QoS-aware composite scheduling using fuzzy proactive and reactive controllers
© Khan et al.; licensee Springer. 2014
Received: 10 March 2013
Accepted: 13 July 2014
Published: 21 August 2014
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) long-term evolution (LTE)/LTE-A 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 delay-sensitive and best-effort traffic). QoS-aware scheduling strategies, such as modified largest weighted delay first (M-LWDF), exponential (EXP), exponential proportional fair (EXP-PF), and the log-based scheduling rules, prioritize delay-sensitive traffic by considering rules based on the head-of-line (HoL) packet delay and the tolerated packet loss rate, whereas they serve best-effort traffic by considering the classical proportional fair (PF) rule. These scheduling rules do not prevent resource starvation for best-effort traffic. On the other side, if both traffic types are scheduled according to the PF rule, then delay-sensitive 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 intra-class and inter-class fairness than state-of-the-art scheduling rules. The proposed scheduling framework enables to appropriately balance delay requirements of traffic, system throughput, and fairness.
3rd Generation Partnership Project (3GPP) Release 8, and its subsequent modifications, define the long-term evolution (LTE) standard  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 trade-off 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 channel-aware and channel-unaware, 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 end-user 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 sub-bands.
In [2–5], resource allocation is modeled as a convex optimization problem. The water-filling 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.
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 delay-sensitive applications and does not provide a priority differentiation between delay-sensitive and best-effort flows.
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) , modified largest weighted delay first (M-LWDF) , and exponential proportional fair (EXP-PF)  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  for delay-sensitive applications over an LTE system. According to , M-LWDF is the best scheduling rule for delay-sensitive applications in terms of fairness and efficiency. A very good survey on these scheduling strategies for LTE is provided in . 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 multi-user 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 delay-sensitive traffic, these scheduling rules cannot provide fairness for users with relatively low signal-to-interference noise ratio (SINR) .
In this work, we address the following issues of the third class of strategies:
Intra-class fairness issues for delay-sensitive traffic: scheduling rules for delay-sensitive traffic consider the ratio of instantaneous channel quality and time-averaged throughput (proportional fair rule) along with either the linear , logarithmic , or exponential [11, 15] function of the head-of-line (HoL) delay . 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 delay-sensitive 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.
Inter-class fairness issues: in the literature , composite scheduling rules serve the best-effort traffic by using the classical proportional fair rule, i.e., ratio of instantaneous channel quality to the time-averaged throughput [9, 17–19]. They prioritize delay-sensitive 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 delay-sensitive and best-effort traffic classes. In other words, the higher the difference among the scheduling priorities of traffic classes, the lower will be the multi-user channel diversity exploitation. In LTE, multi-user channel diversity has more significance since it is a multi-carrier system which allows multi-user diversity exploitation in the time and frequency domain.
By using the concept of fuzzy logic priority , we couple the flow’s delay urgency (ratio of packet’s HoL delay and delay bound) with the time-averaged channel quality. Instead of exploiting the time-averaged throughput and the linear, logarithmic, or exponential function of the HoL delay, we use a fuzzy function of the HoL delay coupled with time-averaged channel quality as introduced in . In , the HoL delay along with the time-averaged 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 delay-sensitive as well as the best-effort 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 delay-sensitive 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 delay-sensitive as well as the best-effort 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 logic-based 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/LTE-A system. The single-cell 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 delay-sensitive traffic, we consider video and VoIP traffic (the scheduling framework can accommodate all LTE service classes), whereas for best-effort 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 delay-sensitive 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 best-effort traffic. We consider the HoL delay for best-effort traffic, and we assign a target delay for the flows of this traffic class. However, since we can assume best-effort 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 is the instantaneous subband spectral efficiency of user i at PRB φ. χmax is a constant, i.e., the spectral efficiency (5.5547 bits/s/Hz) corresponding to the maximum CQI feedback, and MPRB is the number of PRBs available for allocation at each scheduling epoch.
Given the available information about:
the HoL packet delay for each flow ,
the channel quality of each flow on each PRB, hence the resulting spectral efficiency ,
the tolerated delay bound Hmax,
the QoS performance of the delay-sensitive flows in terms of packet loss ratio, and of the best-effort flows in terms of time-averaged throughput ,
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 trade-off between fairness and efficiency is achieved.
In order to mathematically formulate the problem, let us define the following parameters:
: Throughput achieved by flow i at scheduling instant n.
I: Total number of flows in the system. It is the sum of delay-sensitive Idelay-sensitive and best-effort Ibest-effort flows.
: Number of transmitted packets of flow i over the moving average transmission window t w .
: Number of dropped packets of flow i over the moving average transmission window t w .
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 plrthr. If the packet loss rate exceeds the threshold, then the indicator function is 0. It is important to note that fairness for delay-sensitive traffic is guaranteed when the PLR over a short moving average window , for instance one second, is below the prescribed threshold for each of the delay-sensitive flows in the system. As noted in , when the scheduler achieves short-term fairness, then the long-term 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 PRB-independent part and a PRB-specific part. The PRB-independent part calculated for a user describes the ‘urgency’ of an assignment as time-domain priority, whereas the PRB-specific 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.
If is low AND is low THEN μ p is medium
If is low AND is high THEN μ p is low
If is high AND is low THEN μ p is high
If is high AND 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.
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, and , 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 and are fuzzified by the low membership function as shown in the figure.
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 if-then-else 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.
‘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.
3.2 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, .
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 time-averaged 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 time-averaged 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 ( and ) and reactive ( and ) inputs.
3.3 Dynamic resource controller
If is low AND is low THEN μ max is high
If is high AND is low THEN μ max is low
If is high AND is high THEN μ max is low
If is low AND 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, μmax is maximum as given by the centroid of the highest area triangle membership function as shown in Figure 6. On the other hand, μmax 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.
The main rationale of utilizing DRC is to serve the following three goals:
Utilization of delay tolerant nature of the best-effort traffic: according to the policy guidelines of the QoS architecture in the 3GPP standard, the resource allocation probability of the best-effort traffic class should be minimum in situations where the network becomes congested with delay-sensitive traffic. When the traffic load reaches the network capacity, the increase in average packet’s latency of the delay-sensitive traffic decreases the maximum limit of the output fuzzy set for the best-effort flows as shown in Figure 7. Since best-effort traffic is delay tolerant, the decreased maximum limit of the output fuzzy set ensures delay-sensitive traffic gets priority over best-effort 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 delay-sensitive and best-effort 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 delay-sensitive flows w.r.t the best-effort 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 delay-sensitive flows causes a reduction in the output fuzzy set of the best-effort traffic as shown in Figure 7. When the network becomes heavily congested, then delay bound violations occur for the delay-sensitive flows. The delay bound violation further reduces the output fuzzy set of the best-effort traffic as shown in Figure 7. Thus, decreasing the resource allocation probability of the best-effort 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 state-of-the-art scheduling rules serve best-effort flows with the classical delay-insensitive PF rule and prioritize the delay-sensitive 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 delay-sensitive and best-effort 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
where is the average throughput at scheduling instant n-1. is the number of bits transmitted at scheduling instant n-1. n w is the size of the time-average window also known as the exponential averaging constant. The higher the size of the time-average window, the higher the impact of the instantaneous channel quality.
4.2 Simulation scenario
Simulation parameters - downlink LTE scheduling for delay-sensitive and best-effort traffic
Bandwidth, carrier frequency
5 MHz, 2.1 GHz
UE distribution, cell radius
Uniform, 1 km
3GPP-TU (typical urban)
Log-normal shadow fading
Up to 3 synchronous
Block fading (1 ms)
15 to 100 km/h (users moving
independently at variable speed)
CQI averaging method
Mutual information effective
Hmax, PLRthr (video)
Hmax, PLRthr (VoIP)
100 ms, 1% 
Hmax, Rmin (best-effort)
300 ms, 200 Kbps 
Number of video, VoIP and
18, 27, and 9
Average rate requirements
530, 64, and 400 Kbps
VoIP and best-effort users
n c (Time-averaged channel
and n w (Time-averaged
It has been reported in  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 best-effort and VoIP traffic. Specifically, we selected a loaded network with 64% video, 11% VoIP, and 25% best-effort 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  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 time-averaged channel quality over the period, n c =100 ms. All the benchmark scheduling rules utilize the time-averaged 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 delay-sensitive and best-effort traffic.
Tunable parameters for FCS strategy
set for video
set for VoIP
4.3 Results and discussion
Next, we analyze the impact of the time-domain parameter α t . An increase in the time-domain priority parameter (FCS3, Figure 9) allocates relatively more resources to the worst channel flows since time-domain priority is a fuzzy function of the HoL packet delay, PLR, and time-averaged 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 delay-sensitive flows. Under high load, the time-domain priority of the delay-sensitive flows will always be higher than best-effort flows. Therefore, increase in α t will further enhance the priority difference and results in a reduction in the throughput of best-effort flows.
When compared to the state-of-the-art scheduling rules, the FCS strategy improves the fairness performance for delay-sensitive 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, state-of-the-art 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 delay-sensitive 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 delay-sensitive 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 state-of-the-art scheduling rules prioritize best-effort flows by using the classical proportional fair Eq. 21. These rules prioritize delay-sensitive 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 best-effort and delay-sensitive flows, as given in Equation 19. The priority differentiation between the best-effort and delay-sensitive 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 multi-user channel diversity across all the flows. This allows FCS rule to achieve intra-class and inter-class fairness which is not the case in state-of-the-art scheduling rules. The priority of the best-effort traffic class is dynamic and changes according to the QoS performance of the delay-sensitive flows.
We proposed a composite scheduling strategy for downlink scheduling at the MAC layer for delay-sensitive 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 intra-class as well as inter-class fairness. The design of the scheduling rule is robust, and it serves well in diverse channel and rate requirements.
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