Feedback control algorithm for optimal throughput in IEEE 802.11e EDCA networks

ABSTRACT The minimum contention window () value of the EDCA protocol gives priority access to the different categories of traffic on the WLAN and also affects the rate of collision and delays experienced on the WLAN. In the IEEE 802.11e standard, the values for the parameter are recommended values and should be adapted to WLAN conditions for optimal performance of the network but these recommended values are generally used as the de facto values for contention on the WLAN. This is due to the difficulty of assessing current conditions on the WLAN in real time due to the dynamic nature of the WLAN. In this paper, we propose a dynamic feedback based control algorithm (FCA) that assesses the WLAN and outputs contention window value with respect to number of active nodes on the WLAN. The controller can also be tuned based on network design requirements.


Introduction
The IEEE 802.11 Wireless Local Area network (WLAN) is a widely deployed communication technology due to its cost effectiveness, ease of deployment, flexibility and lack of mobility constraints. With increasing bandwidth, wireless networks are now experiencing more users who generate network traffic requiring service guarantees making it imperative that methods of enhancing performance on the wireless network be researched.
Initially, the IEEE 802.11 WLAN technology only provide best effort services with no quality of service (QoS) assurances due to the fact that the contention based Distributed Coordination Function (DCF) shares network capacity equally among contending users. Stations operating the DCF channel access scheme contend for air time with the same contention parameter values which implies that time sensitive traffic are not given priority in accessing the wireless medium. In order to incorporate quality of service, the Enhanced Distributed Channel Access (EDCA) scheme was introduced which gives different traffic classes different contention parameter values to use in accessing the WLAN. One of the channel access parameters is the Contention Window (CW). With EDCA, the CW min and CW max values varies with traffic type thereby regulating the backoff interval for different traffic classes and ensure quicker access for delay sensitive traffic. The IEEE 802.11e standard has recommended CONTACT Ibukunoluwa Akinyemi i.akinyemi@lboro.ac.uk values for CW min and CW max which are not fixed but can be varied based on WLAN scenario and configuration but the reality is that these values are static and cannot by dynamically tuned because of the dynamic nature of WLANs.
In this work, we develop an algorithm that dynamically tunes the CW value based on number of contending stations on the WLAN and a pre-determined throughput value to be maintained on the wireless network. The FCA algorithm is based on the theory of feedback control and a block diagram representation is shown in Figure 1. The contention window parameter advertised by the access point (AP) on the WLAN is dynamically tuned because it has been shown through experiments in Giuseppe Bianchi and Oliveri (1996) that value of CW affects the throughput achievable on a wireless network. We also propose the use of a Proportional-Integral (PI) controller for the tuning process.
The remainder of this paper is organized as follows: Section 2 discusses related work in the use of controller algorithms in solving network problems, Section 3 shows the analysis of the throughput model used, Section 4 describes the delay analysis used to obtain the degree of saturation on the network, Section 5 gives the analysis and derivation of the proposed PI controller, Section 6 shows the results while Section 7 concludes this paper.

Related work
Dynamic tuning of the CW parameter has been a major source of consideration in order to improve on the limitation of the EDCA protocol. There has been schemes proposed most of which are concerned with mode of sensing the level of activity on the WLAN. In sensing the level of activity on the WLAN, authors in Romdhani et al. (2003), Jun et al. (2009) andNaoum-Sawaya et al. (2005) used the number of packets sent and the number of retransmissions within a specified period to calculated and judge the intensity of traffic on the WLAN and some multiplication factor is used to tune the CW values accordingly. Authors in Nafaa et al. (2005) proposed a sliding contention window (SCW) algorithm where a slider with a lower and upper limit value within the CW min and CW max values is used. Each traffic type uses contention window values within a SCW slider range with upper and lower slider limits of the slides chosen within the specified IEEE 802.11e CW range. As the network gets busy, the slider range is adjusted by a Sliding Factor (SF) which is AC specific. The challenge with most of these approaches shown above is the heuristic nature of the algorithm.
In order to incorporate a theoretical approach to improve on the current challenge, we use the concept of control theory. While applying control theory is not new in network communications as can be seen in Hollot et al. (2001) and Yao et al. (2014).
In literature, authors in Annese et al. (2004), Boggia et al. (2003), Grieco et al. (2003) and Boggia et al. (2005Boggia et al. ( , 2007; used the concept of feedback control in controlling bandwidth allocation to different traffic streams during the contention free period of the hybrid coordination function (HCF). Queue length of the different traffic type is fed back to the HCF Controlled Channel Access (HCCA) scheduler so that more appropriate bandwidth allocation is made to drain long traffic queues.
In  and , optimal control techniques were used in the allocation of optimal contention window values to traffic categories in EDCA such that pre-defined delay constraints are met.
In this work, we consider particularly the use of feedback control in Patras et al. (2011), Patras et al. (2009, 2012 and Serrano et al. (2013) were the Distributed Adaptive Control Algorithm (DAC) and Centralised Adaptive Control Algorithm (CAC) were introduced for efficient transmission in ad-hoc and centralized WLANs. The authors set the collision rate on the WLAN as control variable which consequently controls throughput on the network. The major weakness of the DAC and CAC PI algorithms is the lack of flexibility in being able to tune controller performance. DAC and CAC PI controller models are based on network configuration parameters and can only give one PI configuration set per network scenario thus removing controller tuning flexibility. This makes it impossible to tune the controller based on design/controller performance requirements such as settling time and gain margins yielding a suboptimal controller with slow controller performance on the network as number of nodes increase.
In this paper, we control throughput directly and propose a control algorithm (FCA) that dynamically tunes the CW parameter on a single AC network while considering number of nodes on the WLAN, degree of saturation and frame generation rate on the WLAN. We also ensure that the proposed controllers can be tuned based on controller performance requirements and with optimal gain margins.

Throughput model
This section presents the throughput model for the unsaturated WLAN. For a network with n number of stations, the system throughput S is defined as the average rate of successful transmission of frames across the network. This is represented as: where l data is the length in bytes of the packet to be transmitted, m is the number of packets in one TXOP burst and we set the TXOP to the maximum limit for the AC under consideration. P s is the probability of a successful transmission on the network which occurs when only a single node out of the n possible nodes on the WLAN transmits and P s is given as where τ , which denotes the probability that a station transmits in a random slot time has been derived following the model in KosekSzott et al. (2011). We derived this expression for unsaturated network scenario and with the number of retransmission attempts on the WLAN set to zero. With this, where CW is the size of the congestion window, P p is the frame generation probability and is given as P p = 1 − e −λT cs and ρ = λD T is the probability of saturation for stations on the WLAN. D T is the total delay experienced by the head of line (HOL) frame and λ is the packet arrival rate. P blk is the probability that the backoff counter of a station is frozen when the WLAN is busy and this is given as: Also, we note that a contention slot can either be in an empty state or a busy state so we define the duration of a contention slot (T cs ) as the sum of the timings of these states multiplied by their corresponding probability, thus, where the parameter P b is the probability that the channel is busy and is given as and the probability of having an idle channel is given as 1 − P b . A busy channel could either contain a successful transmission or a collision. Thus, the probability of a collision on the network is given as For transmission on the WLAN, we assume basic mode of transmission where T e denotes the duration of an empty slot and the value is dependent on the physical layer characteristics of the wireless medium. T s is the time for a successful transmission and this is given as where T data = T PHYhdr + l data /r is the time taken to transmit one MPDU at the physical layer data rate r and the corresponding physical layer header PHYhdr. T c is the duration of collision and this is given as EIFS is the station wait time following collision on the channel and is given as: EIFS = T ACK + SIFS + DIFS. This concludes the throughput analysis.

Delay analysis
In order to analyse the degree of saturation on the network, we consider the delay experienced by the HOL frame as time it spends from the beginning of contending for channel access till the last bit of the packet has been successfully sent. In the analysis, we set CW min and CW max as a singular value W as retransmission is not considered in our analysis.

Expected countdown delay (D cd )
This is the average number of idle slots a station counts down during backoff stage without considering times that the backoff counter is frozen. D cd is given as

Expected blocking delay (D b )
Blocking delay is the estimated delay experienced by a frame due to freezing its counter when the medium is sensed as busy. This freeze time depends on whether freezing the counter was due to a successful transmission or a collision of another STA on the WLAN. Thus,

Collision delay (D col )
For a STA transmitting, one of the possible outcome is collision. The delay experienced from collision is estimated as: where P col is the conditional probability that a transmitted frame of a station experiences collision. This occurs if one of the remaining (n − 1) stations attempts transmission and this is represented as

Transmission delay (D trans )
The transmission delay is time taken to successful transmit a frame multiplied by the probability that the frame does not collide In this work, we assume number of retransmission is zero implying CW min = CW max = CW. Then, The average total delay D T experienced by the HOL frame is then calculated as the sum of the different components analysed above, which gives: This enables us to calculate the probability of saturation ρ on the WLAN.

Controller algorithm
In this section, we derive mathematical model for the PI controller algorithm. The control system is set up as depicted in Figure 2 and we consider each component of the block diagram.

Optimal throughput
Our control aim is to maintain optimal throughput performance on the WLAN by the AP giving the appropriate value of W. To achieve this, we set a reference value, S opt , as shown in the control system shown in Figure 2. The value of S opt is obtained by finding τ opt for each network scenario and applying this to the throughput expression in Equation (1). We adopt the τ opt expression in Patras et al. (2009Patras et al. ( , 2012 which is given as: Substituting Equation (13) in Equation (1) we have where

WLAN transfer function
We represent the WLAN by the transfer function H(z). To calculate H(z), we obtain the linear relationship between the input W and output S obs of the WLAN. From Equations (1) and (3), we see that the relationship between the input and output of the WLAN is not linear so we proceed with linearization about a stable point to obtain a suitable transfer function as follows: The partial derivative ∂τ /∂W is given in Equation (17), where By using Equations (16) and (17), we obtain the linearized model for the WLAN transfer function H(z) which is given in Equation (18).

PI controller
The controller, C(z), is located in the access point (AP) and is expressed with a transfer function given as: It receives as input the control error which is the difference between the throughput measured on the WLAN and our design goal S opt , it then gives as output a control signal which is the optimal W value for the current condition on the WLAN.
To obtain the throughput measurement on the WLAN, the AP calculates the total number of packets successfully transmitted between each beacon frame interval of 100 ms and uses that rate for S obs .
From the Figure 2, we derive the closed loop transfer function G(z) as: substituting the controller parameters, we get:  From the closed loop transfer function G(z), we note that there are two zeros at: Also, we have: and

Simulation and performance evaluation
In this section, we evaluate our proposed algorithm through simulations using the control toolbox simulator in Matlab/Simulink Package. The 802.11 OFDM physical layer parameters were used in obtaining the throughput values used in obtaining the WLAN transfer functions and the reference value S opt . These physical layer parameters are as shown in Table 1. Since the aim of this work is to maintain optimum performance on the network through a PI controller, our simulations revolves around analysis of the effectiveness of our designed controller.
Our simulations were carried out for different network conditions with nodes ranging from 1 to 20 and we have shown output for n = 2.
In Figure 3, we show the system output. The controller was able to drive the WLAN to operate with throughput that is equal to the reference value with a settling time   of about 10 s thus attaining optimal throughput on the WLAN. This confirms the accuracy of the equivalent block transfer function since steady state error is zero when G(1) = 1 In Figure 4, we show that the difference between the system output and the reference value attains zero at steady state while Figures 5-7 shows the corresponding root locus and Bode plots for the system.
We also considered the effect of the zero location on the transient response of the proposed controller. When z 2 is located on the positive real axis, we have a controller situation where K p > K i . The resulting poles are real with one on the positive axis and the other on the negative axis. We achieve higher gain margins as distance between the two poles increases giving more room for gain adjustments/tuning. Optimal configuration is achieved at location z 2 = 0.05 which corresponds to a system that is critically damped for a 10 s settling time.
When location of the zero moves to the negative real axis, a second order system results where the closed loop pole locations can either be on the real axis or they could be complex conjugates and controller situation is K p < K i . Maximum gain was achieved at z 2 = −0.34. Further left from the −0.33 mark, the gain margin begins to drop (Table 2). For K p < K i situation, we maintained z 2 = −0.34 and as the poles move into the complex plane, the transient response is faster but with some compromise in the gain margin and possibility of instability occurring (Figure 8).
At z 2 = 0, we have K p = K i In Figure 9, we have shown the controller output when n = 2, n = 10 and n = 20. Particularly, we compare this with Figure 10 and note the possibility of maintaining controller design requirements, in this case T s = 20seconds, irrespective of the number of nodes on the WLAN as against CAC where T s increases as number of nodes increase.
In Figure 11, we show the implementation of the designed controller on the wlan and the performance is compared to that of EDCA. We see that FCA was able to maintain a fairly stable performance on the network. Figure 12 shows the delay output experienced The total air-time used on the WLAN consists of the time for transmissions, both successful transmissions and collisions. This is shown in Figure 13 and is given as: In Figure 14, we show how the algorithm responds to change in stations joining and leaving the WLAN. We start with one station at time t = 0 s, three stations at t = 30 s, two station at t = 60 s, four stations at 90s and five stations at t = 12 s. The diagram shows that the algorithm was stable and adapt to changes.

Conclusion and future work
In this paper, we have looked at the design of a PI controller for use in tuning the contention window parameter on the WLAN and the optimization of the controller parameters. Particularly, we focused on the different possible transient response of the controller and the importance of proper tuning of the controller in order to achieve design requirements and optimal gain margins. In future, we intend implement this algorithm using the NS-2 simulator and compare the effectiveness on the  WLAN with other approaches. We then extend the controller design for use in heterogeneous WLAN for the purpose of improving throughput while maintaining fairness on the WLAN.

Disclosure statement
No potential conflict of interest was reported by the authors.