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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION Volume 1, Number 1, January 2005

Website: http://AIMsciences.org pp. 1–??

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL WITHIN INTRANETS USING ATM ABR SERVICE

Lixin Xu School of Mechatronic Engineering Beijing Institute of Technology Beijing, 100081 P. R. China

Wanquan Liu Department of Computing Curtin University of Technology Perth, WA 6102 Australia

(Communicated by Dr. Houdou Qi) Abstract. In this paper, a new neural network adaptive control strategy based on Host Gate Way Rate Control Protocol (HGRCP) is proposed for intranet congestion management. The control algorithm is based on the Elman recurrent neural network via using the ABR service of an ATM backbone network. Simulations confirm that the proposed algorithm will produce lower queue level variance at the gateway. Meanwhile, the learning capability can be improved significantly.

1. Introduction. Intranet is a rapidly growing inter-networking technology for connecting the hosts within an enterprise network using the standard Internet protocols such as Transmission Control Protocol/Internet Protocol (TCP/IP). It is well known that the enterprise network of an organization is connected to the global Internet via an access-gateway and access-link. Traffic that flows between the enterprise network and the rest of the Internet travels through this gateway and access-link. At the access-gateway, traffic from many hosts within the organization is statistically multiplexed onto the access-link. If the traffic rate momentarily exceeds the access-link bandwidth, some packets will be dropped. In order to prevent or reduce such loss, some buffers have been set up to temporarily accommodate the excess traffic. These data are transmitted later once the traffic burst is over. In intranet management, we should consider about both the inbound and outbound traffic. For inbound traffic, we can use IP filter installed in gateway or other protocol control flow algorithms to control the traffic. In this paper, we mainly investigate the outbound traffic issue since it is closely related to the ABR explicit rate service in ATM network [7]. For bursty data traffic, the bandwidth of the conventional leased line is not utilized efficiently. The organization has to pay for the bandwidth for the entire 2000 Mathematics Subject Classification. 93C83, 93C40, 94C30, 94C12. Key words and phrases. Recurrent Neural Network, Adaptive Control, Intranets, Traffic Management, ATM Networks, ABR Service. Research partially supported by ARC Fellowship Scheme from Australian Research Council.

1

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 2

INTERNET

ENTERPRISE NETWORK ' x

$

x Host

Public ATM Network

x Access Gateway

ABR Connection

x x & Inside Enterprise

% Outside Enterprise

Figure 1. Interconnection of an enterprise network to the Internet via ATM ABR service. duration whether there is traffic or not. The cost of maintaining leased lines is, therefore, very high. With Asynchronous Transfer Mode (ATM) [1], a high speed cell-switching network is supposed to become the world-wide standard for the next generation of telecommunication networks [9]. With ATM, different services have different priorities with different prices. It is expected that such leased lines will be replaced by ATM virtual circuits (VCs). Interconnection of an enterprise network to the global Internet via such an ATM VC is shown in Figure 1. Unlike the constant bandwidth leased lines, ATM networks provide an Available Bit Rate (ABR) service for data communications, where the bandwidth of the VC is controlled by the ATM network and varies between specified minimum and maximum values negotiated during the VC set-up process. If there are enough resources available in the ATM network, the gateway may be allowed to transmit at the maximum rate. However, if congestion occurs within the ATM network, the gateway may be asked to reduce the transmission rate. With different services provided by ATM network, One enterprise intranet may buy a small portion of services with CBR for high quality requirement and most of services with ABR for lower prices.

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

Since an ABR connection allows a gateway to utilize only the available bandwidth within the ATM network, it is expected that the cost of data communications will be significantly reduced with the use of the ABR service. Such cost reduction may become a major driving force in the near future for replacing the existing leased lines with ATM ABR connections for connecting enterprise networks to the global Internet [10]. One major problem with the ABR service is the potential congestion that might be experienced in the access-gateway due to occasional throttling of the access-link bandwidth in the ATM network. The ABR (explicit rate) feedback control simply shifts the congestion within the ATM network to the edge of the ATM network (in this case the access-gateway) and hence increased buffering is required in the accessgateway [2, 3, 4] to cope with this congestion. If there is not enough buffer in the gateway, some data will be lost which may significantly degrade the performance of enterprise applications. While implementing large buffers in the gateway may prevent data loss, it may increase the delay in the gateway with standard internet TCP/IP suite. Such undesirable delay may cause retransmissions for some TCP packets from the hosts which would exacerbate the congestion in the gateway. It is, therefore, desirable to implement a traffic management mechanism in the intranet to control the transmission rates of the intranet hosts according to the current available bandwidth of the access-link and keep the buffering requirement in the gateway to a minimum. Reducing the buffering requirement also helps reduce the production cost of accessgateways. The design objectives of such a traffic management mechanism would be to (i) guarantee the stability of the traffic control system, (ii) minimize buffer level variance (or fluctuation) at the access-gateway due to fluctuation in the ABR access-link bandwidth and (iii) minimize packet loss at the access-gateway due to buffer overflow. There is no suitable traffic management mechanism available in the standard Internet protocol suite which can effectively control the transmission rates of intranet hosts connected to the Internet using an ABR access-link though some control flow algorithms are proposed recently [8, 11]. It was shown in [2] that the implicit flowcontrol mechanism embedded in the Internet protocol suite is not capable of controlling the traffic rates of the intranet hosts satisfactorily since the system remains unstable, susceptible to large buffer level variances and hence has the potential for high packet loss for small buffers. Because of the lack of stability and large buffer level variance, quite large buffers are required in the gateway to minimize packet loss and improve the performance of intranet applications. In paper [5], a new design of traffic management mechanism for enterprise networks is presented, taking the varying bandwidth of the access-link into consideration. Implementation of this mechanism in the intranet is expected to significantly reduce the buffering requirement in the access-gateway. The traffic management problem was formulated as a classical feedback control system in [5]. The current buffer level and the bandwidth of the ABR link in the gateway are periodically fed back to a “controller” which calculates the allowed intranet traffic rate to the gateway to keep the buffer level at a desired set point. As it is noted that the control strategy of HGRCP in [4, 5] employed a constant proportional gain plus feed forward control. The proposed controller there is not adaptive to the noise of the network. In this paper, we develop a more complex control algorithm based on neural network approach. The contributions of this paper are in two fold: one

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 4

rate-signal controller  ~

6 feedback

Global

q q

z :

q  ~

buffer

access-gateway

ABR access-link

Internet

input-traffic

hosts in the enterprise network Figure 2. Schematic diagram of the proposed traffic management mechanism. is that neural network approach is adopted here, which enhances the performance of the whole control system. The other is that the proposed sophisticated control architecture will provide adaptive control law for the practical control system as shown in the simulations. The remainder of the paper is organized as follows. A description of the proposed traffic management mechanism is provided in Section 2. The model description in Section 3. The recurrent neural network and learning algorithm are presented in Section 4. The simulation results are presented in Section 5. Finally, conclusions will be provided in Section 6. 2. The Proposed Traffic Management Mechanism. The proposed traffic management mechanism uses feedback rate signals from the access-gateway to the intranet hosts to control the traffic rates of the hosts to keep the buffer level in the gateway at a desired set point qr (see Figure 2). The explicit rates allowed to individual hosts via the rate signals are controlled by a controller in the gateway. The controller calculates the optimum aggregate rate R for the entire intranet according to the current buffer level q and the access-link bandwidth B in the gateway which are periodically fed back to the controller. The aggregate rate R is then distributed to individual hosts (via the rate signals) according to a desired rate allocation policy [11]. A schematic diagram of the proposed traffic management mechanism is shown in Figure 2. The heart of the proposed traffic management mechanism lies along the design of controller in the gateway. If the controller does not calculate the aggregate intranet traffic rate R correctly, the control system may become unstable and the buffer level q in the gateway may far exceed (large variance) the desired set point qr which will cause buffer overflow and high packet loss for small buffers. The performance of the traffic management mechanism, therefore, depends significantly on the design of the controller in the gateway.

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

3. Problem Description and Analysis. The controller and the buffer in the gateway form a feedback control system where the current buffer level q is periodically fed back to the controller for effective calculation of the optimum intranet traffic rate R. By analyzing the control system, it is possible to study the stability, buffer level variance and packet loss probability of the proposed traffic management mechanism. In this section, the design of the control system is presented and the selection of the control parameters can guarantee the stability and minimize buffer level variance. 3.1. Design. In this section, the design of the feedback control system is presented. 3.1.1. Buffer. This is a key component of the control system. The goal of the control system is to maintain the buffer level q at a desired set point qr . The input to the buffer is the aggregate traffic rate R from all the hosts in the local intranet sending traffic to the Internet through the access-gateway. An appropriate R is calculated by the controller. In addition to the controlled input R, there is another input to the buffer — the transmission rate B of the access-link. This is considered as a disturbance to the system and is beyond the control of the controller. Any fluctuation in B will cause q to deviate from qr . This effect of disturbance on q is fed back to the controller which will adjust R to bring q back to qr . It is assumed in the paper that the minimum cell rate for B is zero for convenience. The buffer level dynamics can be expressed as an approximation of the following fluid flow model m0 = win − wout where m0 is the rate of change of mass, win is the rate of flow in, and wout is the rate of flow out. Therefore, the aggregate rate R will affect the buffer level according to the following equation: q(n + 1) − q(n) = R(n) − B(n) T q(n + 1) = q(n) + TR(n) − TB(n)

(3.1)

where q(n + 1) and q(n) are the buffer levels measured at the (n + 1) − th and n − th sampling instants respectively and T is the sampling period. Taking the z-transform of Eq. (3.1), one will obtain the following transfer function between buffer output (occupancy level) q and buffer input R q(z) =

T (R(z) − B(z)) z−1

(3.2)

where q(z), R(z) and B(z) are z-transform of q(t), R(t) and B(z) respectively. 3.1.2. Controller. The main function of this component is to calculate the required input rate R to the access-link as a function of the current buffer level q. R is the output of the controller and at the same time the input to the buffer. The input to the controller is the error, the difference between the desired buffer level qr and the current observed queue length q.

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 6

The transfer function of the controller depends on the choice of controller. The simplest controller is a proportional controller [6] whose output is directly proportional to the input. The adjustment of R according to a proportional controller is simply given by R(n) = K(qr − q(n)) = Ke(n)

(3.3)

where K is the gain of the controller and e is the observed error in the output. The advantage of using a proportional controller is simplicity; There is only one parameter (gain K) to be adjusted and the stability analysis of the control system becomes simpler. However, a major drawback of a proportional controller is its non-zero steady-state error in the output as explained below. In the steady state, the input rate R is supposed to be equal to the output rate (transmission rate of the access-link) B. This results in (from Eq. (3.3)) the B for the proportional feedback controller. In other words, if a simple finite error K B instead proportional controller is used, the buffer level will be stabilized at qr − K of at qr . The performance of a proportional feedback controller can be significantly improved (by reducing or eliminating the steady state error) by adding integral1 control, which yields a PI (proportional plus integral) controller. However, integral control typically reduces the stability of the system. In order to increase the stability, derivative2 control is usually used in conjunction with a PI controller to form a PID controller [6]. A PID controller provides an acceptable degree of error reduction simultaneously with acceptable degree of stability. However, a PID controller has three adjustable parameters involved, those increase the complexity of the control system. Moreover, it responds to a disturbance only after an error has been caused by a disturbance. If a PID controller were used for the control system, the network administrator would have to adjust three control parameters to achieve the optimum performance. Adjusting such parameters can be quite time consuming. An improper set of parameters may result in large error, which in turn could degrade the performance of the control mechanism significantly. Recently, a new controller was designed in [20] for this issue and it has been demonstrated that the network performance has been enhanced greatly. However, the proposed controller can not cope with the dynamic change of the available bandwidth. In this paper, the objective is to design a control system, which provides an acceptable level of error reduction simultaneously with an acceptable level of stability with a minimum number of control parameters. One way to reduce the steady state error is to measure the disturbance and take appropriate actions before the disturbance has any effect (error) on the output. This type of control is called feed forward control [6]. Disturbance feed forward can be a very effective strategy for reducing error if (i) the effect of the disturbance on the output is known and (ii) the disturbance can be measured easily and accurately. In addition to reducing the error, disturbance feed forward has the benefit of not affecting the feedback loop (and hence the stability 1 An integral controller uses the equation[6]: R(n) = R(n − 1) + K e(n), where R is the input 1 and e is the error in the output. 2 A derivative controller uses the equation[6]: R(n) = K [e(n) − e(n − 1)], where R is the input 2 and e is the error in the output.

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

B(n)

qr

 e(n) +  - 6

R(n) -

K

-

? +- 

T z−1

feedback

Figure 3. Block diagram of a proportional controller with disturbance feed forward properties of the controller) in a feedback control system. And, importantly, disturbance feed forward can counteract the effect of the disturbance before significant error is caused. With the proportional rate control system described above, both the effect of disturbance on the buffer level and the measurement3 of disturbance can be easily obtained. From Eq. (3.3) it can be seen that for a given K, the higher the B, the greater the magnitude of the error in the steady state (R = B). The steady state error can be eliminated if the disturbance B is feed forward to the controller in the manner shown in Figure 3. 3.2. Modelling the Available Bandwidth. The internet available bandwidth B(t) is very important to the management of the local network system. One of the main contributors to the change of available bandwidth in the ATM network is the bursty traffic rate of VBR sources. If the ABR (ER) connection is multiplexed with several VBR sources, B(n) is the difference between the ABR peak rate C and the aggregated rate of VBR sources. If the VBR sources are modelled as ON-OFF sources (in the literature, bursty traffic expected for ATM networks are usually modelled as ON-OFF sources [18, 19]), then from [5] the available bandwidth B can be modelled by the following first order stochastic difference equation B(n + 1) = αB(n) + (1 − α)βW (n)

(3.4)

where W (n) is a random (white-noise) signal, α is the correlation coefficient of B(n), and β is a constant indicating the magnitude of the noise. For α = 1, there is no noise and the available bit rate remains constant ; for α = 0, B is a pure random number. In practice, α will be a fraction between 0 and 1. Although the control system in Figure 3 will keep the buffer level at the desired set point of qr in the steady state, sudden fluctuation in the available bandwidth of the access-link will cause momentary shifts of the buffer level from qr . Therefore, the variance σq2 of the buffer level around the desired set point qr is an important performance metric for the intranet traffic management system. If the variance is large, there may be buffer overflow and data loss in the access gateway. 3 The disturbance in this case is simply the transmission rate of the access-link, which can be obtained from the ABR rate feedback.

q(n) -

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 8

4. Recurrent Neural Network Approach. In order to achieve a better performance for the network system, a neural network approach will be used to design a controller in this paper. The whole structure of the controller is as depicted in Figure 5. The controller can be decomposed as two parts. One is the proportional controller K which can guarantee the stability of the system. The other part is the neural network (NN) part which can be used to compensate the disturbance brought by B. The NN part can be adjusted in real time to adapt the change B. This paper addresses the design of neural controller, which provides an adaptive learning mechanism. Its detail will be described in the next subsection. It has three inputs, i.e., the expected buffer size qr , the output of the system q and the disturbance B. The aim of the learning algorithm in NN is to minimize the following objective adaptively E(n) = K(qr − q(n))2 The output of NN will be used as a part of the input of the network management system. Next, the NN will be described in detail. 4.1. Recurrent Neural Network. It has been shown in [12] that the feedforward neural network can approximate a continuous nonlinear function at any required accuracy. The Elman network [13], one type of recurrent neural network, has been proven to be capable to approximate the trajectory of a given dynamical system with any fixed finite length of time [14]. In a recurrent neural network, the information flow can be in two directions via different connections, the feedforward and feedback connections. Therefore, the information can propagate from input neurons to output neurons. The Elman neural network structure is shown in Figure 4. The dynamic equation can be described as below. Y (k) = W1 σ(W2 X(k) + W3 O(k − 1) + W0 ); (4.5) where Y (k) is the network output,X(k) is the network input,O(k − 1) is the output of hidden neurons at time k − 1. W1 is the output weighting and W2 is the input weighting. W3 is a weighting for hidden neuron feedback and W0 ia a network threshold. σ is sigmoidal function [17]. The following theorem shows that this kind of neural network has a universal approximation capability for tracking a dynamic system. Theorem 4.1. Consider a discrete-time nonlinear system Y ∗ (k) = φ(X(k), Y ∗ (k − 1)) ˆ where X(k) is the input and Y ∗ (k) is output, φ is continuous in compact subset K. + Then for any given ε > 0 and N0 ∈ Z , Then there exists an Elman neural network depicted in (4.5) such that with the same initial condition, the output of the Elman network Y (k) and the dynamic state Y ∗ (k) will satisfy the following condition |Y ∗ (k) − Y (k)| < ε for all k > N0 . The proof of Theorem 4.1 can be found in [14]. This theorem implies that the Elman neural network can be trained to track any nonlinear trajectories. This is a very important result for Elman network and it is also our motivation to select this type of neural network in this paper. In practice, due to the the learning time constraint, we will update the weights of the Elman neural networks for few epoches (within the sample steps). In this

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

paper, feedback weight W3 will be selected as an unit matrix, i.e., every hidden neuron only has the delayed feedback of itself. 4.2. The Learning Algorithm in Elman Neural Network. With the Elman neural network given in Figure 4, a learning algorithm is usually required to minimize an objective function E(k). For such purpose, a stochastic optimization algorithm reported in [15, 16]is adopted because of its reduced computational burden and good convergence property. Let Wi,j denote the connection weighting between neuron i and neuron j, during the kth step iteration Wi,j (k) = Wi,j (k − 1) + σi,j (k)

(4.6)

where 

−σ according possibility Pi,j (k) +σ according possibility 1 − Pi,j (k) where σ is a very small positive number, possibility Pi,j (k) is the Bolzeman distribution given below. 1 (4.7) Pi,j (k) = −Ci,j (k) 1 + e T (k) where T (k) is called temperature variable, Ci,j (k) is the relative measurement between the change of weighting and performance error. σi,j (k) =

Ci,j (k) = ∆Wi,j (k)∆E(k)

(4.8)

∆Wi,j (k) = Wi,j (k − 1) − Wi,j (k − 2)

(4.9)

∆E(k) = E(k − 1) − E(k − 2) (4.10) T (k) should be chosen as a large positive number in the initial state, and it will be updated every M iterations according to the mean ∆E(k). 4.3. Stability Analysis. Stability is a very important requirement for any traffic rate control system. If the system is not stable, the buffer level in the gateway may increase without bound causing buffer overflow. A variety of methods exist to asses the stability of a linear control system. Here we adopt the transfer function approach. It can be seen that the open loop transfer function from R to q is T q(z) = R(z) (4.11) z−1 With feedback control R(k) = −Kq(k) + v(k) where v(k) is an added control input. Then, the closed loop transfer function will be T q(z) = v(z) (4.12) z − 1 + KT where v(z) is the z-transform of vk). Remember that the adaptive controller is the proportional controller plus a neural network feedforward controller and the feed forward control does not change the stability [6], So the closed loop will be stable if system (4.12) is stable. Then, it can be deduced that the closed loop system is stable if K is less than or equal to T2 as reported in [5]. The stability only depends on the sampling time T .

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 10

5. Simulation. In order to validate the effectiveness of the proposed controller, one needs to initiate the Elman network with some training data. Here we call this stage as Off-line Training. 5.1. Off-line Training. First, the structure of the neural network approach for off-line training is showed in Figure 5. The expected buffer value is set to be qr = 5. The initial states of the Elman network are assumed to be zero. The number of hidden neuron in Elman neural network is 3. The parameter α = 0.5, β = 4 are used to generate the random noisy signal B(k), which is shown in Figure 6. Sampling time is selected as 0.5 second and 1000 sampling points are involved in the training data set. After 100000 epoches training, the training error is shown in Figure 7. It can be seen that the error is decreasing significantly with the learning iterations. Figure 8 presents the output of normal proportion controller with K = 3. Also the result of neural network adaptive controller with same B(k) is showed in Figure 9. The testing output driven by new random signal B(k) is given in Figure 10. Comparing these results, it can be found that the neural network adaptive controller has improved the performance greatly. Further. one can calculate the variance of error signal (qr − q(n)), and it is the 1.1449 for proportion controller and 0.1269 for neural network adaptive controller after 100000 epoches training, and 0.1083 for neural network adaptive controller with new B(k) testing signal. From these figures, one can find that the dynamical neural network can compensate the errors caused by B(k) significantly. 5.2. Packet Loss Probability. Here we consider the buffer overflow caused by proportion controller and neural network adaptive controller. We define L as the buffer length and qr is the half of the buffer length. To simplify the loss probability calculation, the number N of output q(n) being larger than L is counted. Define the packet loss probability N P = 1000 where 1000 is the data batch number for each buffer size. With this in mind, one can compare the packet loss results for proportion controller and neural network adaptive controller, which is shown in Figure 12. In this figure, P1 stands for proportion controller, and P2 stands for neural network adaptive controller. It can be seen that the neural network adaptive controller is much better. 5.3. On-Line Learning. One important feature of the proposed controller is its adaptivity to the change of the noise signal B(k). Next we will show the responses of the adaptive controller to different noise signals. First, 3000 sampling points are generated in which the first 1000 points are generated with the parameter β = 4 in (3.4), the left 2000 points are produced from (3.4) with β = 7. The initial weightings are from the off-line training results. B(k) is shown in Figure 13, and the on-line learning error is shown in Figure 14. The variance of error caused by initial weightings is 0.3540 and it is reduced to 0.2493 after two iterations. The longer it learns, the less error variance is expected. 6. Conclusions. The traffic rate control at the access-gateway of enterprise networks connected to the Internet using the ATM ABR service is further investigated in this paper. The model of a rate-based traffic management mechanism between the gateway and the enterprise network has been presented. A new adaptive controller based on Elman recurrent neural network has been designed in this paper.

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

Compared with the existing management schemes, the advantage of this new controller is its adaptivity to the available internet bandwidth. Simulations showed the effectiveness of the new approach. Acknowledgement. We thank the reviewers for some very useful suggestions.

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 12

Figure 4. Elman Neural Network Structure

Figure 5. Neural Network Adaptive controller Structure

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

Figure 6. Noise Signal B(k) with α = 0.5, β = 4

Figure 7. The training error of ALOPEX algorithm

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 14

Figure 8. The proportion control output

Figure 9. The neural network adaptive control output after 100000 epoches training

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

Figure 10. The neural network adaptive control testing output

Figure 11. The variance change for proportional controller and adaptive controller

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL 16

Figure 12. The Packet loss probability

Figure 13. The varied noise signal with β = 4 and β = 7

A NEW RECURRENT NEURAL NETWORK ADAPTIVE APPROACH FOR HOST-GATE WAY RATE CONTROL PROTOCOL

Figure 14. On-line adaptive learning error. REFERENCES [1] M. D. Prycker. (1995): Asynchronous Transfer Mode, Prentice Hall, Third edition. [2] M. Hassan, (1997) Impact of Variable Bandwidth on the performance of Data communications over ATM-ABR based LAN Interconnection. In 20th Australian Computer Science Conference. Sydney, Australia, 422-429 [3] S. Kalyanaraman, R. Jain, S. Fahmy, R. Goyal, and S. Kim, (1996) Performance of TCP over ABR on ATM backbone and with various VBR Traffic Patterns. ATM Forum Contributions. 96-1406 [4] M. Hassan, J.W. Breen and M. Atiquzzaman, (1999) HGRCP: A Rate-Based Flow Control Mechanism for Intranets Interconnected by ATM Networks, Computer Network and ISDN Systems. 31(22), 2361-2379. [5] M. Hassan, H. Sirisena and M. Atiquzzaman, (1999) A Congestion Control Mechanism for Enterprise Network Traffic over ATM Networks, Computer Communications, 22(14), 12961306. [6] C. C. Bissel, (1994) Control Engineering, Chapman and Hall, 2nd edition. [7] Paolo Narvaez and Kai-Yeung Siu, (1998) Acknowledge Bucket Scheme for Regulating TCP Flow over ATM, Computer Networks and ISDN systems, 30(19), 1775-1779. [8] B. Williamson, C. Farrell and D. Reid (1999) A consolidated flow control strategy for TCP over ABR using active networks. Proceedings of the IEEE International Conference on Computer Communication Networks (ICCCN’99).508-513. [9] Mahbub Hassan and M. Atiquzzaman, (2000) Performance of TCP/IP over ATM Networks, Artech House, Boston. [10] W. Stallings, (1998): High-Speed Networks, TCP/IP and ATM Design Principles, Prentice Hall. [11] Hoang, D. B. and Wang, Z. (1999): Performance of TCP Applications over ATM networks with ABR and UBR services-a simulation analysis, Computer Communications, 802-815. [12] G. Cybenko. (1989): Approximation by Superpositions of A Sigmoidal Function, Math. of Control,Signals,Systems 2(4), 303-314. [13] J. L. Elman. (1990): Find Structure in Time, Cognitive Science 12, 179-211. [14] L. X. Xu. (1999) Approximation Capability of Elman Neural Network, Proceedings of 14th World Congress of International Federation of Automatic Control. Beijing, China.

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[15] E. Harth, E. Tzanakou. (1974): ALOPEX: A Stochastic Method for Determing Visual Receptive Fields, Vision Res., 14(10), 1475-1482. [16] K. P. Unnikrishnan, K. P. Venugopal.(1992): Learning in Connectionist networks Using the Alopex Algorithm. Proceedings of IJCNN, Baltimore, 1, 926-931. [17] Simon Haykin, (1999) Neural Networks, Prentince Hall Press. [18] J. W. Roberts, (1992): Management Committee of the COST224 Project: Performance Evaluation and Design of Multiservice Network. Commission of the European Communities. [19] E. P. Rathgeb, (1991): Modeling and Performance Comparison of Policing Mechanisms for ATM Networks. IEEE Journal on selected areas in communications, 9(3): 325-334. [20] W. Q. Liu, Thanh Huu Tran and Harsha Sirisena (2002): A new state space cont rol scheme for host-gate way rate control protocol within intranets using ATM ABR service, Computer Communications, 25, 1799-1810.

Received for publication Nov. 2004.