2 Department of ECE, Jayaram College of Engineering and Technology, Pagalavadi, Trichy,

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1 End-to-End Congestion Control using Polynomial Algorithms in Wired TCP Networs M.Chandrasearan, M.Kalpana, 2 and Dr.R.S.D.Wahida Banu 3 Assistant Professor, Department of ECE, Government College of Engineering, Salem 636 0, India.mcs23@rediffmail.com 2 Department of ECE, Jayaram College of Engineering and Technology, Pagalavadi, Trichy, India.alps_aila@yahoo.com 3 Assistant Professor, Department of CSE, Government College of Engineering, Salem 636 0, India rsdwb@yahoo.com Abstract This paper introduces and analyses a class of nonlinear congestion control algorithms called polynomial congestion control algorithms. They generalize the AIMD algorithms used for the TCP connections. These algorithms provide additive increase and multiplicative decrease using the polynomial of the current window size. There are infinite numbers of TCP-compatible polynomial algorithms by assuming polynomial of different order. This paper analyses the performance of two models of these generalized algorithms for the TCP networs. TCP compatibility of these algorithms is evaluated using the simulations done using ns2, a discrete event simulator. One such model is also proved to be TCP- compatible. The results of simulation are compared withthat of TCP and TCP/Reno. Keywords: Congestion control, TCP, non-linear algorithms, AIMD, ns2, Mobile ad hoc networs.. Introduction. The rapid growth of the Internet has spared the demand of several applications, which require the stability of the Internet. The stability of Internet depends on transmission errors, bandwidth sharing of sources that use common bottlenec lins, round trip time (RTT) and mainly due to congestion. TCP/IP is the standard networ protocol stac on the Internet. TCP s end-to-end congestion control mechanism reacts to pacet loss by adjusting the number of outstanding unacnowledged data segments allowed in the networ [], [8]. Such algorithms are implemented in its protocol, TCP. [2], [3] and [4]. In the existing algorithms, increasing the congestion window linearly with time increases the bandwidth of the TCP connection and when the congestion is detected, the window size is multiplicatively reduced by a factor of two. TCP is not well suited for several emerging applications including streaming and real time audio and video because it increases end-to-end delay and delay variations. In this paper a new class of nonlinear congestion control algorithms for Internet Transport Protocols and applications are presented for analysis. The authors see to develop a family of algorithms for applications such as Internet audio and video that does not react well to rate reductions, because the rate reduction technique used for these applications will result into the degradation in userperceived quality [5], [6]. TCP-compatibility of the generalized Additive Increase and Multiplicative Decrease (AIMD) congestion control algorithms are studied and the proposed algorithms are simulated wired TCP networ. In this paper the performance of the proposed algorithms in Mobile Ad hoc Networs that uses TCP are also studied. The rest of this paper is organized as follows: section 2 discusses the window based TCP congestion control mechanism. Section 3 discusses about the proposed generalized congestion control algorithms called Polynomial algorithms and the two models used for our simulations. Section 4 discusses the implementation details and TCP compatibility of one such model. In section 5 the implementation details, simulation and analysis of the two models for wired TCP networ are explained. Simulation of the proposed models for Mobile Ad hoc Networs are given in section 6. This paper finally concludes in section Window Based Congestion Control for TCP Networs. TCP is a connection-oriented protocol that offers reliable data transfer as well as flow and congestion control. [8]. TCP maintains a congestion window that controls the number of outstanding unacnowledged data pacets in the networ. Sending data consumes slots in the window of the sender and the sender can send pacets only as long as free slots are available. On start-up, TCP performs slowstart, during which the rate roughly doubles each round-trip time to quicly gain its fair share of bandwidth. In steady state, TCP uses the AIMD mechanism to detect additional bandwidth and to react to congestion. When there is no indication of loss, TCP increases the congestion window by one slot per round-trip time. In case of pacet loss, indicated by a timeout, the congestion window is reduced to one slot and TCP reenters the slowstart phase. Pacet loss ind icated b y three duplicate results in a window reduction to half of its previous size. The AIMD algorithm may be expressed as given in [8], [9] and [0]. ACKs I: W t+rf W t + α ; α > 0 D: W t+δtf ( - β ) W t;0< β < () where I In cr e a s e in window as a result of the receipt of one window of acnowledgement in a round-trip-time (RTT) and D Decrease in window size on detection of congestion by the sender W t Window size at time t R RTT of the flow and α and β Increase and Decrease Rule constants.

2 3. Polynomial Congestion Control Algorithms This section discusses the properties of polynomial congestion control algorithms. The window adjustment policy is only one component of the congestion control protocol derived from polynomial algorithms. Other mechanisms such as congestion detection (loss, ECN etc.), retransmissions (if required), estimation of Round-trip-time etc., remain the same as TCP [7]. The authors propose a generalization of the AIMD rules in the following manner, in order to study and understand the notions of TCP compatibility and the trade off between the increase and decrease rules. The polynomial rules are given below: I : Wt+R f Wt + ( α / Wt ) + ( α / Wt ) 2 + ( α / Wt ) ; α > 0 D: Wt+δtf Wt - ( β Wt ) l - ( β Wt ) 2l - ( β Wt ) 3l ; 0 < β < (2) These rules generalize the class of all congestion control algorithms based on window size adjustment. Now for the analysis of the algorithms the above rules are restrict ed into a Model as given below. I: W t+r f W t + ( α / W t ) D: W t+δtf W t - ( β W t ) l (3) For various values of and l the above rules show the forms of various increase and decrease rules () For = 0, l = the rules show AIMD. I: W t+r f W t + D: W t+δtf W t - β W t (4) (2) For = -, l = the rules show Multiplicative Increase and Multiplicative Decrease (MIMD) I: W t+r f W t + W t / α D: W t+δtf W t - β W t (5) (3) For = -, l = 0 the rules show Multiplicative Increase and Additive Decrease (MIAD) I: W t+r f W t + W t / α D: W t+δtf W t - (6) (4) For = 0, l = 0 the rule show Additive Increase and Additive Decrease (AIAD) I: W t+r f W t + D:W t+δtf W t - (7) The polynomial algorithms of different order are obtained by including the higher order terms. For example, the authors assume the general rules restricted to the first two terms only (second order polynomial algorithms) as shown below: I: W t+r f W t + ( α / W t ) + ( α / W t ) 2 ; α > 0 D: W t+δtf W t - ( β W t ) l - ( β W t ) 2l ; 0 < β < (8) Using the above second order polynomial rules and assuming various values of and l the following general polynomial algorithms are obtained: () For = 0, l = 0 the rules show AIAD. I: W t+rf W t + 2 D: W t+δtf W t - 2 (9) (2) For =, l = the rules show PIPD. I: W t+r f W t+ ( α / W t) + ( α / W t ) 2 D: W t+δtf W t - ( β W t) - ( β W t) 2 (0) (3) For = 0, l = the rules show Additive Increase and Polynomial Decrease (AIPD) and (4) For =, l = 0 the rules show Polynomial Increase and Additive Decrease (PIAD). By choosing different values of α and β in equations (3) and (8), they became the members of the polynomial family. All possible algorithms that may be used for the window size adjustment for the congestion avoidance are obtained by including the higher order terms 4. Implementation The authors have implemented the algorithms represented by equations (3) and (8) and these polynomial algorithms are named as MIMD and PIPD. Both these algorithms are implemented to study the variation of window size and the resulting throughput with respect to time. The algorithm begins in the slowstart state []. In this state, the congestion window size is doubled for every window of pacets acnowledged. Upon the first congestion indication, the congestion window size is cut in half and the session enters into the polynomial congestion control state. In this state the congestion window size is increased by [( α / W t ) +(α / W t ) 2 + ( α / W t ) ] for each new acnowledgement received, where W t is the current congestion window size. The algorithm reduces the window size when congestion is detected. Congestion is detected by two events: (i) triple-duplicate ACK and (ii) timeout. If by triple-duplicate ACK, the algorithm reduces the window size by [( β W t ) l -( β W t ) 2l -( β W t ) 3l -... ]. If the congestion indication is by time-out, the window size is set to. The algorithms for MIMD and PIPD are implemented as explained above. The window size and throughput of these algorithms are compared with the standard congestion algorithms for TCP and TCP/Reno [8], [2]. 4.. Throughput The throughput of the MIMD polynomial algorithm is analysed now as a function of the loss- rate it experiences. The analysis is similar to the analysis explained in [8], [9]. T h e following analysis is made by using the Increase rule of MIMD of the polynomial algorithms and by linear interpolation of window size between W t and Wt+R : dw dt + = α () W R W α t = + C (2) + R where C is the constant of integration. The functional form of this curve is shown in figure. The two parameters which are of interest are T d, and N d mared in the figure ; where T d is the time between two successive pacet drops, and N d is the number of pacets received between two successive drops.

3 W m Fig. Functional form of window vs. time curve Let W m be the maximum value of the window W t at time t 2, at which congestion occurs. Then the expressions for T d and N d are evaluated as given below: T d = t 2 t R α ( + ) + l l + = W - ( Wm β Wm ) + l l + R Wm α ( + ) = ( β W ) = W α R W + + ( ) m l l β Wm ( + ) l β R + m (3) α + N d is the shaded area under the curve in figure. l T d W ( ) N d= ( + ) + α R + α t dt R R Calculating the integral results into l N β +l+ d = W m ( + ) t + T d t t 2 (4) (5) α The average throughput, λ of a flow using the polynomial congestion control Model is the number of pacets sent between successive drops (N d ) divided by the duration between drops (T d ). The pacet loss probability p = / N d. Writing λ and p in terms of Wm by substituting the expressions for N d and T d yield: λ / p /+l+ (6) This implies that for polynomial Model to be TCPcompatible as per [9], λ must vary as / p 0.5, and hence +l =. (Refer [8], [3]). This can be extended to find the throughput of the polynomial Model 2 also. The authors have restricted the analysis for the Model and in future attempt N d t will be made to prove the TCP-compatibility of the throughput relation for the Model 2 and other polynomial models. 5. Simulation and Analysis Wired TCP Networs This section presents the results of ns-2 [4] simulation of various polynomial algorithms in wired TCP networs. T h e a u t h o r s investigated the connections running the TCPcompatible polynomial algorithms MIMD and PIPD represented by equations 3 and 8. The simulations use the topology shown in figure 2. It consists of 4 connections sharing a bottlenec lin with total bandwidth equal to 2Mbps, where all connections have an almost identical round-trip propagation delay equal to 20ms. Each polynomial flow uses a modified TCP with AIMD algorithm replaced by the polynomial family; other mechanisms lie slow-start and time-out remain unchanged as already mentioned in the implementation section of this paper. Each source always has data to send, modeled using networ simulator s FTP application. The figures and graphs display the information of the observed values. The results are obtained using the Drop Tail buffer management algorithm at the bottlenec gateway [5], [6]. Figures 3 and 5 shows the variation of window size over a simulation period of 200 sec for TCP, TCP/Reno, and MIMD and PIPD models. The increase and decrease parameters α and β are also changed. The results show that PIPD model seems to be TCP-compatible and MIMD model consumes most of the bandwidth. Fig 2. Simulation Topology (simulated using ns2) Figures 4 and 6 show the throughput of the TCP, TCP/Reno, MIMD and PIPD models for two different values of increase and decrease parameters, α and β. The throughput (λ ) is modeled using the equation (7). c s λ = (7) R p

4 Figure 3.Window size vs time of TCP, TCP/Reno, MIMD Model and IPDModel2. ( α= 0.75 and β = 0.25 ) Figure 6.Throughput size vs time of TCP, TCP/Reno, MIMD Model and IPDModel2. ( α=.75 and β = 0. ) where s is the segment size, R is the round trip time, p is the pacet loss rate and c is a constant value commonly approximated as The graphs show that the throughput of MIMD model is very high and PIPD model is comparable with that of TCP and TCP/Reno. Figure 4.Throughput vs time of TCP, TCP/Reno, MIMD Model and IPDModel2. ( = 0.75 and = 0.25 ) Figure 5. Window size vs time of TCP, TCP/Reno, MIMD Model and IPDModel2. ( α=.75 and β = 0. ) 6. Simulation and Analysis Mobile Ad hoc Networs A Mobile Ad hoc Networ is a networ in which a group of mobile computing devices communicate among themselves using wireless radios, without the aid of a fixed networing infrastructure [7], [8]. They can be used anywhere that a fixed infrastructure does not exist, or is not desirable.. Mobile ad hoc networs provide an extension to the Internet. Since TCP/IP is the standard networ protocol on the Internet, its use over mobile ad hoc networ is a certainty [9], [20]. In this paper the performance of the proposed window based Polynomial congestion control algorithms over the mobile ad hoc networs are also analysed and compared with the standard algorithms implemented for TCP and TCP/Reno. A mobile networ is simulated with the proposed algorithms using the four routing algorithms used for Mobile ad hoc networs: Dynamic Source Routing (DSR), Dynamic Destination Sequenced Distance Vector (DSDV) Routing, Ad-hoc On- demand Distance Vector (AODV) Routing and Temporarily Ordered Routing Algorithm (TORA) [9], [2]. Even though the TCP congestion control algorithms in the form implemented for the wired networs can not be used for mobile ad hoc networs, a study is carried to compare the performance assuming the pacet drop is only due to congestion. But in practical scenario the pacet drop is also due to other facts such as transmission loss, radio lin failure, node movements and node failure etc. The throughput is evaluated based on the equation (7). Figure 7 shows the comparison of the total throughput of TCP, TCP/Reno, and MIMD and PIPD congestion control for each of the four routing algorithms.

5 Total Throughput Throughput in Kbps TCP/Reno TCP MIMD PIPD AODV DSDV DSR TORA Figure 7. Total throughput of TCP, TCP/Reno, MIMD and PIPD Algorithm The results show that the PIPD and MIMD algorithms improved the total throughput regardless of the routing method used. 7. Conclusion In this paper, the authors presented and evaluated a family of nonlinear congestion control algorithms, called polynomial algorithms. The Model and Model 2 of the polynomial family are considered for experimentation. These polynomial algorithms generalize the familiar class of linear algorithms. The authors showed that for one of the restricted model of the polynomial family, Model, the throughput λ / p /+l+, where p is the pacet loss rate it encounters. This shows that the model is TCP compatible. The simulation results showed good performance and interactions between polynomial algorithms (Model and Model 2) and TCP in wired and mobile ad hoc networs. The algorithms MIMD and PIPD obtain higher long-term throughput than TCP and TCP/Reno. The figures 3, 4, 5 and 6 show the variation of congestion window and throughput with respect to time for the TCP, TCP/Reno, MIMD and PIPD Algorithms in the case of wired networ topology shown in figure 2. Figure 7 display the total throughput for the algorithms using different routing methods in mobile ad hoc networ. The results show that the two proposed algorithms results in two higher long term throughput compared with TCP and TCP/Reno. REFERENCES []. Van Jacobson, "Congestion Avoidance and Control," ACM Computer Communication Review, vol.8, pp , Aug Proceedings of the Sigcomm '88 Symposium in Stanford, CA, August 988. [2]. Congestion Control Schemes for TCP/IP Networs current implementation in BSD Unix. Douglas E. Comer, Internetworing with TCP/IP Volume I, Englewood Cliffs, New Jersey, Prentice Hall, 99. [3]. W. R. Stevens, TCP/IP Illustrated, Volume, Addison-Wesley, Reading, MA, November 994. [4]. M. Allman and V. Paxson, TCP Congestion Control, Internet Engineering Tas Force, April 999, RFC 258. [5]. Sally Floyd and Kevin Fall, Promoting the use of end-to-end congestion control in the Internet, IEEE/ACM Transactions on Networing, vol. 7(4), pp , August 999. [6]. R. Rejaie, M. Handley, and D. Estrin, RAP: An End-to-end Rate-based Congestion Control Mechanism for Real time Streams in the Internet, in Proc. IEEE INFOCOM, March 999, vol. 3, pp [7]. Sally Floyd, "TCP and Explicit Congestion Notification," ACM Computer Communication Review, vol. 24, pp. 8-23, Oct [8]. Shudong Jin, Liang Guo, Ibrahim Matta, and Azer Bestavros, A spectrum of TCP-friendly window-based congestion control algorithms, Tech. Rep. BU-CS , Computer Science Department, Boston University, July 200, Available at [9]. Deepa Bansal and Hari Balarishnan, Binomial congestion control algorithms, in Proceedings of IEEE INFOCOM, April 200. [0]. Y. Richard Yang and Simon S. Lam, General AIMD congestion control, in Proceedings of ICNP, November []. Zheng Wang and Jon Crowcroft, "A New Congestion Control Scheme: Slow Start and Search (Tri-S)," ACM Computer Communication Review, vol. 2, pp 32-43, Jan 99 [2]. Lawrence S. Bramo and Sean W. O'Malley, "TCP Vegas: New Techniques for Congestion Detection and Avoidance," in SIGCOMM '94 Conference on Communications Architectures and Protocols, (London, United Kingdom), pp , Oct [3]. D. Bansal and H. Balarishnan, TCP-friendly Congestion Control for Real-time Streaming Applications, Tech. Rep. MIT-LCS-TR-806, MIT Laboratory for Computer Science, May 2000 [4]. ns-2 Networ Simulator, [5]. S. Floyd and V. Jacobson, Random Early Detection Gateways for Congestion Avoidance, IEEE/ACM Transactions on Networing, vol., no. 4, Aug. 993 [6]. Tejas Koje Vijay Kaadia, Analysis of Congestion Control Strategies For TCP Variants Using Droptail and RED Queuing Disciplines Department of Computer Science University of Southern California, Los Angeles [7]. Xiang Chen, Hongqiang Zhai,Jianfeng Wang, and Yuguang Fang, TCP Performance over Mobile Ad Hoc Networs [8]. Jorg Widmer, Robert denda, and Martin Mauve, A Survey on TCP- Friendly Congestion Control. [9]. K.Sundaresan, V.Anantharaman, H-Y Hsieh, and R.Sivaumar. ATP: a reliable transport protocol for ad hoc networs, ACM Mobihoc, Jun [20]. G.Holland, and N.H.Vaidya, Analysis of TCP performance over mobile ad hoc networs, ACM MOBICOM 99, Seattle, August 999. [2]. K.Chen, Y.Xue, and K.nahstedt, On setting TCP s congestion window limit in mobile ad hoc networs, IEEE ICC 03, Anchorage, Alasa, May 2003.