Adaptive rate‐based congestion control with weighted fairness through multi‐loop gradient projection internal model controller
2015; Institution of Engineering and Technology; Volume: 9; Issue: 18 Linguagem: Inglês
10.1049/iet-cta.2015.0057
ISSN1751-8652
AutoresLadan Khoshnevisan, Farzad Rajaei Salmasi,
Tópico(s)Wireless Networks and Protocols
ResumoIET Control Theory & ApplicationsVolume 9, Issue 18 p. 2641-2647 Research ArticlesFree Access Adaptive rate-based congestion control with weighted fairness through multi-loop gradient projection internal model controller Ladan Khoshnevisan, Corresponding Author Ladan Khoshnevisan l.khoshnevisan@ece.ut.ac.ir Electrical Engineering Department, Faculty of Engineering, University of Tehran, Tehran, IranSearch for more papers by this authorFarzad R. Salmasi, Farzad R. Salmasi Electrical Engineering Department, Faculty of Engineering, University of Tehran, Tehran, IranSearch for more papers by this author Ladan Khoshnevisan, Corresponding Author Ladan Khoshnevisan l.khoshnevisan@ece.ut.ac.ir Electrical Engineering Department, Faculty of Engineering, University of Tehran, Tehran, IranSearch for more papers by this authorFarzad R. Salmasi, Farzad R. Salmasi Electrical Engineering Department, Faculty of Engineering, University of Tehran, Tehran, IranSearch for more papers by this author First published: 01 December 2015 https://doi.org/10.1049/iet-cta.2015.0057Citations: 10AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract As a transmission control protocol (TCP) implementation imposes the sources with small round trip time (RTT) to allocate the bottleneck unfairly, an adaptive congestion control is necessary to avoid packet loss along with fairness. The main idea of this paper is to design an adaptive rate-based queue management scheme based on gradient projection method and internal model control for network sources with different RTT values. The goal is to achieve weighted fairness, maximum utilisation and compatibility with both large and small RTTs. The communication network consisting of a bottleneck link and N TCP sources is considered as a multi-input single-output system. In the proposed approach, the number of the active TCP sources is determined adaptively and the utilisation factors are updated. For this purpose, the gradient method is used to design the adaptation rule for the utilisation factors in order to obtain weighted fairness, and then the projection method is augmented with the gradient procedure to achieve maximum bottleneck utilisation. The proposed procedure can tolerate both large and small RTTs, and consequently, it can be used in a wide range of communication networks. Extensive simulations based on network simulator NS2 and Simulink validate the analytical results. 1 Introduction Due to the expansion of the internet users, congestion control strategies have gained an important role in the communication networks. Transmission control protocol (TCP), which is mainly used in the transport layer of a communication network, controls the congestion using time out mechanism and acknowledgments [1, 2]. Therefore, designing an active queue management (AQM), which can be implemented in the routers, is imperative to decrease the end-to-end delay and packet loss in a network. The average window size and queue length are the most used variables for designing AQM procedures such as random early detection [3], straightforward AQM [4], proportional integral [5], Smith [6], internal model control (IMC)-Smith [7] and observer-based protocols [8]. Some papers such as Lim et al. in [9] have considered the mean queuing delay and some others such as Hsu and Lin in [10] have developed procedures for large-scale networks; however, in a communication network the number of the users is not fixed. Some procedures are proposed to overcome this problem such as [11, 12] and IMC procedure [13] which similarly used the average window size and the queue length. However the fairness cannot be obtained in the network. Fairness in a communication network means to apportion the bottleneck link to the sources with special shares [14]. TCP implementation in a communication network imposes the sources with small rand trip time (RTT) to allocate the bottleneck link and consequently, cause the connections with large RTT to use the bottleneck with extremely small sending rates [15, 16]. In other words, sources utilise the bottleneck without fairness. So far, there has been no consideration of fairness through the average window size and queue length. Therefore, the rate-based study is essential to achieve fairness in a network. Some authors such as Aweya et al. in [17] proposed a rate-based method using the aggregate rate through which the fairness could not be obtained. Quet et al. in [18] adjust constant values for the sending rates, which also lacks fairness because the fairness is not to determine a penalty to each rate [19]. Also, the robustness against the variations in the number of the sources is not obtained in the mentioned paper [18, 20]. In this study, the communication network consisting of a bottleneck link and TCP sources is considered as a multi-input single-output system with the queue length as the system output and the packet drop probabilities as the system inputs. As shown by the authors in [13], IMC method results in a good performance for a network with large RTT value. Consequently, the main contribution of this paper is to design an adaptive AQM to avoid congestion and disturbance rejection based on IMC procedure, with the advantages of weighted fairness, maximum utilisation and no oscillations and delay jitter. The number of the active sources and utilisation factors are determined adaptively. First, the gradient method is used to design an adaptive law for the utilisation factors to obtain weighted fairness, and then the projection method is combined with the gradient procedure to achieve maximum bottleneck utilisation. The proposed procedure can tolerate both large and small RTT values, and consequently, it can be used in a wide range of communication networks. It will be shown through analytical computations that the queue length converges to the desired value, which results in no congestion in the network. Also it is shown that the sending rates tend to the designed rates based on the adaptive law for the utilisation factors, which results in weighted fairness and maximum bottleneck utilisation. Simulation results based on network simulator NS2 and Simulink confirm the claims and also show that there is no oscillations in the response, which cause that the network operate with no delay jitter. The contribution of this article can be summarised as designing adaptive rate-based congestion controller for a communication network with all of the aforementioned advantages. 2 Network model Most of the utilised models for AQM are based on average window size and queue length, such as the one proposed by Misra et al. [21]. Nevertheless, as the TCP implementation imposes the sources with different RTT values to send their packets unfairly, such approaches result in poor performance in achieving fairness. Consecutively, rate-based fluid flow model is used to design an effective AQM, as explained in the following subsection. 2.1 Fluid flow model of a TCP/AQM A single bottleneck rate-based fluid flow model of a TCP source is introduced in [22, 23]. This model is described by the following non-linear equation in which the slow start and timeout mechanism is ignored (1) (2)where is the rate of the th TCP source (packets/s), is the round trip time (RTT) of the th TCP source (s), is the propagation delay (s) for each source, is the TCP packet marking probability, is the queue length, is the link capacity (packets/s) and is the number of active TCP sources. Moreover, is a parameter that represents type of the TCP source. It is assumed that the RTT value is constant for each TCP source that is . TCP window size increases by one during each RTT in congestion avoidance mode. On the other hand, the sending rate ( is proportional to the window size. So it is approximated that . The queue dynamic of the bottleneck is considered as in (2) [18]. Considering the steady-state values of the packet marking probability and round trip time , the steady-state throughput is given as follows (3)where is the steady-state weight (utilisation factor) which is determined to specify fairness of the network. It can be inferred from (2) and (3) that the th source sends at the rate through which of the bottleneck capacity is occupied. Therefore (4)which means the maximum bottleneck utilisation. As it is usually preferred to give different weights to different sources with various RTTs, { ; } are considered to have different values for each source. This kind of fairness is called weighted fair queuing [24]. If is considered to be 2/3, which is suitable for the Reno TCP source, the steady-state throughput of the TCP is obtained similar to the value obtained in [25]. By linearisation of (1) and (2) around the operating point [26], the following equations are obtained (5) (6)where and are the perturbed values about the operating point. As a result, the transfer function from the packet marking probability to the sending rate of the th TCP source () and from the sending aggregate rate to the queue length () are obtained as follows (7) (8)The schematic of the plant is shown in Fig. 1. Fig. 1Open in figure viewerPowerPoint Schematic of the TCP network In Fig. 1, denotes the th active source, represents the drop probability of the TCP packets and is the queue length at time . So it can be inferred from Fig. 1 that the sending rates of the sources are decoupled from each other. As a result, the system description as a multi-input single-output system is as follows (9)where is given by (10)One of the schemes for congestion control is to stabilise the steady-state sending rate at the desired value through which the total sending rate does not exceed the bandwidth capacity. James Aweya et al. in [17] proposed a controller by considering the aggregate sending rate. Due to the dependence of the RTT on the propagation delay and therefore on the distance between sources to the destination, RTT varies among different sources. As a result, some sources with small RTT allocate the bottleneck link to themselves. In other words, the network is not fair. The fairness of TCP sources cannot be guaranteed using the method designed in [17]. In this study, the sending rate of each source is considered. Through our method not only the congestion can be avoided but also the weighted fairness can be satisfied. 3 Adaptive weighted fair queuing procedure 3.1 Gradient method A TCP network with no fair queuing procedure manages the queue with no fairness. Consequently, sources with small delays allocate the link, and therefore, the other sources are not allowed to use the bandwidth. Thus, fair queuing is used in routers through which the bandwidth capacity is apportioned among some queues. Due to the requirement of fair queuing, the steady-state weights () are designed adaptively and proportionally to the delays of each source. Theorem 1..For a TCP network with sources and a bottleneck link, the following adaptive law for the utilisation weight parameters causes the system to operate fairly (11)where diag () is the weighting matrix which determines the convergence speed. The proof is given in the Appendix. 3.2 Gradient projection method In a communication network, it is ideal to use all the bottleneck link capacity, as shown by (4). Therefore, it is necessary to use another procedure called projection along with gradient method through which not only the fairness but also the maximum utilisation is obtained. Theorem 2..In a TCP network with sources and a bottleneck link the following adaptive law for the utilisation weight parameters causes the system to operate fairly with maximum utilisation (12)where is the identity matrix and { ; } have been defined previously. The proof is provided in the Appendix. The reference value for the steady-state utilisation weights are given by (13)where is the number of active sources. The active source is obtained based on the following rule (14)By substituting (13) into (14), it can be inferred that through gradient projection method weighted fair queuing with respect to the delay of each source along with maximum utilisation will be achieved. 4 TDF-IM controller designing The adaptive two degree-of-freedom internal model control (TDF-IMC) loop is depicted in Fig. 2 for this system, where is the multi-input single-output system to be controlled, is the aggregate rate and is the queue length which is used in the online parameter estimator subsystem to estimate the utilisation factors (, ). is the inner model of the system which is decomposed as below (15)where is the minimum phase part and is the all pass part. is the set point tracking controller and is the disturbance rejection controller which is designed adaptively. It can be seen from Fig. 2 that (16)Therefore, when the model matches the real process model that is , we have (17)As it can be inferred from (17), designing of the set point tracking controller and the disturbance rejection controller is decoupled from each other. Set point tracking controller is designed based on the IMC procedure as follows (18)Disturbance rejection controller is also designed based on the IMC procedure as follows (19)where is the minimum phase part of the inner model with the estimated value of the utilisation factors that is and are the relative degrees of . and are the tuning parameters of the set point tracking controller and the disturbance rejection controller, respectively, which determine the speed of the dynamic response. Fig. 2Open in figure viewerPowerPoint TDF-IMC system 5 Performance analysis The main purpose of our study is to design the AQM to avoid buffer overflow for congestion avoidance with the advantage of having weighted fairness among sources in spite of variations in the number of TCP sources. To evaluate the method proposed here tracking problem is taken under consideration. 5.1 Congestion avoidance and weighted fairness Important objectives of rate-based congestion control are to stabilise the steady-state queue length (congestion control) and the steady-state flow rate to the desired value (for satisfying the fair queuing). As a result the queue length and flow rate tracking are considered here. In this part it is assumed that the model is matched with the real system. In the disturbance free case it can be inferred from (17) that the output of the system is as follows (20)The reference input of the system is considered as a step function with the desired value for the queue length. Therefore, we have (21)The parameter estimations converge to the desired value . Therefore, based on the certainty equivalence principle, the adaptive controller performance tends to the controller performance with known parameter . As a result the steady-state value of the output signal is obtained as follows (22)Therefore, it can be assured that the queue length will converge to the desired value and the congestion in the router will be controlled. Also the convergence speed grows when decreases (controller parameter). On the other hand, (22) illustrates that the system is stable for large and small RTT values. From (7) and (17) the flow rate signal is obtained as follows (23)Consequently, the steady state of the flow rate for each source is obtained through final theorem as below (24)As the propagation delay () is much smaller than the queuing delay, (24) can be rewritten as follows (25)Therefore, the flow rates converge approximately to the desired value postulated for the steady-state rate. So weighted fair queuing can be obtained via this procedure. 6 Simulation results via Network Simulator 2 and SIMULINK In this section the simulation results of the closed-loop system are illustrated through a professional Network Simulator, called NS2, and also SIMULINK. The network topology is considered as a dumbbell with a single common bottleneck channel. A network scenario is considered for NS2 simulation in which the link bandwidth is 1.875 Mb/s with eight TCP flows and the packet size of 1300 bytes. TCP connections with FTP flows are considered for the sender–receiver pairs. TCP Reno is chosen for the transport agent. More detailed software information about NS2 will be discussed in the Appendix. Ten TCP sources are considered with different RTT values for SIMULINK. It is considered that the RTT value of the first source is smaller than the tenth. Therefore, it is expected that the utilisation factor of the first source is smaller than the tenth. The congestion avoidance and weighted fairness are scrutinised. The parameter estimation, queue length evolution, sending rates for each source and the aggregate rate will be demonstrated to evaluate the TCP performance. As it can be inferred from Fig. 3, the utilisation factors converge to the desired value in (13) quickly and therefore, due to the certainty equivalence the adaptive controller will operate appropriately. Fig. 3Open in figure viewerPowerPoint Estimated utilisation factors The queue length profile is demonstrated in Fig. 4 which shows that the queue length converges to the desired value and also there are no oscillations in the transient response. Therefore, the congestion is avoided through this procedure with no delay jitter. Fig. 4Open in figure viewerPowerPoint Queue length evolution Due to (13), the lower rate is designated for the user with lower RTT value to avoid link allocation with one user. This result is also shown in Fig. 5 where the RTT value of the first source is considered higher than that of the second source. Therefore, the AQM procedure proposed here makes the system to operate fairly. Fig. 5Open in figure viewerPowerPoint Sending rates of each source (dashed line is for the first user and solid line belongs to the tenth user) It is illustrated in Fig. 6 that the aggregate rate obtained via adaptive TDF-IMC procedure is near the bottleneck link capacity. As a result the maximum utilisation is obtained via the proposed procedure. Moreover, the result with PI procedure, which is a rate-based congestion controller, is too sluggish. On the other hand, PI procedure has no control on the source rates and therefore, fairness cannot be obtained via PI procedure. So adaptive TDF-IMC procedure overcomes the PI method in [17]. Fig. 6Open in figure viewerPowerPoint Aggregate sending rate of the sources with a Adaptive TDF-IMC procedure b PI procedure In NS2 simulation eight users are assumed in the network in which the first, third, fifth and seventh sources have the delay of 40 ms and the second, fourth, sixth and eighth source have the delay of 80 ms. The queue length desired value is considered to be 100 packets. Moreover, the bottleneck link capacity is considered to be 1442 packets/s. The queue length evolution which is obtained by the NS2 simulation is illustrated in Fig. 7. Fig. 7Open in figure viewerPowerPoint Queue length evolution with eight users via the NS2 simulation As it can be inferred from Fig. 7, the queue length tends to the desired value. Therefore, it is verified that the congestion is avoided effectively through this procedure. The rates of two sources that have different RTT values are shown in Fig. 8. Fig. 8Open in figure viewerPowerPoint Sending rates of two sources via NS2 simulation (solid line is related to the source with smaller RTT value and the dashed line is for the source with larger RTT value) From Fig. 8 it can be seen that the source that has smaller RTT value sends packets with smaller rate. Therefore, it is verified through NS2 simulation that the weighted fairness is obtained via this procedure. Conclusively, it is shown that the procedure proposes an AQM to avoid congestion in the network with the advantages of fairness and maximum utilisation. Also the results represent no oscillations and therefore, the network operates with no delay jitter. 7 Conclusion As the buffer capacity is limited and the number of the internet users increases every day, utilisation of congestion control schemes is essential in a communication network. Due to the time-out mechanism and acknowledgement using in a TCP network, the congestion is controlled after its occurrence. Therefore, AQM is imperative to avoid packet loss and decrease end-to-end delay resulted from the congestion. In this paper an adaptive rate-based congestion control is proposed based on gradient projection method and IMC to avoid congestion along with weighted fairness and maximum utilisation. On the other hand, the TCP network makes the sources with small RTT to allocate the bottleneck link and consequently cause unfairness in the network. To tackle this problem, the utilisation factors are determined adaptively based on the gradient method such that the lower rate is designated to the source with smaller value of RTT. Furthermore, in a communication network the number of active sources is not fixed and it is necessary to use the maximum bottleneck capacity to obtain maximum utility. For this end, the projection method is augmented with the gradient procedure, and the number of the sources is determined adaptively. Simulation results confirmed that the proposed approach avoids congestion with the advantages of fairness, maximum utilisation and fast response with no oscillation, simultaneously. Also, it is illustrated that the method results in no oscillations in the response and therefore, imposes the network to operate with no delay jitter. Appendix In this appendix, the proofs of the theorems are provided based on the gradient procedure and gradient projection method [27]. Also the detailed software structure is prepared. 8.1 Proof of Theorem 1 To obtain the adaptive law for the utilisation weight parameters, input of the queue transfer function is considered to be (26)Therefore, (6) can be reformulated as follows (27)The new variable is defined to be (28)As a result (27) can be rewritten as follows (29)where (30)To obtain the utilisation weights adaptively, the estimation model is as follows (31)where is the estimate of and is the estimate of the parameter. Therefore, the error signal is as follows (32) (33)where is the normalising signal, which is designed to guarantee that is bounded [24]. To minimise the error signal which is imposed by the parameter estimation, the following cost function is considered (34)The gradient of the cost function (34) will be obtained as below (35)Based on the gradient method the adaptive law is given by (36)where is a weighting matrix which determines the convergence speed of the estimation. Dynamics of the parameter estimation error is determined to be (37)Considering the Lyapunov like function as follows (38)Consequently, is negative semi-definite. As and , has a limit and therefore it is bounded. So based on (38) the estimation error is bounded, that is and and will converge to zero. 8.2 Proof of Theorem 2 The following problem formulation is considered to gain the appropriate adaptive law (39)Based on the projection method (40)where is obtained in (35) and . Furthermore, we have (41)As a result (40) can be reformulated as (42)Therefore, the following equation can be obtained (43)By substituting (35) and (43) into (42), (12) will be obtained. For the stability analysis the Lyapunov theorem is used. To this aim (40) is considered as below (44)The Lyapunov like function in (38) is used again. Therefore, we have (45)As is convex, . On the other hand, . Consequently, the projection method makes more negative and therefore, the results obtained in the previous section through gradient method are valid. 8.3 Detailed software architecture For the NS2 implementation, the controllers (18) and (19) and also the adaptive law for the gradient projection method (12) should be discretised. Based on bilinear transformation for discretisation, we have (46)where is the sampling frequency which is assumed to be 10–20 times higher than the loop bandwidth. Therefore, the difference equations at , in which is equal to , can be obtained using the discrete-time transfer functions. By converting the difference equations to pseudo codes, producing the C++ source file and updating the Make-file in NS2, the new AQM can be built. 9 References 1Shorten R. King C., and Wirth F. et al.: ‘Modelling TCP congestion control dynamics in drop-tail environments’, Automatica, 2007, 43, pp. 441– 449 (doi: https://doi.org/10.1016/j.automatica.2006.07.026) 2Alonso J. 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