 Research Article
 Open access
 Published:
Fairness and QoS Guarantees of WiMAX OFDMA Scheduling with Fuzzy Controls
EURASIP Journal on Wireless Communications and Networking volumeÂ 2009, ArticleÂ number:Â 512507 (2009)
Abstract
A fairness and QoS guaranteed scheduling approach with fuzzy controls (FQFCs) is proposed for WiMAX OFDMA systems. The controllers, respectively, adjust priority and transmission opportunity (TXOP) for each WiMAX connection according to QoS requirements and service classes. The FQFC provides intra and interclass fairness guarantees by making connections within the same class achieve equal degree of QoS while at the same time making those without QoS requirements equally share the remaining resources. Even in dynamic environments such as mobile WiMAX networks with timevariant traffic specifications, the FQFC fairly guarantees delay, throughput, and jitter, which are seldom achieved at the same time by stateoftheart solutions.
1. Introduction
IEEE 802.16 standard (WiMAX) [1, 2] is one of the most popular standards for fixed and mobile broadband wireless access systems to provide last mile access. Due to various users with diverse QoS requirements and wireless communication technologies, the resource scheduler plays an important role to provide fairness and QoS guarantees. As summarized in [3], a resource scheduler in wireless multimedia networks needs to possess the following features: efficient link utilization, delay bound, low implementation complexity, throughput, scalability, and fairness.
For WiMAX and OFDMA systems, various scheduling algorithms have been proposed for achieving QoS guarantees. For example, Liu et al. [4] proposed a prioritybased scheduler which assigns each connection a priority updated according to QoS parameters and channel state and then assigns time slots to connections according to the order of priority values. The method has low implementation complexity because the scheduler simply updates the priority of each connection per frame and allocates time slots to the connection with the highest priority. However, it does not consider fairness and jitter issues which are important metrics for realtime applications. To maintain low implementation complexity under considering fairness and jitter, we use the prioritybased scheduling scheme for initial priority assignment and afterward, the proposed a fairness and QoS guaranteed scheduling approach with fuzzy controls (FQFC) mechanism takes care of the scheduling job using fuzzy control approach. Many algorithms have been proposed to deal with the fairness problem, and can be briefly divided into two categories. The first category is to reduce the resource allocation problem into an optimization problem. Based on the optimization theory, for example, [5, 6] have good performance on spectrum efficiency and system utilization. They formulate the crosslayer optimization problem to maximize the average utility of all active users subject to certain constraints. However, in addition to implementation complexity, these methods still suffer some problems. To achieve optimal spectrum efficiency, the optimization approaches may, on the other hand, fail to provide QoS guarantees. Moreover, the relation between traffic specifications and network state is uncertain. Uncertainty and dynamics in mobile environment make exact modeling of objective function and constraints impossible when performing the optimization steps. In this paper, the FQFC adopts fuzzy control technique to deal with the modeling problem. The reason we use fuzzy control is to tackle uncertainty and dynamics in wireless communication environment. Among soft computing methods, inference based on probability theory is also widely used for modeling uncertainty and dynamics. However, the controller based on probability must rely on statistical observations to perform inference. Correctness of statistical information is based on the law of large number. In case that gathering large amount of statistic information in short time is difficult, it will be infeasible. Moreover, inference based on probability usually assumes some specific probability model for result of feedback observation to follow. As shown in [7], a single model usually fails to represent the behaviors of dynamic environments such as mobile wireless networks with sudden bursts or changes.
The second category is a utilitybased scheduler. A utility function is a measure of relative satisfaction from users' requirements. The schemes in [8, 9] apply utility functions to maximize the total utility of all connections. Utilitybased optimization approaches did guarantee QoS of some connections but also starve others. On the other hand, some approaches such as [10, 11] propose utilityfair bandwidth adaptation schemes for multiclass traffic in wireless networks. Rather than achieving resource fairness, the bandwidth adaptation schemes make sure that all connections can obtain similar utility values to achieve the socalled utility fairness. These schemes are effective in both achieving utility fairness and increasing network resource utilization. However, the utilityfair schemes may fail to provide QoS guarantees since it does not consider the priority of the connections.
In this paper, our objective is to provide efficient control for both QoS and fairness guarantees of WiMAX OFDMA scheduling. For QoS guarantees, we address the problem of headofline (HOL) delay and jitter control for real time applications and throughput control for nonrealtime applications. The FQFC scheduler assigns each connection a priority and TXOP, and adjusts them according to channel quality, QoS requirements, and service classes. Due to uncertainty and dynamics of the environment, it is difficult to find out the mapping between priority and QoS requirements. For fuzzy inference, it is the simplest way to model a complex system when there is few and uncertain information available. In the field of controller design, fuzzy controller is one of the most popular approaches. Moreover, fuzzy control has been widely used in researches on communication networks such as [7, 12â€“17]. However, there are few articles talking about using fuzzy control for WiMAX. In this paper, the FQFC model is developed for WiMAX OFDMA systems and is proved that both fairness and QoS are guaranteed. Other fuzzy control methods [14â€“17] may be proved to achieve certain degree of QoS. However, fairness is seldom assured in these and stateoftheart approaches. Then, we define two types of fairness including intraclass and interclass fairness. To achieve intraclass fairness, we set up a reference goal to each connection according to the QoS requirements, and make the connections achieve the goal by priority scheduling and TXOP allocation. If each connection can achieve its QoS requirement, intraclass fairness is guaranteed. For achieving interclass fairness, the FQFC does not allocate superfluous resources out of what required. Compared to stateoftheart methods, connections of highpriority classes release more resources to lower priority ones. Thus, the FQFC makes the connections without QoS requirements evenly share the remaining resources. Based on the priority scheduling and TXOP allocation methods, the FQFC provides both intraclass and interclass fairness with QoS guarantees and featuring low implementation complexity.
This paper is organized as follows. In Section 2, we introduce background including network configuration, MAC QoS, PHY resource allocation, and fairness descriptions. Section 3 describes the FQFC mechanism and depicts the design of the fuzzy controllers for each service class. In Section 4, we investigate the mechanism performance of QoS and fairness through simulations. Finally, we conclude the paper in Section 5.
2. Background
2.1. Network Configuration
WiMAX specifies two communication modes which form different topologiesâ€”pointtomultipoint (PMP) and mesh modes. In PMP mode, a base station (BS) centrally allocates downlink (from BS to SS) and uplink (from SS to BS) resources to subscriber stations (SSs). All SSs are only allowed to communicate with a BS. In mesh mode, SS can act as a router to assist its neighbor to relay data. In the 802.16 standard, this mode is optional and is not discussed in this paper. Hence, we focus on proposing a downlink scheduling algorithm to provide QoS guarantees in PMP mode.
IEEE 802.16 WiMAX PHY adopts the orthogonal frequencydivision multiple access (OFDMA) technology based on OFDM modulation. The OFDMA technology allows multiple users transmitting packets at the same OFDMA symbol via different subchannels, such that wireless resources are utilized ultimately.
2.2. Scheduling Services in MAC Layer
IEEE 802.16 MAC protocol is connectionoriented; each connection is assigned a connection ID (CID) and a single scheduling service determined by a set of QoS parameters. Four scheduling services in the 802.16 standard are supported: unsolicited grant service (UGS), realtime polling service (rtPS), nonrealtime polling service (nrtPS), and best effort (BE). The UGS supports realtime constant bitrate data streams, such as voice over IP (VoIP) without silence suppression. The QoS parameters of UGS service are minimum reserved traffic rate, the tolerated jitter, maximum latency, and request/transmission policy. The rtPS supports realtime variablerate data streams, such as MPEG video or VoIP with silence suppression. The QoS parameters of rtPS are maximum latency, request/transmission policy, minimum reserved traffic rate, and traffic priority. The nrtPS supports delaytolerant variablerate data streams, such as FTP. The QoS parameters of nrtPS are minimum reserved traffic rate, request/transmission policy, and traffic priority. The BE supports besteffort data streams. The QoS parameter is request/transmission policy. In IEEE 802.16e [2], an additional service class called extended realtime polling service (ertPS) has superior efficiency than both UGS and rtPS. It supports realtime variablerate data streams, such as VoIP with silence suppression. The QoS parameters of ertPS are minimum reserved traffic rate, maximum latency, request/transmission policy, and the tolerated jitter. Hence, considering the QoS requirements of the four class services, we calculate the reference goal as traffic specification (TSPEC) according to these QoS parameters.
2.3. Resource Allocations in PHY Layer
IEEE 802.16 OFDMA system defines two types of subcarrier permutations, distributed subcarrier permutation and adjacent subcarrier permutation. The former permutation type includes partially and fully used subcarriers (PUSC and FUSC) which are pseudorandomly selected and grouped into subchannels, while the later includes adaptive modulation and coding (AMC), and only adjacent subcarriers are clustered to form subchannels. Dispersing noise and interference in fast changing environment, the PUSC and FUSC modes are suitable for mobile networks. For AMC mode, the BS allocates appropriate subchannels for connections with larger SNR to enhance system performance, and it is suitable for fixed or low mobility environment. To support mobile WiMAX, the FQFC scheduling and allocation are based on distributed subcarrier permutation.
In OFDMA, the basic allocation unit is a slot that composes of one subchannel along with an OFDMA symbol, such that the resource allocation becomes a twodimensional problem. By using the distributed subcarrier permutation, all subchannels are the socalled equally adequate for all SSs [18], and our resource allocation is based on Raster algorithm [18], in which the frame is filled row by row, from left to right and from top to bottom, and efficiently reduces the burst numbers.
2.4. Fairness
In wireless networks, the fairness definition is not straightforward. As described in [19], a fair resource allocation usually does not produce equal connection data rate because the diverse connections also suffer from diverse channel conditions, network states, and dynamics. The dynamics result from mobility and timevariant traffic specifications (TSPECs). Moreover, WiMAX needs to provide QoS guarantees for four classes of scheduling services. Therefore, for fairness, it is necessary to consider QoS guarantees for different class connections. We define two types of fairness described as follows.

(i)
Intraclass fairness: the connections within the same class achieve equal degree of QoS.

(ii)
Interclass fairness: the connections with QoS requirements achieve exactly their demands, and those without QoS requirements equally share the remaining resources.
Hence, our objective is to achieve both intraclass and interclass fairness.
2.5. Fuzzy Controller
Classical controller requires modeling of the physical reality. This is significant in control problems; however, it is difficult or even impossible to construct precise mathematical models. The difficulty may result from timevariant system behaviors, dynamics, and uncertainty in mobile wireless communication environment. Fuzzy controllers perform well under these circumstances. A general fuzzy controller consists of four components: a fuzzifier, a fuzzy rule base, a fuzzy inference engine, and a defuzzifier. The interconnections among these components and the controlled process are shown in Figure 1. The fuzzifier maps crisp input into appropriate fuzzy sets to express uncertainties. The fuzzy inference engine uses the fuzzified measurements to evaluate the fuzzy implication results. Finally, the defuzzifier deals with confliction of fuzzy implications and transforms the fuzzy implication results back to the crisp output. Two conditions are usually monitored by the controller: error and the derivative of the error . With and , the fuzzy controller issues control actions.
3. Design of the Proposed Scheduling Mechanism
In this section, we describe the scheduling mechanism for multiple connections with various QoS requirements. The FQFC scheduler assigns two variables with fuzzy inference values for each connection with CID , that is, the priority and the maximum number of packets that connection can transmit in a frame duration. The FQFC scheduler first initializes the two variables based on the characteristics of connections and adjusts them, respectively, by two fuzzy controllers to adapt to the dynamics of system. As shown in Figure 2, the priority controller adjusts according to channel quality, QoS requirements, and service classes. With the priority, the FQFC decides the transmission order of connections. The TXOP controller adapts according to transmission rate and the queue length difference between two contiguous transmissions of the MAC layer.
3.1. Controller Design for ertPS & rtPS
Unlike the UGS class having the highest priority that constant bandwidth can be achieved by allocating fixed number of slots [1], the two service classes, rtPS and ertPS, that both support the realtime variable bitrate data streaming require efficient and effective control to achieve QoS guarantees and fairness. A realtime connection of these two classes usually has two QoS specifications, maximum allowable latency (deadline) and jitter. The FQFC control for realtime connections comprises three steps: (1) set up goal delay and tolerable range, (2) adjust priority according to recent HOL delay, and (3) adjust TXOP according to the jitter requirement. The main idea is that the FQFC maintains the delay and jitter of each connection below the delay and jitter goals, respectively. First, we set the goal delay and the tolerable range. Figure 3 shows the control mechanism for realtime connections. Goal delay controller determines goal delay and tolerable range bounded by the lower and upper bounds. Then, the priority controller decides transmission order of connections, and the TXOP controller decides the number of transmitted packets to maintain the jitter. We describe the design of the three controllers as follows.
3.1.1. Goal Delay Controller
The purpose of the goal delay controller is to control delay and jitter within a tolerable range. If the delay exceeds the tolerable range, the FQFC increases the priority. If the delay is below the tolerable range, the FQFC decreases the priority. As shown in Figure 2, to avoid packet dropping, the goal delay is below the deadline. Since system load and transmission rate affect HOL delay obviously, we use them to decide the goal delay. Due to uncertainty and that the TSPEC changes rapidly in mobile WiMAX environment, we cannot use exact formulation to represent the goal delay. Therefore, we divide the delay space into three parts and use fuzzy sets S (small), M (medium), and L (large) to represent these three parts, respectively. Then, we decide which part that the goal delay belongs to according to the system load and transmission rate. The goal delay controller selects a goal delay and sets its upper and lower bounds to form a tolerable range for control. We denote , , and as the goal delay of connection in the th frame and its upper and lower bounds, respectively. The goal delay controller uses triangular and trapezoidal membership functions as shown in Figure 4. The fuzzy input variables are system load (SL) and transmission rate (TR), and the output function is the goal delay (GD). The fuzzy sets of SL, TR, and GD are defined as follows:
â€‰
â€‰
â€‰
According to system load, the controller decides the goal delay by the following fuzzy rules.

(R1)
If system load is L, then is S.

(R2)
If system load is M, then is M.

(R3)
If system load is H, then is L.
The following controller uses normalized data rate with respect to the transmission rate in the highest modulation mode to decide the goal delay .

(R1)
If transmission rate is F, then is S.

(R2)
If transmission rate is M, then is M.

(R3)
If transmission rate is S, then is L.
Using Mandamni implication and the centroid defuzzifier, we obtain the outputs, and . Considering system load and transmission rate, the final goal delay is
where and are the weighting factors of system load and transmission rate, respectively.
With goal delay and required jitter , we define and as the upper and lower bounds of the tolerable range, where and .
3.1.2. Priority Controller for Real Time Services
Figure 5 shows the control system including the priority controller, the WiMAX system plant, and the delay observer. The delay observer detects the HOL delay . Then, the priority controller compares it with the delay requirement , and adjusts priority . If is around zero, the control system is stabilized around the requirement.
In our design, we denote negative, zero, and positive forces with fuzzy singletons S, M, and L. The control actions of these singletons at the conclusion parts of fuzzy rules are as follows:
S:
M:
L:
where is the priority influence of connection in the th frame. The priority controller must confirm that the HOL delay will not exceed the deadline. Hence, it adapts according to the time duration between goal delay and the deadline. Let be the deadline, be the guard time before the deadline, be the maximum priority of realtime connections, and be the frame duration. Then, we have
As we can see in (2), when the goal delay is closer to the deadline, the adaptation force of the priority is larger. We depict the priority initialization and controlled direction as follows.
(a) Priority Setting. When the connection is in an initial stage or the HOL delay is below , the priority controller assigns the connection a priority according to channel quality, QoS requirement, and service classes. For a realtime connection , the priority in the th frame is assigned by (3) which was proposed in [4]:
where is the maximum priority of realtime connections, is the data rate of connection in the highest modulation mode, and is the data rate of connection in the th frame. is the normalized data rate and the connection with high received SNR results in higher priority. is the delay requirement indicator:
where is the deadline, is the guard time before the deadline, and denotes the HOL delay. If , the larger denotes the higher satisfaction of delay requirement, which causes lower priority. If , the HOL delay has been over the guard time of deadline. The connection should get resources immediately to avoid packet losses. Hence, the priority is set as . When is zero, the connection is under deep fading and should not be scheduled.
(b) Priority Controller. Let the controller action be the priority . One of the input is the difference between the actual value of the observed HOL delay and the desired value , that is, . The universe of is . The variable has three linguistic values N, E, and P which represent fuzzy concepts "Negative," "Equal," and "Positive," respectively. The fuzzy sets N, E, and P are characterized by the membership functions shown in Figure 6.
The other input of the controller is the difference between two errors, which is defined as . Substituting to , we obtain . The universe of is . The linguistic values of , , , and also representing fuzzy concepts "Negative," "Equal," and "Positive," respectively, are characterized by the membership functions as shown in Figure 7, where and . Sign of these values constitutes four cases as shown in Figure 7. The membership functions are timevariant and change along with the variable .
We consider four cases to design the fuzzy rule base as follows.
Case 1.
If HOL delay is too large, that is, , the priority should be increased with the large (L) step.
Case 2.
If , maintaining priority at the median (M) level is fine.
Case 3.
If , maintaining priority at the median (M) level is fine.
Case 4.
If HOL delay is too small, that is, , the priority should be decreased with negative decrement (S).
Therefore, expanding the above cases with changing rate , we have the linguistic inference rules

(R1)
If is P and is , then is L,

(R2)
If is P and is , then is M,

(R3)
If is P and is , then is M,

(R4)
If is E and is , then is M,

(R5)
If is E and is , then is M,

(R6)
If is E and is , then is M,

(R7)
If is N and is , then is M,

(R8)
If is N and is , then is M,

(R9)
If is N and is , then is S.
Using Mandamni implication and the centroid defuzzifier, we obtain the control action responding each HOL delay .
The priority controller makes the delay fall in the tolerable range which is below the deadline. Hence, each connection in the realtime class achieves the QoS specification, while intraclass fairness is guaranteed. When the delay is below the tolerable range, the controller decreases the priority for releasing the resources. This scheme guarantees the jitter and interclass fairness at the same time.
(c) Priority Adaptation for Fairness. For making the connections within the same class achieve equal degree of QoS, the priority controller adapts by further considering the packet loss rate. All connections should receive the same packet loss rate. To compensate the packet losses in the th frame, we define the loss rate as and the scaling by
where is a constant to normalize the loss rate according to the predefined precision. According to (5), if the connection drops packets due to out of the deadline, the priority controller allocates more resources by increasing the priority for achieving intraclass fairness. Even if all connections are in an extremely bad environment, they will suffer the same loss rate.
3.1.3. TXOP Controller
The TXOP controller initiates the TXOP based on frame duration and packet interval of the th connection as (6)
According to deficit round robin [20], the TXOP increases as the number of packets in a queue increases. Let denote the number of packets in queue in the th frame. The controller stores the bounded difference in the deficit counter of connection in the th frame. Then, we add to as follows:
To avoid burst transmission, TXOP has an upper bound in
3.2. Controller Design for nrtPS
The nrtPS connection supports delaytolerant variablerate data streams and guarantees minimum reserved rate. The control mechanism for nrtPS connections can be divided into three steps: (1) setting up minimum reserved rate and an upper bound, (2) adjusting the priority according to average throughput of nrtPS connections and the required jitter of realtime connections, and (3) adjusting TXOP of nrtPS connections according to the required jitter. Figure 8 shows the control mechanism for nrtPS connection.
If the average throughput is lower than minimum reserved rate, the priority controller raises the priority to increase the throughput. Moreover, the controller needs to prevent large jitter from overhigh priority. Besides, if the average throughput exceeds the upper bound, the controller decreases the priority to release the resource. We depict the controller design as follows.
3.2.1. Priority Controller
The priority controller in nrtPS class is easier than in the realtime class. The QoS requirement is only to guarantee the minimum reserved rate. Hence, we do not use fuzzy control and simply use the prioritybased scheduler for nrtPS connections. Let denote the average throughput of connection in the th frame, and let denote the instantaneous data rate of connection in the th frame. The average throughput in the th frame is usually estimated over a time constant using moving average as
where means connection is scheduled in the th frame.
For an nrtPS connection , the priority in the th frame is defined as
where is the priority decrement, is the maximum priority of nrtPS connection, and is the throughput requirement indicator which is the ratio of average throughput with respect to the minimum reserved rate
If , the throughput requirement is satisfied, and the controller decreases the priority to release resource. When implying that the average throughput is less than the minimum reserved rate, the connection should get more resources immediately to achieve the requirement. Hence, at this time, the priority is set to the maximum . The priority decrement is further defined as
where is the packet length, is the upper bound of which is the maximum sustained rate in the traffic specification, and is a constant representing system load.
3.2.2. TXOP Setting
For nrtPS, the FQFC sets according to the throughput upper bound as
3.2.3. TXOP Adaptation for Fairness
For intraclass fairness, all nrtPS connections should have the same throughput ratio of average throughput with respect to minimum reserved rate. Via setting the upper bound in (13), we control the average throughput within the range between the minimum reserved rate and the upper bound, and we make the throughput ratio of all nrtPS connections the same. For interclass fairness, the average throughput will not exceed the upper bound. Hence, we can release more resources to the connections without QoS requirements.
3.3. Controller Design for BE
3.3.1. Priority Setting
For a BE connection , the priority in the th frame is defined as
where is the maximum priority of BE connection. All BE connections have the same priority. For intraclass fairness, we adopt the round robin scheduling for BE connections.
3.3.2. TXOP Setting
For fair resource allocation, the FQFC sets the according to the frame duration and the packet interval of the th connection as (14):
In this paper, we also perform priority adaptation. Therefore, the overhead, especially the complexity, will be slightly higher than that of the priorityonly method. Since in centralized PMP mode, all traffic flows are managed by base stations which have much more powerful computing ability than SSs, the additional computation overhead will not give any sensibly negative effect. Moreover, the proposed controllers do not use any control/management packets for fairness and QoS purposes. There is no additional network overhead caused by the proposed FQFC.
4. Evaluations and Simulation Results
We first introduce intraclass and interclass fairness criteria and then according to these criteria, we evaluate the performances of the fairness.
4.1. Fairness Criteria
The descriptions of fairness indices are as follows.
4.1.1. Intraclass Fairness Index
Intraclass fairness means that the connections within the same class achieve equal QoS guarantees. Because the connections in different service classes have different QoS requirements, we define respective intraclass fairness indices for realtime, nrtPS, and BE classes.
(a) RealTime Connection. A connection belonging to the realtime class requires strict maximum allowable latency (deadline) and the tolerated jitter. Packet loss occurs when packet delay is out of the deadline. Hence, we use loss rate and jitter to evaluate the intraclass fairness of realtime connections. We define a realtime indicator as
where , , and are the loss rate, jitter, and the tolerated jitter of connection , respectively. If the jitter is larger than the tolerated jitter, the connection does not achieve QoS guarantees and we set the realtime indicator to one. Otherwise, we set the realtime indicator as the loss rate. Then, we utilize the realtime indicator to compute the real time fairness index. If the realtime indicators of all connections are closer to each other, the better intraclass fairness is achieved. We define the realtime fairness index as the standard deviation of the realtime indicators of all rtPS connections as follows:
where is the number of connections in the real time class, and is the average realtime indicator. Thus, a smaller value of represents better intraclass fairness of the realtime class.
(b) nrtPS Connection. A connection belonging to the nrtPS class requires minimum reserved rate. Hence, we use the average throughput to evaluate the intraclass class fairness of nrtPS connections. We define a nrtPS indicator as
where and are the average throughput and minimum reserved rate of connection , respectively. Then, we introduce the throughput indicator to compute the nrtPS fairness index. The nrtPS fairness index is defined as the standard deviation of the throughput indicator of connections in the same nrtPS class as follows:
where is the number of connections in nrtPS class, and is the average nrtPS indicator. Similar to the , a smaller value represents better intraclass fairness of the nrtPS class.
(c) BE Connection. A connection belonging to BE requires no QoS metrics. We introduce the average throughput to compute the BE fairness index. The BE fairness index is defined as the standard deviation of the average throughput of connections in the same BE class as follows:
where is the number of connections in BE class, and is the average throughput in the BE class. Smaller represents better intraclass fairness of the BE class.
4.1.2. Interclass Fairness Index
According to the definition of interclass fairness, the interclass fairness has two folds: (1) the connections with QoS requirements achieve the demands; (2) the connections without QoS requirements equally share the remaining resources.
For the first fold, we introduce a requirement indicator to show the degree of the connection close to the demands as
where is a tunable parameter which determines the tolerable range. and are the average state and the QoS goal of class , respectively. In the realtime class, the average state is the mean loss rate, and its goal loss rate is zero. In the nrtPS class, the QoS parameter is the average throughput, and the goal is the minimum reserved rate. The smaller the difference between the average state and the QoS goal is, the larger requirement indicator is. When the mean allocated resources for a class are away from the requirement, no matter above or below the goal, the requirement indicator decreases. When the allocated resources reach the requirements exactly, not only the QoS is guaranteed but also the remaining resources are most preserved at the same time.
The BE class has no QoS requirement. For the second part, we introduce Jain's fairness index [21] as the BE fairness index:
where is the number of connections without QoS requirements. The index equals to one indicates perfect fairness in the class without QoS requirements. Then, we utilize the requirement indicator and the BE fairness index to define the interclass fairness index as follows:
In (23), is the number of classes with QoS requirements, and is the weighting factor of class , which determines the importance of the class. and are the weighting factors of the classes with and without QoS requirements, respectively. In contrast to the indices of intraclass fairness, a larger value indicates better interclass fairness.
4.2. Simulation Configuration
The parameters used in this simulation are listed in Table 1, where OFDM FFT size represents the number of subcarriers an OFDMA symbol composes. The packet length is 1024 bits, and the maximum priority of each service class is and , and for best effort, . The weighting factors , , in (23) are all 0.5. Each connection uses a fixed modulation. The FQFC allocates fixed number of time slots to UGS connections. The FQFC adopts persistent resource allocation [1, 22, 23] for UGS service because it has the highest priority. We focus on the performance of realtime, nrtPS, and BE connections. Besides, in our survey, the prioritybased scheduler was proposed only for WiMAX OFDM PHY [4]. FQFC outperforms many stateofthe art schedulers for WiMAX OFDM PHY. To present the improvement by FQFC, we modify the prioritybased scheduler in [4] to work with WiMAX OFDMA PHY by using the Raster algorithm and regard it as the priorityonly scheduler. Then, FQFC fuzzy controllers further improve the fairness and QoS performance of the priorityonly scheduler. There are four simulation scenarios as follows.

(i)
Scenario 1. We set 20 realtime connections. The QoS requirements of realtime connection are the loss rate, deadline, and required jitter. The traffic rates of connections are 8 connections in 1â€‰Mbps, 10 connections in 500â€‰kbps, and 2 connections in 250â€‰kbps. This scenario is to verify the guarantees of maximum latency, the tolerated jitter, and the intraclass fairness in realtime class. It is difficult to find out the mapping between priority and QoS requirements. We prove that the FQFC can efficiently control the delay.

(ii)
Scenario 2. We set 10 realtime connections and 10 nrtPS connections. The QoS parameter of nrtPS connection is the minimum reserved rate. The traffic rates are 2 realtime connections in 1â€‰Mbps, 8 realtime connections in 500â€‰kbps, 5 nrtPS connections in 1â€‰Mbps, and 5 nrtPS connections in 500â€‰kbps. This scenario is to verify the guarantees of minimum reserved rate and fair resource allocation of the FQFC scheme.

(iii)
Scenario 3. We set 10 realtime connections, 10 nrtPS connections, and 10 BE connections. BE connection has no QoS requirement. The traffic rates are 1 realtime connection in 1â€‰Mbps, 9 realtime connections in 500â€‰kbps, 3 nrtPS connections in 750â€‰kbps, 2 nrtPS connections in 500â€‰kbps, 5 nrtPS connections in 1â€‰Mbps, and 10 BE connections in 100â€‰kbps. This scenario is to verify the fair resource allocation of FQFC.

(iv)
Scenario 4. In this scenario, we simulate the wireless link degrades. This will cause the modulation to change. The experiment is designed to test the robustness of the FQFC whether it can efficiently track the goal delay when the channel quality degrades. The simulated network consists of 1 BS and 10 SS (numbered from 1 to 10). In the downlink, each SS with number has 1 realtime, 1 nrtPS, and 1 BE connection with CID , , , respectively. The connections from SS1 to SS5 apply with QPSK modulation, and connections from SS6 to SS7 apply with 16QAM modulation. All the other connections initially adopt 64QAM modulation. This is for simulating the different channel conditions.
4.3. Performance Evaluation for Fairness and QoS Guarantees
4.3.1. Scenario 1: Intraclass Fairness and QoS Guarantees of Real Time Connections
We compare the FQFC with the priorityonly scheduler [4]. The QoS is in terms of average delay, delay jitter, and packet loss rate. As illustrated in Figure 9, although the priorityonly scheduler controls delay of connection to be below the deadline, it cannot guarantee tolerant jitter. Under the same simulation conditions, FQFC guarantees both delay and jitter requirements as shown in Figure 10. The average delay is close to the goal delay. The result also shows that it is useful by controlling the HOL delay in the tolerable range to guarantee the required jitter.
For intraclass fairness evaluation, from Figure 10, we can see that the jitter of the connections using FQFC is still smaller than the tolerated jitter in Figure 9. Figure 11 shows the delay outage probabilities of the FQFC and the priorityonly scheduler. The FQFC disperses the outage probability for intraclass fairness. Moreover, as summarized in Table 2, the intraclass fairness index of the FQFC is much lower than the one of the priorityonly scheduler and is almost near to zero. Hence, the FQFC guarantees the intraclass fairness for realtime connections.
4.3.2. Scenario 2: Intraclass Fairness and QoS Guarantees of RealTime and nrtPS Connections
For QoS evaluation, we introduce the throughput indicator defined as the ratio of the average throughput with respect to the minimum reserved rate. In Figures 12 and 13, even adding nrtPS connections, the FQFC still guarantees the delay and jitter specifications of realtime connections. Then, we evaluate nrtPS connections by throughput indicators. Figure 14 shows that all nrtPS connections with FQFC control keep their throughput indicators almost the same about 1.15. The result means that the FQFC guarantees minimum reserved rate. For the connections with priorityonlybased scheduler [4], the throughput indicators of the last four nrtPS connections are higher than the others since priorityonlybased scheduler provides more resources to the connections using highbitrate modulation. The FQFC focuses on making the connections of the same class achieve the equal degree of QoS. As illustrated in Table 2, for nrtPS, the intraclass fairness index of the FQFC is close to zero which is much lower than the one of the priorityonly scheduler. Hence, the FQFC also guarantees the intraclass fairness for the connections of the nrtPS class.
4.3.3. Scenario 3: Intraand Interclass Fairness and QoS Guarantees of All Classes
For QoS evaluation, Figures 15, 16, and 17 show that the FQFC guarantees the delay and jitter of realtime connections as well as guarantees the throughput of nrtPS connections. Even for users with diverse QoS requirements, the FQFC still provides QoS guarantees. For BE connections, although they have no QoS requirement, the remnant resources should be fairly allocated to all BE connections. In Figure 18, BE connections under FQFC control obtain throughputs and are not starved.
For intraclass fairness evaluation of the BE class, we compare the FQFC with the priorityonly scheduler regarding average throughput. Figure 18 shows that the average throughputs of all BE connections under the FQFC control are nearly the same. The priorityonly scheduler provides more resource to the last four BE connections since they employ higher rate modulation. Table 2 shows that the intraclass fairness index of the FQFC is close to zero, which is much lower than the one of the priorityonly scheduler. For every realtime connection, FQFC sets the goal delay below the deadline for a certain distance in terms of the tolerable jitter. Since the goal is for priority and TXOP controllers to follow, intraclass fairness is achieved when realtime connections have almost the same loss rate and jitter performances based on the intraclass fairness criteria. For nrtPS connections, the FQFC control algorithm maintains their ratios of throughput achievement over minimum reserved rate as close to 1 as possible. Again, as long as BE connections can evenly share the remained resources from realtime and nrtPS connections, intraclass fairness of BE connections is achieved. Hence, the FQFC guarantees the intraclass fairness for the BE classes.
For interclass fairness evaluation, in Figure 17, the throughput indicator of the FQFC is lower than the one of the priorityonly scheduler since the FQFC always preserves resources for lower priority classes. This causes the BE connections get more resources. For interclass fairness comparison, the FQFC outperforms priorityonly scheduler as shown in Figure 18. Table 3 shows that the interclass fairness index of the FQFC is close to one. Hence, in addition to intraclass fairness, the FQFC also guarantees the interclass fairness. For priorityonly scheduler, every realtime connection grabs as many channel resources as possible. Though delays can be lower than the deadlines, delay and jitter differences among connections are not maintained. For nrtPS connections, the differences of throughput ratios are not controlled in priorityonly scheduler. The differences of channel resources grasped by the BE connections are, therefore, obvious.
4.3.4. Scenario 4: Link Degradation
In this scenario, we evaluate the robustness of the FQFC against wireless link degradation. At the 4.0th second, the wireless link from BS to SS3 degrades, and the PHY layer adaptation mechanism changes the modulation over this link from 64QAM to QPSK. At the 6.0th second, this link recovers to 64QAM. Figures 19 and 20, respectively, show the PDU delay of realtime connection 3 and the average throughput of nrtPS connections 13 in SS3, where the link degradation occurs at the 4.0th second. Figure 20 also shows the average throughput of nrtPS connection 13 which is an external connection out of SS3. Figure 21 shows the average throughput of BE connections 23 and 25. The simulation shows that

(i)
when the link degradation occurs, the FQFC adjusts the goal delay and the tolerable range according to the updated modulation. The FQFC continues to make the delay of realtime connection 3 fall in the tolerable range as shown in Figure 19. Hence, the FQFC can efficiently control the delay according to the goal delay and the tolerable range;

(ii)
the service curves of nrtPS connections 11 and 13 in Figure 20 distinguish a throughput drop from the 4.0th second to the 6.0th second, whereas FQFC still maintains the throughput to meet the QoS requirements. The service curves of BE connections 23 and 25 in Figure 21 also distinguish a throughput drop from the 4.0th second to the 6.0th second. The resources are released to guarantee the QoS of realtime connection 7 as shown in Figure 19. For intraclass fairness in nrtPS connections and BE connections, all nrtPS connections keep almost the same resource usage ratio. For interclass fairness, nrtPS and BE connections release resources to guarantee the QoS of realtime connections. Hence, the FQFC guarantees both QoS and fairness even in case that wireless link degrades.
5. Conclusions
A fairness and QoS guaranteed scheduling approach with fuzzy controls FQFC algorithm is proposed for WiMAX OFDMA systems. Different from the utilityfairness, new fairness and QoS evaluation criteria in terms of loss rate, jitter, and throughput are proposed for different classes. The proposed FQFC scheme controls the delay, jitter, and throughput QoS parameters efficiently providing both fairness and QoS guarantees. Rather than using hard computation approaches such as utilitybased optimizations, we use fuzzy controller to perform scheduling and resource allocations to resolve mapping among priority, transmission opportunity, and QoS requirements. The proposed FQFC scheme provides both intra and interclass fairness guarantees in addition to QoS guarantees while implementation is with low complexity.
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Chen, CL., Lee, JW., Wu, CY. et al. Fairness and QoS Guarantees of WiMAX OFDMA Scheduling with Fuzzy Controls. J Wireless Com Network 2009, 512507 (2009). https://doi.org/10.1155/2009/512507
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DOI: https://doi.org/10.1155/2009/512507