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congestion control. As a result, the Differentiated Services. (Diff-Serv) architecture was proposed [1] to deliver aggregated quality of service (QoS) in IP networks.

Congestion Control in Differentiated Services Networks using Fuzzy Logic Chrysostomos Chrysostomou, Andreas Pitsillides, George Hadjipollas, Marios Polycarpou, and Ahmet Sekercioglu

Abstract— The provision of quality of service (QoS) in a differentiated services (Diff-Serv) environment requires an adequate differentiation between high-priority/assured and low-priority/best-effort classes of service in the presence of congestion, giving priority/preference to assured-tagged traffic. For this purpose, a new active queue management scheme, implemented within the Diff-Serv framework, is presented that provides congestion control in TCP/IP networks using a fuzzy logic control approach. The proposed fuzzy logic approach for congestion control allows the use of linguistic knowledge to capture the dynamics of nonlinear probability marking functions, uses multiple inputs to capture the dynamic state of the network more accurately, and can offer effective implementation. A simulation study over a wide range of traffic conditions - considering multiple bottleneck links - shows that the fuzzy logic based controller outperforms the Random Early Detection (RED) implementation for DiffServ in terms of link utilization, packet losses, and queue fluctuations and delays. Also, the proposed scheme can offer better differentiation among assured and best-effort traffic, thus it can provide better QoS to different types of data streams, such as TCP/FTP traffic or TCP/Web-like traffic, whilst maintaining high utilization.

I. INTRODUCTION The rapid growth of the Internet and increased demand to use the Internet for time-sensitive applications necessitate the design and utilization of new network architectures to include more effective congestion control algorithms in addition to the standard TCP based congestion control. As a result, the Differentiated Services (Diff-Serv) architecture was proposed [1] to deliver aggregated quality of service (QoS) in IP networks. It should also be mentioned that, even for the present Internet architecture, network congestion control remains a critical C. Chrysostomou*, A. Pitsillides, and G. Hadjipollas are with the Department of Computer Science, University of Cyprus, 1678 Nicosia, Cyprus (*corresponding author phone: +357-22892700; fax: +35722892701; e-mail: {cchrys, andreas.pitsillides, hpollas} M. Polycarpou is with the Department of Electrical and Computer Engineering, University of Cyprus, 1678 Nicosia, Cyprus (e-mail: [email protected]). A. Sekercioglu is with the Centre for Telecommunications and Information Engineering, Monash University, Melbourne, Australia (email: [email protected]).

and high priority issue, and is unlikely to disappear in the near future. Furthermore, if we consider the current utilization trends, congestion in the Internet may become unmanageable unless effective, robust, and efficient methods for congestion control are developed. The development of such effective congestion control protocols will require cooperation between networking and control researchers. Recently, active queue management (AQM) mechanisms [2] have been proposed to provide high network utilization with low loss and delay (e.g. random early detection – RED [3]). RIO [4], a RED implementation within the framework of the Diff-Serv architecture, was proposed to preferentially drop packets. The AQM approach can be contrasted with the “Tail Drop” (TD) queue management approach, employed by common Internet routers, where the discard policy of arriving packets is based on the overflow of the output port buffer. Contrary to TD, AQM mechanisms [2] start dropping packets earlier in order to be able to notify traffic sources about the incipient stages of congestion. AQM allows the router to separate policies of dropping packets from the policies for indicating congestion. The use of Explicit Congestion Notification (ECN) [5] was proposed in order to provide TCP an alternative to packet drops as a mechanism for detecting incipient congestion in the network. The ECN scheme requires both end-to-end and network support. An AQM-enabled gateway can mark a packet either by dropping it or by setting a bit in the packet’s header if the transport protocol is capable of reacting to ECN. The use of ECN for notification of congestion to the end-nodes generally prevents unnecessary packet drops. In this paper, we present a fuzzy logic based approach for delivering an improved and more predictable congestion control implementation within the Diff-Serv architecture. Fuzzy logic control is a technique from the computational intelligence literature, designed to deal with “soft” information processing [6]-[7]. During the last two decades, fuzzy logic has been widely considered in feedback control application (see, for example [8]-[9]). Fuzzy logic becomes especially useful in capturing human

expert or operator’s qualitative control experience into the control algorithm, using linguistic rules. The application of fuzzy control techniques to the problem of congestion control in networks is suitable due to the difficulties in obtaining a precise mathematical model using conventional analytical methods, while some intuitive understanding of congestion control is available. In this paper we use fuzzy logic techniques to develop a new AQM scheme, implemented within the Diff-Serv framework - using a two-class Fuzzy Explicit Marking (FEM) controller (FEM In/Out – FIO) - to provide congestion control. The FEM controller was proposed recently [10] to provide congestion control in TCP/IP besteffort networks. The proposed fuzzy control system is designed to regulate the queues of IP routers at a predefined level, by achieving a specified target queue length (TQL), in order to maintain both high utilization and low mean delay. A fuzzy inference engine (FIE) is designed to operate on router buffer queues, and uses linguistic rules to mark packets in TCP/IP networks. In a Diff-Serv framework a two-class FEM controller is designed to operate on the core routers’ buffer queues, called FEM In/Out (FIO). Two identical FEM controllers are used, one for each differentiated class of service (that is, assured and best-effort), and two different TQLs are introduced, one for each FEM controller. The proposed fuzzy logic strategy is shown via simulations (by considering multiple bottleneck links) to be robust with respect to traffic modeling uncertainties and system nonlinearities, yet provide tight control. As a result, it can effectively regulate the queues of the bottleneck links, while achieving high utilization, low loss and delay. It also achieves an adequate differentiation between the two traffic classes of service in the presence of congestion, by preferentially marking the lowest-priority packets, while controlling the queue at the predefined levels, and providing QoS. The paper is organized as follows. Section II discusses key aspects of Diff-Serv congestion control. In Section III we briefly review some of the properties of fuzzy logic control and present our proposed fuzzy logic based congestion control scheme, namely FIO. Then Section IV presents simulation examples and discusses the performance of FIO under multiple bottleneck links. Finally in Section V we present our conclusions. II. DIFFERENTIATED SERVICES – CONGESTION CONTROL – AQM MECHANISMS Since Integrated Services failed to be adopted for widespread use, the IETF (Internet Engineering Task Force) proposed a more evolutionary approach that did not require significant changes to the Internet infrastructure and provided differentiation of services (Diff-Serv) [1].

The Diff-Serv working group has defined two broad aggregate behavior groups: the Expedited Forwarding (EF) Per-Hop Behaviour (PHB) and the Assured Forwarding (AF) PHB. The EF-PHB can be used to build a low loss, low latency, low jitter, assured bandwidth end-to-end service, thus indirectly providing some QoS. In order to ensure that every packet marked with EF receives this service, EF requires from every router to allocate enough forwarding resources so that the rate of incoming EF packets is always less than or equal to the rate at which the router can forward them. This can be done through a Service Level Agreement during the connection setup. In order to preserve this property on an end-to-end basis, EF requires traffic shaping and reshaping in the network. The AF-PHB group provides delivery of IP packets in four independently forwarded AF classes. Within each AF class two or three drop preference levels are used to differentiate flows. The idea behind AF is to preferentially drop best-effort packets and non-contract conforming packets when there is congestion. By limiting the amount of AF traffic in the network and by managing the besteffort traffic appropriately, routers can ensure low loss behavior to packets marked with the EF PHB. AQM mechanisms have recently been proposed [2], with the aim to provide high link utilization with low loss rate and queuing delay, while responding quickly to load changes. Several schemes have been proposed to provide congestion control in TCP/IP networks. RED [3], which was the first AQM algorithm proposed, simply sets some minimum and maximum marking thresholds in the router queues. In case the average queue size exceeds the minimum threshold, RED starts randomly marking packets based on a probability depending on the average queue length, whereas if it exceeds the maximum threshold every packet is dropped. Diff-Serv will try to provide some QoS using a Diff-Serv aware congestion control algorithm. The most popular algorithms used for Diff-Serv implementation, to preferentially drop non-contract conforming against conforming packets, are based on RED [3]. The RED implementation for Diff-Serv, called RED In/Out (RIO) [4], defines different thresholds for each class of service. RIO uses the same mechanism as in RED, but is configured with two different sets of parameters, one for “In” packets, and one for “Out” packets. The discrimination against “Out” packets is created by carefully choosing the parameters of minimum and maximum thresholds, and maximum mark probability. Best-effort (“Out”) packets have the lowest minimum and maximum thresholds, and therefore they are marked earlier than packets of Assured class (“In”). They are also marked with a higher probability by setting the maximum mark probability higher than the


Qerror (kT) Fig. 1. Fuzzy logic controlled AQM system model.

one for packets of Assured class. The properties of RED and its variants have been extensively studied in the past few years. Issues of concern include: problems with performance of RED under different scenarios of operation and loading conditions [11]; the correct tuning of RED parameters implies a “global” parameterization that is very difficult, if not impossible to achieve as it is shown in [12]; some researchers have advocated against using RED, in part because of this tuning difficulty [13]; linearity of the dropping function has been questioned by a number of researchers (see for example [14]). III. FUZZY LOGIC CONTROL – IMPLEMENTATION OF FIO FOR DIFF-SERV A. Fuzzy Logic Fuzzy logic is one of the tools of what is commonly known as Computational Intelligence (CI). CI is an area of fundamental and applied research involving numerical information processing. While these techniques are not a panacea (and it’s important to view them as supplementing proven traditional techniques), we are beginning to see a lot of interest not only from the academic research community (e.g. [15]), but also from industry (e.g. [16]). Fuzzy Logic Control (FLC) may be viewed as a way of designing feedback controllers in situations where rigorous control theoretic approaches cannot be used due to difficulties in obtaining a formal analytical model, while at the same time some intuitive understanding of the process is available. The control algorithm is encapsulated as a set of linguistic rules. FLC has been applied successfully for controlling systems in which analytical models are not easily obtainable or the model itself, if available, is too complex and possibly highly nonlinear. In recent years, a number of research papers using fuzzy logic investigating solutions to congestion control issues in networking, especially to ATM networks, have been published (e.g. [17]). A survey is given in [15]. Moreover, fuzzy logic is recently applied [10] to TCP/IP best-effort networks providing congestion control (by considering the case of a single bottleneck link). B. FIO Implementation for Diff-Serv Our design of a fuzzy control system is based on a fuzzy





Qerror (kT - T) Z PS H H VB VB S B T VS Z T Z Z Z Z



logic controlled AQM scheme - namely Fuzzy Explicit Marking (FEM ) [10] that provides congestion control in TCP/IP best-effort networks. Our design is implemented within the Diff-Serv framework to provide congestion control in TCP/IP networks (considering multiple bottleneck links). For this purpose, a two-class FEM controller – FEM In/Out (FIO) - is designed and used for Diff-Serv control. The system model of FEM is shown in Fig. 1, where all quantities are considered at the discrete instant kT, with T the sampling period; e(kT) = qdes – q is the error on the controlled variable queue length, q, at each sampling period; e(kT – T) is the error of queue length with a delay T (at the previous sampling period); p(kT) is the mark probability; and SGi and SGo are scaling gains. The proposed fuzzy control system is designed to regulate the queues of IP routers by achieving a specified desired TQL, qdes, in order to maintain both high utilization and low mean delay. A fuzzy inference engine (FIE) is designed to operate on router buffer queues, and uses linguistic rules to mark packets in TCP/IP networks. As shown in Fig. 1, the FIE dynamically calculates the mark probability behavior based on two network-queue state inputs: the error on the queue length (i.e., the difference between the desired (TQL) and the current instantaneous queue length) for two consecutive sample periods (which can be interpreted as a prediction horizon). FEM controller has been implemented with marking capabilities, so that FEM-like routers have the option of either dropping a packet or setting its ECN bit in the packet header, instead of relying solely on packet drops (for the rest of the paper, by marking a packet it is meant setting its ECN bit). The decision of marking a packet is based on the mark probability, which is dynamically calculated by the FIE. The scaling gains, SGi and SGo, shown in Fig. 1, are defined as the maximum values of the universe of discourse of the FIE input and output variables, respectively. In order to achieve a normalized range of the FIE input variables from -1 to 1, the input scaling gain SGi is set to be equal to -1/(qdes–QueueBufferSize), if the instantaneous queue length is greater than the TQL; otherwise SGi is equal to 1/qdes. The output scaling gain SGo is determined so that the range of outputs that is possible is the maximum, but also ensuring that the input to the plant will not saturate around

(a) linguistic input variables

Fig. 2. Decision surface of the fuzzy inference engine. The control surface is shaped by the rule base and the linguistic values of the linguistic variables.

the maximum. SGo is set to a value indicating the maximum mark probability that can also be adjusted in response of changes of the queue length. The FIE uses linguistic rules to calculate the mark probability based on the input from the queues (see Table I1). Usually multi-input FIEs can offer better ability to linguistically describe the system dynamics. The dynamic way of calculating the mark probability by the FIE comes from the fact that according to the error of queue length for two consecutive sample periods, a different set of fuzzy rules, and so inference apply. Based on these rules and inferences, the mark probability is calculated more dynamically than the classical RED approach. This point can be illustrated by observing the visualization of the decision surface of the FIE used in the FEM scheme (see Fig. 2). An inspection of this decision surface and the linguistic rules shown in Table I provides hints on the operation of FEM. The mark probability behaviour under the region of equilibrium (i.e., where the error on the queue length is close to zero) is smoothly calculated. On the other hand, the rules are aggressive about increasing the probability of packet marking sharply in the region beyond the equilibrium point. These rules reflect the particular views and experiences of the designer, and are easy to relate to human reasoning processes and gathered experiences. Usually, to define the linguistic values of a fuzzy variable, Gaussian, triangular or trapezoidal shaped membership functions are used. Since triangular and trapezoidal shaped functions offer more computational simplicity, we have selected them for our rule base (see Fig. 3). Then, the rule base is fine tuned by observing the progress of simulation, such as packet marking and delay 1 Table I content notations: negative/positive very big (NVB/PVB), negative/positive big (NB/PB), negative/positive small (NS/PS), zero (Z), huge (H), very big (VB), big (B), small (S), very small (VS), tiny (T).

(b) linguistic output variable Fig. 3. Membership functions of the linguistic values representing the input variables “normalized error on queue length for two consecutive sample periods”, and the output variable “mark probability”.

occurrences, and throughput curves. The tuning can be done with different objectives in mind. For example, any gain in throughput must be traded off by a possible increase in the delay experienced at the terminal queues. Alternatively, an adaptive fuzzy logic control method [18] can be used, which is based on tuning the parameters of the fuzzy logic controller on line, using measurements from the system. The tuning objective can be based on a desired optimization criterion, for example, a trade-off between maximization of throughput with minimization of end-toend delay experienced by the users. This is part of our future work. In a Diff-Serv framework, a two-class FEM controller is designed to operate on the core routers’ buffer queue, called FEM In/Out (FIO), where “In” and “Out” terms are used to distinguish packets that are classified into different classes of service, such as assured and best-effort classes. Both assured and best-effort packets share a FIO queue. FIO comprises of two identical FEM controllers, one for each class of service (that is, assured and best-effort), and we introduce two different TQLs, on the total queue length, one for each FEM controller. The TQL for best-effort is lower than the one for assured traffic. That is, best-effort packets are more likely to be marked than the assured ones. The idea behind this is to regulate the queue, if possible, to the lower TQL, in order to get a mark probability for the assured traffic closed to zero. In the presence of large amount of assured traffic, compared with the one of besteffort traffic, the queue can be regulated at the higher TQL, where the mark probability for best-effort traffic would be closed to one. Therefore, we can accomplish a bounded


1 2 3 4 5 6

Utilization (%)



Besteffort 67.09 97.38 6.80 28.72 34.66 50.20 0.50 0.58 16.36 20.66 0.015 0.01

Loss Rate (%)



32.58 0.16 92.82 67.62 58.92 43.23 98.56 97.29 82.37 77.59 99.95 99.95

99.67 97.54 99.62 96.34 93.58 93.43 99.06 97.87 98.73 98.25 99.97 99.96

Fig. 4. Network topology.

delay, by regulating the queue between the two TQLs, depending on the dynamic network traffic conditions. FIO can achieve an adequate differentiation between the two classes of service in the presence of congestion, by preferentially marking the lowest-priority best-effort packets, and giving priority/preference to assured-tagged traffic, while controlling the queue at the predefined levels, and providing QoS. The design of the proposed fuzzy logic based congestion control system aim to generally provide better congestion control and better utilization of the network, with lower losses and delays than the classical RED approach [4], especially by introducing additional input variables and online (dynamic) adaptivity of the rule base (self-tuned). IV. SIMULATION RESULTS In this section we evaluate the performance and robustness of the proposed fuzzy logic based scheme, namely FIO, in a wide range of environments, and compare with other published results by taking RIO [4] in the case of a TCP/IP Diff-Serv network, using a recent version of NS-2 [19] simulator. We have conducted a series of simulations in order to evaluate the performance of both FIO and RIO schemes, and examine their capabilities to provide QoS. Two classes of service are set: Assured traffic class, which has the highest priority, and best-effort traffic class, which has the lowest priority in a buffer queue. All results are summarized in Table II, where the

Besteffort 0.13 1.68 1.49 8.76 0.30 5.87 0 21.21 0.009 0.24 0 57.83

Delay (ms)



0 0 0.05 0.07 0.08 0.11 0.38 1.33 0 0.01 0.49 3.35

0.09 1.68 0.15 3.01 0.16 3.37 0.38 1.34 0.007 0.19 0.49 3.36

MeanDelay 63.29 217.89 94.56 105.07 88.04 80.78 110.36 162.38 57.15 78.80 103.31 149.84

StdDeviation 24.07 48.00 26.71 49.94 36.08 70.90 24.84 37.68 16.94 61.03 21.25 44.63

performance-QoS metrics are the bottleneck link utilization, the loss rate and the mean queuing delay with its standard deviation. The sampling period for FIO AQM is fixed to 0.006 sec. The TQL for best-effort traffic is set to 100 packets, whereas the TQL for assured traffic is set to 200 packets, for a buffer size of 500 packets. For RIO, the minimum and maximum thresholds, for best-effort traffic, are set to 50 and 150 packets, respectively. The equivalent values for assured traffic are 100 and 300 packets, respectively. The maximum mark probability for best-effort traffic is set to 0.1, whereas the one for assured traffic is set to 0.02, for both FIO and RIO. The network topology used is shown in Fig. 4. We have considered network topologies with multiple bottleneck links in order to examine the performance of the proposed scheme in more realistic scenarios. We use TCP/Newreno with an advertised window of 240 packets. The size of each packet is 1000 bytes. The buffer size of all queues is 500 packets. We use AQM in the queues of all core links from router-A to router-F. All other links (access links) have a simple Tail Drop queue. The link capacities and propagation delays are set as follows: (C1, d1) = (C8, d8) = (C9, d9) = (100Mbps, 5ms), (C2, d2) = (C4, d4) = (C6, d6) = (15Mbps, 10ms), (C3, d3) = (15Mbps, 60ms), (C5, d5) = (15Mbps, 30ms), and (C7, d7) = (C10, d10) = (C11, d11) = (200Mbps, 5ms), while the number of flows is N1 = 100, N2 = 50, and N3 = 100. N1 flows end up at destination 1, N2 flows end up at destination 2, and N3 flows end up at destination 3. The results show that both bottleneck links (between router-B and C, and between router-D and E) exhibit similar behavior, as far as the performance comparison is concerned. Therefore, due to lack of space, we have chosen the bottleneck link between router-B and router-C to show the results obtained. In Scenario 1-4 the simulation time is 100 sec, while in Scenario 5-6 the simulation time is kept up to 1500 sec.

(a) FIO

(b) RIO Fig. 5. Scenario 1: Queue lengths (queue ranges from 0-500 packets with a time evolution of 100sec; similarly for Fig. 6-8).

(a) FIO

(b) RIO Fig. 6. Scenario 2: Queue lengths.

In Scenario 1 all sources (N1, N2, and N3 flows) are greedy sustained FTP applications. It considers a limited number of flows tagged as assured class traffic; 2 out of 100 flows (among N1 flows) are considered belonging to assured class, whereas the rest, 98 flows, are tagged as best-effort. N2 and N3 flows are considered as being besteffort. Fig. 5 shows the queues of both FIO and RIO, where we can observe that FIO regulates its queue to the lower TQL (100 packets), whereas RIO exhibits very large queue fluctuations that results in degraded utilization, losses and high variance of queuing delay (see Table II). Furthermore, FIO achieves an adequate differentiation between the two traffic classes (it gives a considerable portion of the link utilization to the assured traffic), in contrast with RIO that cannot provide sufficient link utilization for assured class traffic. Scenario 2 increases the number of flows tagged as assured traffic class as follows: 15 out of 100 N1 flows, 5 out of 50 N2 flows, and 5 out of 100 N3 flows. FIO accomplishes a bounded queuing delay, between the two TQLs, that results in high link utilization and minimal losses (see Fig. 6 and Table II). On the other hand, RIO slowly regulates its queue, after a significant transient period with large overshoots that results in lower utilization and higher losses than FIO has. Furthermore, FIO achieves a much higher differentiation between the two traffic

classes, as compared with RIO, thus can provide adequate QoS. Scenario 3 examines the behavior of the AQM schemes under dynamic traffic changes. We use the previous experiment, and provide some time-varying dynamics by stopping the assured-tagged flows at time t = 40 sec, and resuming transmission at time t = 70 sec. The results (see Fig. 7) show that FIO is very robust against the dynamic traffic changes and keeps very good response. Between t = 40 – 70 sec, where only best-effort-tagged flows are active, FIO successfully manage to regulate the queue length at the TQL for best-effort (100 packets), whereas RIO fails to do so. Scenario 4 increases the number of flows tagged as assured traffic to 90 out of 100 N1 flows, and uses all N2 and N3 flows as assured traffic. In the presence of large amount of assured traffic, FIO regulates its queue at the higher TQL (see Fig. 8). RIO, on the other hand, exhibits large queue fluctuations that result in lower utilization and higher losses than FIO has. Scenario 5 introduces TCP/Web-like traffic too. In this experiment, web traffic is considered belonging to assured traffic class, whereas ftp traffic is considered belonging to best-effort traffic class. The number of flows tagged as assured traffic class is set to 15 out of 100 N1 flows, while the rest are tagged as best-effort traffic class. In case of

(a) FIO

(b) RIO Fig. 7. Scenario 3: Queue lengths.

(a) FIO

(b) RIO Fig. 8. Scenario 4: Queue lengths.

web traffic the standard deviation of the queuing delay is mainly determined by the burstiness of the arriving traffic. Due to the high traffic variability, there exists a large possibility for high queueing delays. Even with these circumstances, the results (see Fig. 9) show that FIO manages to maintain the queue around the lower TQL, while RIO exhibits larger queue fluctuations that results in higher delays and losses. Scenario 6 uses the previous experiment, but it increases the number of flows tagged as assured traffic to 90 out of 100 N1 flows (where the 15 flows are Web-like traffic), and uses all N2 and N3 flows as assured traffic. FIO manages to maintain better the queue around the higher TQL (200 packets), in contrast with RIO (see Fig. 10). From the results (see Table II) it can be seen that FIO can ensure acceptable QoS in a Diff-Serv network by regulating the queues of the bottleneck links, while achieving high utilization, minimal losses and low delay, as compared to RIO. V. CONCLUSIONS We have presented a new AQM scheme implemented in TCP/IP networks - within the differentiated services framework - using fuzzy logic techniques to provide effective congestion control by achieving high utilization, low losses and delays. The proposed scheme, which we refer to as Fuzzy Explicit Marking In/Out (FIO) – a two-

class FEM controller -, is contrasted with the classical RED approach for Diff-Serv through a wide range of scenarios by considering multiple bottleneck links. The proposed fuzzy logic approach for congestion control is implemented with marking capabilities (either dropping a packet or setting its ECN bit). In this paper the design of the fuzzy knowledge base is kept simple, using a linguistic interpretation of the system behavior. We have successfully used the reported strength of fuzzy logic and have addressed limitations of existing RED approach implemented in a Diff-Serv framework. This is clearly shown from the simulative evaluation. The FIO controller is shown to exhibit many desirable properties, like robustness and fast system response, and behave better than RED variant (RIO) in terms of queue fluctuations and delays, packet losses, and link utilization, with capabilities of adapting to highly variability and uncertainty in network. The FIO controller also achieves an adequate differentiation between the two classes of service (assured and best-effort) by preferentially marking the lowestpriority packets, while controlling the queue at the predefined levels. We believe that future work can include the design of an adaptive controller, which can tune the parameters of the fuzzy logic controller on line, using measurements from the system, to obtain even better behavior.

(a) FIO

(b) RIO Fig. 9. Scenario 5: Queue lengths (queue ranges from 0-500 packets with a time evolution of 1500sec; similarly for Fig. 10).

(a) FIO

(b) RIO Fig. 10. Scenario 6: Queue lengths.

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