the instantaneous speeds provided and consequently, QoS inequities.Furthermore, RR does not leverage multiuser diversity, resulting in underutilization of bandwidth and very low overall system throughput.
The MaxSNR scheduler is not considered a fair scheduler as it allocates system resources based on the best signal-to-noise ratio, resulting in almost identical results across all users.As user demands for service increase, equity decreases since Max-SNR frequently serves the strongest users.The simulation results shown in Fig. 13 confirm that MaxSNR is not fair as it prioritizes providing a high level of QoS and satisfaction to users near the base station, while penalizing distant users.
The proportional fair scheduler is considered to be the most equitable as it prioritizes and favors remote mobiles by providing each of them with the same number of resource blocks.However, this process is suboptimal since distant mobiles do not have the same spectral efficiency as the closest ones.Despite an equal sharing of the bandwidth between the mobiles, different speeds are obtained, resulting in disparities in packet transfer time and QoS levels.The simulation results shown in Fig. 14 demonstrate that increasing the level of fairness generally improves the overall QoS of a system.

Experiment validation related to throughput evaluation
In this section, we will discuss one of the most important properties of a network system, namely the flow.The flow is generally regarded as a framework for optimizing system performance and a measure of the amount of information that can be Fig. 13 Fairness assessment (Scenario B) transmitted and received per unit time.We will evaluate three scheduling algorithms under three different scenarios to determine the best performance.

Model description
The proposed rate measurement is based on the proportion of resources allocated during different time intervals.In order to evaluate the throughput, we considered three different scenarios using three algorithms: RR, MaxSNR and PF.The simulations were conducted on an OFDM system operating at a frequency band of 2.4 GHz.We assumed that all users had the same amount of data to transmit, and each resource block was assigned to a user for a specific time slot.Table 5 illustrates the simulation parameters used to validate our study.

Analysis and simulation results
The numerical simulation results presented in Fig. 15 indicate that the MaxSNR scheduler achieves the highest capacity, as the algorithm takes into account multiuser diversity and allocates resource blocks to users with the highest signal-to-noise  1 3 Performance evaluation of opportunistic schedulers based… ratio (SNR) at each time interval, regardless of channel conditions and user requirements.As usual and in the same context, the MaxSNR scheduler achieves the best results by allocating resources to users with the highest signal-to-noise ratios, depending on the system capacity.This maximizes the overall system throughput.However, this also means that the scheduler penalizes users who are located far away from the base station.Therefore, the importance of the obtained results, as confirmed in Fig. 16a, cannot be overstated.
Figure 16b shows that the PF algorithm performs optimally, achieving a fairly high level of system throughput without compromising fairness.In this case, users compete for resources that are normalized by their average rates, rather than their signal-to-noise ratios (SNR).PF exploits the fact that the propagation channels between the base station and the users are independent of each other, which leads to multiuser diversity.Unlike round robin, opportunistic schedulers exhibit an inflection point in the throughput evolution when the load increases.

Contribution of opportunistic scheduling to enhance resource allocation efficiency
This paper makes a major contribution to the field of opportunistic scheduling in telecommunication networks, called "Improved Fairness of MaxRate" (IFMR).This new scheduler differs from other existing ones in the literature [14,15] by its ability to operate by determining three different levels of fairness and considers the needs of users individually in terms of throughput.First, it provides empirical evidence of the timeliness of the results obtained.Second, it advances our understanding of the role of schedulers in the management and allocation of mobile radio resources.
To accomplish this contribution, we proposed a new approach to resource scheduling based on the principle of solving an optimization problem with throughput, fairness and satisfaction constraints.Our analysis revealed very satisfactory and significant results compared to other metrics and scheduling algorithms known for their efficiency.In addition, we used a simulation model very close to the real world to explore the role of schedulers in the considered transmission chain.Our results suggest that the considered performance criteria play a key role in the scheduling process and consequently a better management and allocation of resources.Overall, this paper provides a new opportunistic scheduling approach and a state of the art on the existing basic algorithms considered as reference in this research area, namely RR, MaxSNR and PF.

Improved Fairness of MaxRate (IFMR)
As already mentioned in its basic principle, the MaxSNR algorithm allocates radio resources to the user with the largest number of subcarriers m k,n , thereby maximiz- ing the overall system throughput.It should also be noted that MaxSNR gives high priority to users close to the base station (BS), while distant users will be penalized, resulting in a serious inequality among users in the same network.In addition to its major disadvantage of inequality, MaxSNR does not take into account the needs of users when allocating priorities.For all of these reasons, our second contribution is to propose a new scheduling algorithm, derived from the MaxSNR algorithm called "Improved Fairness of MaxRate (IFMR)."This algorithm will be more effective in addressing the problems caused by MaxSNR and overcoming its weaknesses.The proposed IFMR algorithm maintains the ability of MaxSNR to maximize throughput while correcting inequalities.It also increases the number of satisfied users who have reached their desired throughput.

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Performance evaluation of opportunistic schedulers based…

Principle of the IFMR scheduler
In its operating principle, the IFMR algorithm operates in two phases: Preselection phase (Phase 1) The first phase consists of allocating the resource unit (RU) to user i with the largest number of subcarriers m k,n and, therefore, the highest signal-to-noise ratio (SNR) according to the equation (with N as the total number of users).If the user receives their requested throughput, they are no longer considered a resource requester, and the algorithm moves on to serve the next user.

Post-selection phase (Phase 2)
The second phase of the algorithm is subject to a condition.It can only be executed when all users are satisfied in terms of their desired throughput and there are still RUs available in the resource budget.Consequently, the IFMR algorithm assigns the RU to the user i with the largest number of subcarriers m k,n .When a user receives a number of RUs equal to the maximum available resources N ′ , no further RUs will be allocated to them, and the algorithm moves on to the next user.Meanwhile, if the number of RUs for each user is equal to N ′ and there are still other RUs available, the IFMR scheduler updates the number of remaining resources N rest .Figure 17 describes the state transition diagram of the new IFMR scheduler.

IFMR analysis scheduling strategy
This section focuses primarily on the complex problem of opportunistic resource allocation in mobile networks using OFDM technology.Optimal radio resource allocation is indeed a major challenge that allows for better throughput with improved QoS.We have proposed a new resource allocation algorithm called IFMR.
Figure 18 represents a comparative study between this algorithm and other basic schedulers in terms of their ability to meet application constraints has enabled us to greatly simplify the task of evaluating the relative performance of each scheduler studied.In our numerical simulations, we consider a number of users equal to four.For a better representation of the simulation results, each user is represented by a different color.Assuming multimedia traffic (voice, data and video), we assume that 30% of users require a throughput of 80 kbit/s, 30% require 160 kbit/s and 40% require 240 kbit/s.Now, we focus on the allocation of resource units that each user receives over time.To do this, we implement our new IFMR scheduler assuming a number of users equal to 4 and determine the number of subcarriers allocated to each user per time interval.Figure 18 shows that the IFMR algorithm starts the allocation process by assigning one resource unit to each user.At the initial state, the scheduler selects the most favored user based on the value of their m k,n .From these results, we can estimate that each user who has received their desired throughput will be excluded from the allocation process and the algorithm will move on to the next user until all users receive their desired throughputs.As the same Fig.18 also shows, the IFMR allocates the same amount of RU to all users ( N ′ = 5).In the case  Performance evaluation of opportunistic schedulers based… where a resource unit is considered remaining, it will be automatically assigned to the user with the largest m k,n .These results confirm that IFMR guarantees optimal and therefore perfect fairness.

Performance evaluation of the IFMR
The major performance criteria are defined.While the ability of schedulers to maximize the total system throughput is easy to measure, it is not the case for measuring fairness and the number of satisfied users, which pose significant challenges.Indeed, fairness is an abstract term that is difficult to define, and therefore difficult to measure.We will study the performance of the proposed IFMR algorithm and compare it to the reference scheduling algorithms proportional fair (PF), round robin (RR) and MaxSNR.The evaluation of the performance of the IFMR algorithm will be based on three performance criteria, namely: • Equity, • System throughput, • and the number of users satisfied in terms of required throughput.
Two different scenarios arise in this performance evaluation.The first scenario assumes that all users require the same throughput.The second scenario divides users into three different categories based on the type of service they require.Users in the first group have a voice traffic requirement.Users in the second group require data traffic, and users in the third group require video traffic.An evaluation scale is broken down into three levels for each performance criterion corresponding to the numbers: • 0: Unweighted, • 1: Low level, • 2: Intermediate level, • 3: High level.

Equity evaluation
Three different levels of equity are considered in our research.It is therefore evident that a comparison of the equity provided by schedulers must necessarily be made at the same level to ensure fairness.For the first level, equity can be considered in terms of the amount of resources.This often occurs when all users have the same number of resource units (RUs).The second level involves guaranteeing an identical throughput for all users.The third level of equity ensures the same level of satisfaction among users.The simulation results are adopted for the three levels of equity applied to the different scheduling algorithms, namely round robin (RR), maximum signal-to-noise ratio (MaxSNR), proportional fair (PF) and iterative fractional matched resource (IFMR), for both scenarios.We remind that the simulation parameters are the same as those recorded in Table 6.

Scenario 1
The simulation results related to the evaluation of fairness for the three levels are illustrated in Fig. 19.This figure shows that the IFMR algorithm has achieved optimal fairness for all three levels and has significantly improved fairness compared to the three other schedulers: RR, PF and MaxSNR.The figure also shows that the PF and RR algorithms have a high fairness index, which is considered lower than that of the proposed IFMR algorithm.Additionally, the MaxSNR algorithm provides very poor performance and is unable to ensure optimal fairness.It should be noted that the fairness index for levels "2" and "3" is the same for all four schedulers because in the first scenario, all users have the same desired throughput (240 kbits/s).In other words, assigning the same throughput guarantees the same degree of satisfaction.

Scenario 2
Figure 20 illustrates the simulation results for the three levels of fairness for the schedulers RR, MaxSNR, PF and IFMR.In this second scenario, users are divided into Performance evaluation of opportunistic schedulers based… three different categories, imposing a service differentiation constraint.The simulation results show that our proposed new algorithm (IFMR) gives better results than the three other algorithms for all fairness levels.The fairness index remains constant despite the increase in the number of users.The same fairness index (in the case of IFMR) is 1 for levels "1" and "2" and almost 0.83 for level "3." Proportional fair (PF) and round robin (RR) schedulers have a high fairness index.According to the simulation results, this index is between 0.9 and 1 for fairness level "1."The same fairness index varies between [0.8, 1] for level "2" and [0.7, 0.8] for level "3."Meanwhile, the MaxSNR algorithm records the worst performance in terms of fairness since it excludes distant users, i.e., users who are farthest from their access point (base station).

Throughput evaluation
It should be noted that the growth of mobile radio telecommunications is closely linked to the joint resolution of equity optimization and overall system throughput maximization problems.This joint resolution requires an evaluation of the performance of existing schedulers in the literature, as well as that of the newly proposed scheduling algorithm, namely IFMR, in this article.The cost of maximizing throughput by IFMR is therefore an emphasis on the second criterion to be evaluated.Indeed, the capacity of this scheduler (IFMR) to optimize the system throughput compared to other algorithms (in the two scenarios) is the main focus of this second part of performance evaluation.The simulation parameters considered are those in Table 6. Figure 21 illustrates the evolution of system throughput as a function of the number of users for the RR, MaxSNR, PF and IFMR algorithms in two scenarios.According to this same figure, it can be observed that the performance of MaxSNR in terms of throughput for both scenarios significantly exceeds that of PF, RR and IFMR algorithms.This is due to the fact that the scheduler allocates resources only to users with the best channel conditions.As for the proposed IFMR algorithm, it shows a significant improvement over the others.In terms of performance, IFMR approaches that of the MaxSNR algorithm.It surpasses the results obtained by the Performance evaluation of opportunistic schedulers based… PF and RR schedulers quite notably in the two considered scenarios.It can also be observed that the system throughput resulting from the RR algorithm is the lowest.This weakness in terms of system throughput performance is due to the fact that the algorithm assigns RUs to only one user in each time interval, regardless of the user's channel response and throughput requirements.In summary, this figure highlights the good performance offered by the proposed IFMR algorithm in terms of overall system throughput maximization.

Evaluation of the number of satisfied users
To ensure better performance in terms of quality of service, schedulers developed in the literature for sharing and managing radio resources often require constraints on the degree of user satisfaction.It can be easily concluded that the scheduler (IFMR) proposed in this work offers the best performance without any consideration for maximizing the overall cell throughput.To highlight the interest of the proposed algorithm, we analyze the number of satisfied users who have achieved their desired throughput for the two previously presented scenarios.The estimation of the number of satisfied users is performed assuming that all users have the same throughput requirement (240 kbits/s).For the same system and under the same simulation conditions, the estimation of the number of satisfied users is achieved by considering that users are categorized into three different groups.Users in the first group will have voice traffic requirements, those in the second group will have data traffic requirements, and those deploying video traffic will be in the third group.The simulation results recorded in this case are given in Figs.22 and 23.These figures, respectively, illustrating the evolution of the number of satisfied users for the first and second scenarios, show the performance contribution of the proposed IFMR algorithm compared to other schedulers in terms of increasing the number of users who have achieved a notable degree of quality of service and significant desired throughput.

Scenario 1
In this first scenario, our study focused on the ability of schedulers to guarantee the maximum number of satisfied users who have achieved their desired throughput.This translates into ensuring users a considerable degree of quality of service.
Figure 22 shows the evolution of the number of satisfied users obtained for different schedulers, paying particular attention to the difference between the proposed IFMR algorithm and other schedulers.From these initial results, we can conclude that the round robin scheduler provides modest performances and is unable to ensure Performance evaluation of opportunistic schedulers based… a significant number of satisfied users.This is due to the fact that RR assigns all subcarriers to a user at each time interval regardless of user requirements.Indeed, PF and MaxSNR may be considered more relevant than RR, but without ever taking IFMR into consideration.Therefore, the proposed IFMR scheduler represents the best performance and allows for maximum satisfaction of users, as seen from the simulation results in Fig. 22.Additionally, IFMR guarantees optimal satisfaction for all network users.

Scenario 2
In this second scenario, and based on an opportunistic approach, we continue to evaluate the number of satisfied users, that is, the number of users who have achieved their desired throughput.We must recall that the second scenario involves considering users divided into three different groups.The first group consists of users with voice traffic requirements, the second group has data traffic requirements, and the third group has video traffic requirements.It is important to note that all schedulers studied, including our new proposal, show significantly better performance in supporting varied traffic loads and satisfying system users.In this context, MaxSNR and PF still exhibit high-quality service capabilities in terms of satisfied users in processing the three groups of mobiles compared to RR.
Figure 23a highlights this observation.The higher the traffic load, the more marked this difference in treatment, ultimately resulting in a considerable degradation of QoS for distant mobiles.The IFMR scheduler proposed in this paper provides the best degree of QoS for all users compared to the other three schedulers.Our new scheduler enables the highest traffic loads to be achieved with a notable and optimal QoS level for all users.Furthermore, for different loads and types of multimedia traffic, it can be observed that, in addition to ensuring optimal QoS, IFMR guarantees better overall satisfaction than that of reference opportunistic schedulers (PF, MaxSNR and RR). Figure 23b confirms the result of Fig. 23a.In fact, this figure shows that for the IFMR algorithm, all users in the cell achieve their desired throughput.This satisfaction rate reaches its maximum for our proposal; 39% of users are satisfied in the case of PF, 23% of users meet their needs in the case of MaxSNR, and only 12% of users are satisfied in the case of RR.

Conclusion
Scheduling algorithms have been implemented on the downlink as they are a crucial element of the base station.The scheduler is responsible for allocating blocks of resources to different users.We studied three scheduling algorithms: round robin, MaxSNR and PF.Round robin allocates resource blocks to users one after another, while MaxSNR allocates resource blocks to users with the maximum SNR.PF can be considered as a compromise between speed and fairness.
Without specific simulation results related to the study proposed in this paper, it is difficult to provide validation of the simulated models and algorithms (RR, MaxSNR and PF).However, the validation process is based on a series of tests and verifications using a software simulator known as MATLAB.These tests are conducted to ensure that the results obtained from a study on opportunistic scheduling are accurate and reliable.The validation process involves comparing the simulation results obtained by the study to known results and previously published research that proves their validity.This is done through various methods, such as statistical analysis, reproducing the experiment with a well-determined number of iterations or comparing the results with theoretical predictions.Eventually, our validation process may involve checking for errors that could affect the results.This may include conducting sensitivity analyses, varying the simulation data and parameters used, increasing the number of scenarios or using other statistical methods to confirm the results.Ultimately, by deploying such a validation process, we have ensured that the results obtained are consistent and reliable.
The first part of this paper focuses on evaluating the performance of the most well-known schedulers.An analysis of different scheduling policies was conducted in this research.This analysis was used to draw conclusions regarding the strengths and weaknesses of each of the schedulers studied.The performance level of the schedulers was also defined by a set of criteria considered to be highly effective evaluation criteria.The second part of this paper concerns our main contribution.A new scheduler, called IFMR (Improved Fairness of MaxRate), was proposed.The objective of this new proposal is to guarantee perfect fairness among different users in a cell in the first place, optimize system throughput in the second place and maximize the number of satisfied users in the third place.These three main objectives have made this work a cornerstone upon which our main research is based.In this paper, our principal contribution is based on a proposed new scheduler, namely IFMR, and this new scheduler was subjected to a comparative study, allowing us to differentiate ourselves from what already exists in the literature, such as RR, Max-SNR and PF.We also evaluated the performance of this new scheduler proposed.The simulation results showed a significant improvement in performance compared to previous metrics.It was concluded and confirmed by numerical simulation that our contribution allowed us to: • Ensure perfect fairness for the three levels of fairness exceeding those of other schedulers, • Effectively optimize system throughput compared to PF and RR, and guarantee throughput close to that obtained by the MaxSNR algorithm, • Ensure better quality of service (QoS) and maximize the number of satisfied users by meeting users' needs in terms of necessary throughput.
Future work can be done to maximize throughput and promote fairness by improving the scheduling algorithms, such as PF and MaxSNR.The aim would be to propose a scheduler that can benefit the users involved in the proper functioning of the network and possibly penalize others.While opportunistic scheduling algorithms have advantages in terms of maximizing throughput, fairness and service differentiation, another area worth exploring would be to study how to make routing algorithms using an opportunistic approach.With such systems, and after our initial research in this area, network throughput could be greatly increased.

Fig. 7
Fig. 7 Unfairness problem induced by the geographic location of users

Fig. 18
Fig. 18 Allocation of RUs according to IFMR

Fig. 19
Fig.19 Measurement of the three levels of equity in the system: case of scenario 1

Fig. 20
Fig. 20 Measurement of the three levels of equity in the system: case of scenario 2

Fig. 21
Fig. 21 Evaluation of the system throughput in Scenarios 1 and 2

Fig. 22 Fig. 23
Fig. 22 Number of satisfied users: Scenario 1 [37,38]-aware QoS scheduling algorithm the active user that has the highest SNR [signal-to-noise ratio (SNR)][37,38].If we denote the maximum number of bits that can be transmitted during a time interval of the subcarrier n if it is allocated to user k as b k,n , the MaxSNR allocation consists of allocating the time interval and subcarrier n to the user i that has the highest b k,n .

Table 2
Comparison between different algorithms

Table 4
Simulation parameters related to the study of fairness Parameters Scenario A Scenario B Scenario C