QoSaware composite scheduling using fuzzy proactive and reactive controllers
 Nabeel Khan^{1}Email author,
 Maria G Martini^{1} and
 Dirk Staehle^{2}
https://doi.org/10.1186/168714992014138
© Khan et al.; licensee Springer. 2014
Received: 10 March 2013
Accepted: 13 July 2014
Published: 21 August 2014
Abstract
We consider in this paper downlink scheduling for different traffic classes at the MAC layer of wireless systems based on orthogonal frequency division multiple access (OFDMA), such as the recent 3rd Generation Partnership Project (3GPP) longterm evolution (LTE)/LTEA wireless standard. Our goal is to provide via the scheduling decisions quality of service (QoS), but also to guarantee fairness among the different users and traffic classes (including delaysensitive and besteffort traffic). QoSaware scheduling strategies, such as modified largest weighted delay first (MLWDF), exponential (EXP), exponential proportional fair (EXPPF), and the logbased scheduling rules, prioritize delaysensitive traffic by considering rules based on the headofline (HoL) packet delay and the tolerated packet loss rate, whereas they serve besteffort traffic by considering the classical proportional fair (PF) rule. These scheduling rules do not prevent resource starvation for besteffort traffic. On the other side, if both traffic types are scheduled according to the PF rule, then delaysensitive flows suffer from delay bound violations. In order to fairly distribute the resources among different service classes according to their QoS requirements and channel conditions, we employ the concept of fuzzy logic in our scheduling framework. By employing the fuzzy logic concept, we serve all the traffic classes with one priority rule. Simulation results show better intraclass and interclass fairness than stateoftheart scheduling rules. The proposed scheduling framework enables to appropriately balance delay requirements of traffic, system throughput, and fairness.
1 Introduction
3rd Generation Partnership Project (3GPP) Release 8, and its subsequent modifications, define the longterm evolution (LTE) standard [1] that will take the cellular technology in the 2020s. In wireless communication systems, radio resources are shared by multiple users; hence, medium access control (MAC) layer scheduling becomes extremely important in determining the overall performance of an LTE system. The efficiency of the link level, from the LTE base station (eNodeB) to the mobile terminal, largely depends on the design of the scheduler, whose task is to determine which users should be served and to assign resources.
An efficient scheduler must ensure a good tradeoff between efficiency and fairness in the system (according to the service needs of each user) by fully utilizing the available radio resources. MAC layer scheduling strategies can be classified as channelaware and channelunaware, where channel aware scheduling algorithms take channel conditions into account and maximize the system throughput. Note, however, that the main target of mobile operators would be the enduser satisfaction, not merely the maximization of system throughput. Scheduling in the LTE standard is more challenging than in earlier standards mainly because earlier standards were based on single carrier systems, where resources were usually divided in terms of time slots or codes among the users, whereas LTE is a multicarrier system where system resources are shared among users in terms of time and frequency subbands.
 1.
In [2–5], resource allocation is modeled as a convex optimization problem. The waterfilling algorithm is used to solve the convex optimization problem by considering a continuous objective function. Linear integer programming is also widely used in solving the resource allocation problem by first transforming the nonlinear optimization problem into a linear problem. The main drawback of these strategies is the high computation complexity. Since the transmission time interval (TTI) in LTE is only 1 ms, these algorithms are not feasible from an implementation point of view.
 2.
In the second class of approaches, such as in [6–8], scheduling is performed in two steps. The first step consists of resource allocation, which determines the number of resources allocated to each user. The resource allocation step is followed by the resource assignment step, which determines which resources are assigned to each user. This class of scheduling algorithms are specifically designed for delaysensitive applications and does not provide a priority differentiation between delaysensitive and besteffort flows.
 3.
The third approach is the adaptation of TDMA strategies for OFDMA systems. Scheduling rules designed for single carrier systems such as the proportional fair (PF) [9], modified largest weighted delay first (MLWDF) [10], and exponential proportional fair (EXPPF) [11] are adapted for an OFDMA system by calculating these rules on each resource. This adaptation is referred to as an OFDMA/TDMA strategy. These scheduling rules are analyzed by [12] for delaysensitive applications over an LTE system. According to [12], MLWDF is the best scheduling rule for delaysensitive applications in terms of fairness and efficiency. A very good survey on these scheduling strategies for LTE is provided in [13]. As each of these scheduling rules are based on the proportional fair rule, the calculation of these scheduling metrics on each physical resource block (PRB) allows the exploitation of multiuser time and frequency diversities. The complexity of the OFDMA/TDMA approach grows linearly with the number of users and resources. Thus, it can be implemented in real time. However, for delaysensitive traffic, these scheduling rules cannot provide fairness for users with relatively low signaltointerference noise ratio (SINR) [14].
In this work, we address the following issues of the third class of strategies:

Intraclass fairness issues for delaysensitive traffic: scheduling rules for delaysensitive traffic consider the ratio of instantaneous channel quality and timeaveraged throughput (proportional fair rule) along with either the linear [10], logarithmic [15], or exponential [11, 15] function of the headofline (HoL) delay [16]. The HoL delay refers to the amount of time packets that reside in the buffer and is also known as the sojourn time. It is important to note that the video is delaysensitive traffic; hence, packets arriving late are generally not useful at the receiver. Therefore, packets are associated with a predefined HoL delay bound and packets violating the delay bound are dropped from the queue. The utilization of HoL delay and the proportional fair rule in the scheduling decisions are not sufficient to avoid delay bound violation of flows having lower channel quality. Video traffic exhibits highly variable bit rate characteristics, i.e., the instantaneous peak rate is higher than the average rate. Lower channel quality video flows exhibiting peak instantaneous rate have high probability of delay bound violation mainly because of the proportional fair rule in the scheduling decisions. In other words, these scheduling rules achieve higher HoL delay for the packets of flows having higher average rate and lower channel quality. On the other hand, flows having good channel quality and lower average rate are scheduled way before their delay bound. The probability of delay bound violation of the flows exhibiting lower channel quality and higher average rate is very high which results in an unfair system.

Interclass fairness issues: in the literature [13], composite scheduling rules serve the besteffort traffic by using the classical proportional fair rule, i.e., ratio of instantaneous channel quality to the timeaveraged throughput [9, 17–19]. They prioritize delaysensitive traffic by considering either the logarithmic, exponential, or linear function of the HoL delay. However, such composite scheduling strategies result in a higher priority difference between the delaysensitive and besteffort traffic classes. In other words, the higher the difference among the scheduling priorities of traffic classes, the lower will be the multiuser channel diversity exploitation. In LTE, multiuser channel diversity has more significance since it is a multicarrier system which allows multiuser diversity exploitation in the time and frequency domain.
By using the concept of fuzzy logic priority [20], we couple the flow’s delay urgency (ratio of packet’s HoL delay and delay bound) with the timeaveraged channel quality. Instead of exploiting the timeaveraged throughput and the linear, logarithmic, or exponential function of the HoL delay, we use a fuzzy function of the HoL delay coupled with timeaveraged channel quality as introduced in [21]. In [21], the HoL delay along with the timeaveraged channel quality is processed by a fuzzy proactive controller. Further, whenever a flow suffers a delay bound violation, the scheduler reacts to this event and increases the priority of that flow. The delay bound violation input is processed by a fuzzy reactive controller. In this work, we propose a composite scheduling rule for delaysensitive as well as the besteffort traffic. In the earlier work, the scheduling rule considers only the video traffic. In this work, the scheduling rule and scenarios are extended to handle more than one delaysensitive traffic types. Furthermore, the main goal of the proposed composite scheduling rule is to balance the probabilities of quality of service (QoS) violation of the delaysensitive as well as the besteffort traffic types.
The remainder of this paper is organized as follows. Section 2 presents the considered system model and the problem statement. Section 3 presents the details of our fuzzy logicbased scheduling strategy. Section 4 presents the performance evaluation of the proposed approach. In particular, the solutions considered as benchmark for the assessment of our scheduling algorithm are presented in Section 4.1, whereas the simulation setup is presented in Section 4.2; results are presented and discussed in Section 4.3. Conclusions are drawn in Section 5.
2 System model and problem statement
We consider a multiuser downlink single input single output (SISO) LTE/LTEA system. The singlecell scenario comprises an eNodeB MAC scheduler responsible for allocating PRBs to different users in the cell. Each user i is assigned a buffer at the eNodeB, and packets of different traffic classes are streamed into the buffer of the eNodeB. For delaysensitive traffic, we consider video and VoIP traffic (the scheduling framework can accommodate all LTE service classes), whereas for besteffort traffic, we consider constant bit rate (CBR) traffic. The packets of each traffic class entering the buffer are time stamped by the scheduler. Packets of delaysensitive traffic are dropped from the buffer if the HoL packet delay is longer than the target HoL delay bound. The main QoS parameters for video and VoIP flows are the HoL packet delay and the packet loss rate (PLR), whereas throughput is the important QoS parameter for the flows of besteffort traffic. We consider the HoL delay for besteffort traffic, and we assign a target delay for the flows of this traffic class. However, since we can assume besteffort traffic is delay tolerant, therefore, packets violating the target HoL delay are not dropped from the buffer. We use a CQI feedback mechanism, where each user feedbacks information about the channel quality on each PRB. Due to the adoption of adaptive modulation and coding (AMC) in LTE, each CQI value corresponds to a specific value of spectral efficiency for each PRB.
is the average PRB spectral efficiency of user i at scheduling instant n and ${\mathrm{\chi}}_{i,\phi}^{\left(n\right)}$ is the instantaneous subband spectral efficiency of user i at PRB φ. χ_{max} is a constant, i.e., the spectral efficiency (5.5547 bits/s/Hz) corresponding to the maximum CQI feedback, and M_{PRB} is the number of PRBs available for allocation at each scheduling epoch.
Given the available information about:

the HoL packet delay for each flow ${H}_{i}^{\left(n\right)}$,

the channel quality of each flow on each PRB, hence the resulting spectral efficiency ${\mathrm{\chi}}_{i,\phi}^{\left(n\right)}$,

the tolerated delay bound H_{max},

the QoS performance of the delaysensitive flows in terms of packet loss ratio, ${\text{plr}}_{i}^{\left(n\right)}$ and of the besteffort flows in terms of timeaveraged throughput ${R}_{i,\text{ave}}^{\left(n\right)}$,
the scheduling problem is defined as: How to allocate to the different users the M_{ PRB }PRBs in each scheduling interval in order to fulfill the QoS requirements of each of the flows from different traffic classes so that a good tradeoff between fairness and efficiency is achieved.
In order to mathematically formulate the problem, let us define the following parameters:
${R}_{i}^{\left(n\right)}$: Throughput achieved by flow i at scheduling instant n.
I: Total number of flows in the system. It is the sum of delaysensitive I_{delaysensitive} and besteffort I_{besteffort} flows.
where
${P}_{{\text{transmit}}_{i}}^{\left(m\right)}$: Number of transmitted packets of flow i over the moving average transmission window t_{ w }.
${P}_{{\text{drop}}_{i}}^{\left(m\right)}$: Number of dropped packets of flow i over the moving average transmission window t_{ w }.
where
$1\phantom{\rule{0.3em}{0ex}}\text{I}\left({\text{plr}}_{i}^{\left(n\right)}\le {\text{plr}}_{\text{thr}}\right)$ is an indicator function equal to 1 if its argument is true, i.e., when the packet loss rate of flow i is lower or equal than the threshold value plr_{thr}. If the packet loss rate exceeds the threshold, then the indicator function is 0. It is important to note that fairness for delaysensitive traffic is guaranteed when the PLR over a short moving average window [22], for instance one second, is below the prescribed threshold for each of the delaysensitive flows in the system. As noted in [23], when the scheduler achieves shortterm fairness, then the longterm fairness is guaranteed.
The optimal solution of the above problem is not possible without restrictive assumptions on the arrival process of the traffic and changes in channel quality. Therefore, we propose a novel scheduling framework relying on fuzzy logic. Fuzzy logic is ideally suited for problems where a definite mathematical solution is unavailable. The information about the changes in the radio channel and the traffic rate of each user is uncertain. Fuzzy logic can deal with such situations because of its capability to make approximate reasoning. In our proposed scheduling strategy, each PRB is assigned to the user maximizing a defined metric. Our proposed metric is composed of a PRBindependent part and a PRBspecific part. The PRBindependent part calculated for a user describes the ‘urgency’ of an assignment as timedomain priority, whereas the PRBspecific part describes the instantaneous channel quality of the PRB and its relative quality versus other PRBs.
3 Fuzzy composite scheduling framework
The FCS framework consists of fuzzy proactive, reactive, and DRC controllers. It is important to note that the designs of the proactive and reactive controllers are the same. The proactive controller processes the HoL delay whereas the reactive controller processes the QoS violation. In the following, we present a detailed design of the three fuzzy controllers:
3.1 Proactive controller
The rationale behind the weighted sum Equation 7 is discussed in Section 3.1.1.
 1.
If ${H}_{i}^{\prime}$ is low AND ${\chi}_{{H}_{i}^{\prime}}$ is low THEN μ _{ p } is medium
 2.
If ${H}_{i}^{\prime}$ is low AND ${\chi}_{{H}_{i}^{\prime}}$ is high THEN μ _{ p } is low
 3.
If ${H}_{i}^{\prime}$ is high AND ${\chi}_{{H}_{i}^{\prime}}$ is low THEN μ _{ p } is high
 4.
If ${H}_{i}^{\prime}$ is high AND ${\chi}_{{H}_{i}^{\prime}}$ is high THEN μ _{ p } is medium
where low, medium, and high are the output membership functions as shown in Figure 2 and μ_{ p } is the crisp output which along with the reactive controller output quantifies the time domain priority of each user. The main motivation of using the low, medium, and high output membership functions is to prioritize flows suffering from lower channel quality and higher HoL delay. The priority of the users with relatively good channel quality increases from low to medium as the HoL delay increases. On the other hand, the priority of users with lower channel quality increases from medium to high. Therefore, fairness is incorporated in the scheduling decisions through the output membership functions and rules of the fuzzy controllers. The main goal of the frequency domain priority is to improve the system efficiency whereas the time domain priority provides fairness through fuzzy proactive and reactive controllers.
 1.
Fuzzification. This is the process of converting fuzzy input values into a degree of membership for each linguistic term. Each linguistic term, high, medium, and low, characterizes a membership function. For instance, the proactive controller inputs, ${H}_{i}^{\prime}$ and ${\chi}_{{H}_{i}^{\prime}}$, as shown in Figure 4, are fuzzified by the input membership functions low and high. In the figure, the four rows are the four rules of the proactive controller. Rule one comprises only low membership function, therefore input ${H}_{i}^{\prime}$ and ${\chi}_{{H}_{i}^{\prime}}$ are fuzzified by the low membership function as shown in the figure.
 2.
Fuzzy inference. This is the core process of the fuzzy logic system, comprising a mapping from a given input to an output using the membership functions and logical operators in the ifthenelse rules. According to Figure 4, the AND logical operation is performed, according to which the minimum of the two fuzzified inputs is mapped to the output membership function. The result of the fuzzy inference process is the degree of the output membership functions fulfilled by the logical operations between the fuzzified inputs. The result is the truncated output membership functions as shown in the third column of Figure 4.
 3.
‘Defuzzification’ and production of the final ‘crisp’ output. The crisp proactive priority output μ _{ p } produced is shown in Figure 4. The output of each rule is combined to give the final fuzzy set, as shown in the fifth row and third column in Figure 4. The defuzzification process is simply the centroid calculation on the final fuzzy set as shown in Figure 4.
3.1.1 Rationale
3.2 Reactive controller
It is a requirement of the fuzzy logic system that the inputs of the fuzzy controller should lie within the input fuzzy set, i.e., in between 0 and 1. Therefore, we normalize the input with respect to the flow having the maximum QoS violation, ${V}_{j,\text{max}}^{\left(n\right)}$.
3.2.1 Rationale
The rationale behind the design of the reactive controller is the same as that of the proactive controller discussed in Section 3.1.1. The weighted sum of the normalized QoS violations and the timeaveraged channel quality with weights equal to 0.5 makes the system opportunistic (exploiting instantaneous channel improvements) and QoS aware as discussed in Section 3.1.1. The input and output membership functions and the output fuzzy set is the same as that of the proactive controller. It is important to note that we could have used all the inputs, i.e., the HoL packet delay, the QoS violations, and the timeaveraged channel quality, and design a fuzzy priority scheme by defining a set of rules for these three inputs. However, this increases the complexity of the system because, with three inputs, eight rules and more than three output membership functions are required. A fuzzy logic system with two inputs is simpler in terms of implementation and processing. Therefore, by using the same rules and membership functions, the same fuzzy module is called for proactive (${H}_{i}^{\prime}$ and ${\chi}_{{H}_{i}^{\prime}}$) and reactive (${V}_{i}^{\prime}$ and ${\chi}_{{V}_{i}^{\prime}}$) inputs.
3.3 Dynamic resource controller
 1.
If $\overline{{H}_{i}^{\prime}}$ is low AND $\overline{{V}_{i}^{\prime}}$ is low THEN μ _{max} is high
 2.
If $\overline{{H}_{i}^{\prime}}$ is high AND $\overline{{V}_{i}^{\prime}}$ is low THEN μ _{max} is low
 3.
If $\overline{{H}_{i}^{\prime}}$ is high AND $\overline{{V}_{i}^{\prime}}$ is high THEN μ _{max} is low
 4.
If $\overline{{H}_{i}^{\prime}}$ is low AND $\overline{{V}_{i}^{\prime}}$ is high THEN μ _{max} is medium
The input degree of membership is determined by the trapezoidal input membership functions. A lower average packet delay and loss rate causes rule 1 to have a higher degree of membership. Therefore, μ_{max} is maximum as given by the centroid of the highest area triangle membership function as shown in Figure 6. On the other hand, μ_{max} is set to minimum when a higher average HoL delay and packet loss rate causes the smallest area triangle to be defuzzified through rule 2 and rule 3. If the normalized average delay is lower and average PLR is higher than the medium area, triangle is defuzzified as given in rule 4.
3.3.1 Rationale
The main rationale of utilizing DRC is to serve the following three goals:

Utilization of delay tolerant nature of the besteffort traffic: according to the policy guidelines of the QoS architecture in the 3GPP standard, the resource allocation probability of the besteffort traffic class should be minimum in situations where the network becomes congested with delaysensitive traffic. When the traffic load reaches the network capacity, the increase in average packet’s latency of the delaysensitive traffic decreases the maximum limit of the output fuzzy set for the besteffort flows as shown in Figure 7. Since besteffort traffic is delay tolerant, the decreased maximum limit of the output fuzzy set ensures delaysensitive traffic gets priority over besteffort traffic.

Channel diversity exploitation: the main goal of the scheduler is to maximize the system throughput subject to maintaining the deadline violations below the prescribed threshold (Equation 5). At lower normalized average packet latency, the priority difference between the delaysensitive and besteffort flows is minimal. Hence, flows from different traffic classes are scheduled based on their QoS performance and channel quality. Utilization of same output fuzzy set for the DRC, proactive, and reactive controllers: the prioritization of the delaysensitive flows w.r.t the besteffort traffic can be achieved by using the same output fuzzy set for the proactive, reactive, and DRC controllers. When the output fuzzy set of these controllers are same, then the increase in latency of the delaysensitive flows causes a reduction in the output fuzzy set of the besteffort traffic as shown in Figure 7. When the network becomes heavily congested, then delay bound violations occur for the delaysensitive flows. The delay bound violation further reduces the output fuzzy set of the besteffort traffic as shown in Figure 7. Thus, decreasing the resource allocation probability of the besteffort traffic.
3.4 Time domain priority
where α_{ t } is the time domain fairness parameter which enables the operator of the system to tune the fairness level. The higher the value of α_{ t }, the higher will be the time domain priority of users suffering from relatively poor channel quality, higher HoL delay, and higher QoS violations.
3.5 Frequency domain priority
The time domain priority, by utilizing past and current CQI feedbacks, considers the channel quality over a small window. The goal of the time domain priority is to control the fairness among the users. On the other hand, the goal of the frequency domain priority is to improve the system efficiency by considering only the current CQI feedback. Due to multipath propagation and interference from the neighboring users, there is a variable amount of fading on the PRBs of each user. Efficiency as well as fairness can be enhanced if this information is utilized. By employing the CQI feedbacks on each of the PRBs, information on the interference and multipath propagation can be obtained [28, 29].
3.6 Final scheduling priority metric
It is important to note that stateoftheart scheduling rules serve besteffort flows with the classical delayinsensitive PF rule and prioritize the delaysensitive traffic by considering the HoL packet delay. We use the same priority equation given in 19 for all the traffic classes; dynamic prioritization between the delaysensitive and besteffort classes is achieved by using the DRC. More details on the prioritization of different traffic classes is given in the following sections.
4 Performance evaluation
4.1 Benchmark scheduling rules
Benchmark scheduling rules for delaysensitive traffic
Strategy  Priority function 

MLWDF [12]  ${\gamma}_{i}\phantom{\rule{2.35982pt}{0ex}}\frac{{\mathrm{\chi}}_{i,\phi}^{\left(n\right)}}{{R}_{i,\text{ave}}^{\left(n\right)}}\phantom{\rule{2.35982pt}{0ex}}{H}_{i}^{\left(n\right)}$ 
MLWDFQ [39]  ${\gamma}_{i}\phantom{\rule{2.35982pt}{0ex}}\frac{{\mathrm{\chi}}_{i,\phi}^{\left(n\right)}}{{R}_{i,\text{ave}}^{\left(n\right)}}\phantom{\rule{2.35982pt}{0ex}}{N}_{{Q}_{i}}^{\left(n\right)}$ 
EXPPF [12]  ${\gamma}_{i}\phantom{\rule{2.35982pt}{0ex}}\frac{{\mathrm{\chi}}_{i,\phi}^{\left(n\right)}}{{R}_{i,\text{ave}}^{\left(n\right)}}\phantom{\rule{2.35982pt}{0ex}}exp\left(\frac{{\gamma}_{i}{H}_{i}^{\left(n\right)}\overline{{\gamma}_{i}{H}_{i}^{\prime}}}{1+\sqrt{\overline{{\gamma}_{i}{H}_{i}^{\prime}}}}\right)$ 
EXPPFQ [39]  ${\gamma}_{i}\phantom{\rule{2.35982pt}{0ex}}\frac{{\mathrm{\chi}}_{i,\phi}^{\left(n\right)}}{{R}_{i,\text{ave}}^{\left(n\right)}}\phantom{\rule{2.35982pt}{0ex}}exp\left(\frac{{\gamma}_{i}{N}_{{Q}_{i}}^{\left(n\right)}\overline{{\gamma}_{i}{N}_{{Q}_{i}}^{\left(n\right)}}}{1+\sqrt{\overline{{\gamma}_{i}{N}_{{Q}_{i}}^{\left(n\right)}}}}\right)$ 
LOGRULE [15]  ${b}_{i}\phantom{\rule{2.35982pt}{0ex}}log\left[1.1+\left({a}_{i}\frac{{H}_{i}^{\left(n\right)}}{{H}_{i,\text{max}}^{\left(n\right)}}\right)\right]\phantom{\rule{2.35982pt}{0ex}}\underset{i,\phi}{\overset{\left(n\right)}{\mathrm{\chi}}}$ 
EXPRULE [15]  ${b}_{i}\ast \mathit{\text{exp}}\left[\frac{\left({a}_{i}\frac{{H}_{i}^{\left(n\right)}}{{H}_{i,\text{max}}^{\left(n\right)}}\right)}{1+\sqrt{\overline{{H}_{i}^{\prime}}}}\right]\phantom{\rule{2.35982pt}{0ex}}{\mathrm{\chi}}_{i,\phi}^{\left(n\right)}$ 
where ${R}_{i,\text{ave}}^{(n1)}$ is the average throughput at scheduling instant n1. ${R}_{i}^{(n1)}$ is the number of bits transmitted at scheduling instant n1. n_{ w } is the size of the timeaverage window also known as the exponential averaging constant. The higher the size of the timeaverage window, the higher the impact of the instantaneous channel quality.
4.2 Simulation scenario
Simulation parameters  downlink LTE scheduling for delaysensitive and besteffort traffic
Parameters  Value 

Simulator  
Bandwidth, carrier frequency  5 MHz, 2.1 GHz 
UE distribution, cell radius  Uniform, 1 km 
Channel  3GPPTU (typical urban) 
Pathloss model  HataCost231 model 
Shadowing model  Lognormal shadow fading 
HARQ  Up to 3 synchronous 
retransmissions  
Channel fading  Block fading (1 ms) 
UE speed  15 to 100 km/h (users moving 
independently at variable speed)  
CQI averaging method  Mutual information effective 
SNR mapping  
(MIESM) [37]  
H_{max}, PLR_{thr} (video)  
H_{max}, PLR_{thr} (VoIP)  100 ms, 1% [32] 
H_{max}, R_{min} (besteffort)  300 ms, 200 Kbps [32] 
Number of video, VoIP and  18, 27, and 9 
besteffort users  
Average rate requirements  530, 64, and 400 Kbps 
for video,  
VoIP and besteffort users  
n_{ c } (Timeaveraged channel  100 ms 
quality window)  
and n_{ w } (Timeaveraged  
throughput window) 

It has been reported in [35] that by 2015, approximately 66% of mobile’s traffic (in terms of petabytes per month) will be video and the proportion of VoIP traffic will be a minority. Therefore, the proportion of traffic in our simulation scenario is dominated by video followed by the besteffort and VoIP traffic. Specifically, we selected a loaded network with 64% video, 11% VoIP, and 25% besteffort traffic (in terms of average input traffic at the eNodeB).

The proposed scenario corresponds to an average input traffic rate of 14.868 Mbps. In order to evaluate the channel utilization in terms of average spectral efficiency, we simulate an optimum sum rate maximization strategy. The optimum strategy maximizes the system throughput without considering the delay constraints. The average channel quality (in terms of SINR) of the users is set such that the total system throughput, sum throughput of all the flows, produced by the throughput maximization strategy [36] is 13.6 Mbps (2.72 bits/s/Hz). This corresponds to a heavily loaded system where the input traffic is approximately 110%, in terms of bits/s/Hz, of the maximum system capacity. Our main goal is to study the fairness and efficiency performance of the proposed and benchmark scheduling rules when the delay bound and packet loss threshold constraints are considered.
We consider the timeaveraged channel quality over the period, n_{ c }=100 ms. All the benchmark scheduling rules utilize the timeaveraged throughput. In order to have a fair comparison, the exponential averaging constant n_{ w } is set to 100 ms. In the literature, the optimum size of the exponential averaging constant is from 100 to 1,000, with the 100 being utilized in scenarios yielding high fairness in terms of throughput.
The FCS scheduling strategy has the following tunable parameters:

The time domain fairness parameter α_{ t } mainly used to adjust the fairness level.

The output fuzzy set for the DRC, proactive, and reactive controllers. As discussed in Section 3.3.1, the same output fuzzy set is utilized for all the controllers. The membership functions and fuzzy rules of the DRC are set such that by utilizing the same output fuzzy set for all the controllers, dynamic prioritization is achieved between the delaysensitive and besteffort traffic.
Tunable parameters for FCS strategy
Strategy  Output fuzzy  Output fuzzy  α _{ t } 

set for video  set for VoIP  
FCS1  {0, 2}  {0, 2}  2 
FCS2  {0, 2}  {0, 2.2}  2 
FCS3  {0, 2}  {0, 2.2}  3 
4.3 Results and discussion
Next, we analyze the impact of the timedomain parameter α_{ t }. An increase in the timedomain priority parameter (FCS3, Figure 9) allocates relatively more resources to the worst channel flows since timedomain priority is a fuzzy function of the HoL packet delay, PLR, and timeaveraged channel quality. It is important to note that the proportion of video traffic (18 flows with average rate requirements of 540 kbps) is high with respect to the VoIP traffic (27 flows with rate requirements of 64 kbps). Therefore, an increase in α_{ t } results in a significant improvement for video flows as shown in Figure 9. In other words, more resources are allocated to the lower channel quality video flows and as a result, their PLR is reduced at the expense of a slight increase in the PLR of VoIP flows. There is also a marginal increase in the PLR of good channel video flows. According to the figure (FCS3, Figure 9), the worst served video flow has a PLR of approximately 5.4% and the worst served VoIP flow suffers from a PLR of 1.6%. Thus, the FCS3 mode results in an improved fairness performance for the delaysensitive flows. Under high load, the timedomain priority of the delaysensitive flows will always be higher than besteffort flows. Therefore, increase in α_{ t } will further enhance the priority difference and results in a reduction in the throughput of besteffort flows.
When compared to the stateoftheart scheduling rules, the FCS strategy improves the fairness performance for delaysensitive flows mainly due to the fact that this scheduling rule considers the channel quality of a user in a novel way, by taking into account the past and current CQI feedbacks in the time domain priority metric. This allows the users with relatively low channel quality and high HoL delay to be prioritized in the time domain. As a result, the difference in the average waiting time of each flow’s packet is low. On the other hand, stateoftheart scheduling rules favor the good channel quality flows by serving them way before their packet’s delay bound. These scheduling rules are highly unfair for the cell edge users as they require a substantial increase in the SINR of the cell edge users so that their packet’s delay bound requirements are met. In the FCS scheduling strategy, the PLR over the moving average window is kept below the threshold for each of the delaysensitive flows in the system. Therefore, this rule balance different flows’ probabilities of QoS violations. It is important to note that the FCS strategy requires an admission controller to limit the arrival rate of delaysensitive traffic within the achievable rate region. Since fairness is incorporated in the scheduling decisions, an increase in the arrival rate above the system capacity violates the QoS performance of the flows already being served.
All stateoftheart scheduling rules prioritize besteffort flows by using the classical proportional fair Eq. 21. These rules prioritize delaysensitive flows by using the linear, logarithmic, or exponential functions of the HoL delay as reported in Section 4.1. On the other hand, the FCS scheduling rule uses the same priority function for the besteffort and delaysensitive flows, as given in Equation 19. The priority differentiation between the besteffort and delaysensitive traffic classes is controlled by adapting the maximum limit of the output fuzzy set. The same priority function for each traffic class allows the exploitation of multiuser channel diversity across all the flows. This allows FCS rule to achieve intraclass and interclass fairness which is not the case in stateoftheart scheduling rules. The priority of the besteffort traffic class is dynamic and changes according to the QoS performance of the delaysensitive flows.
5 Conclusions
We proposed a composite scheduling strategy for downlink scheduling at the MAC layer for delaysensitive traffic in wireless systems based on OFDMA. This strategy uses novel concept of providing fairness using fuzzy logic membership functions and its rule base, instead of relying on the rate based proportional fair strategies employed in the literature. Furthermore, we provide a framework for service class differentiation among different traffic classes by utilizing the fuzzy logic priority scheme. Our approach leads to a framework which provides intraclass as well as interclass fairness. The design of the scheduling rule is robust, and it serves well in diverse channel and rate requirements.
Declarations
Authors’ Affiliations
References
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