Improving Computational Efficiency using Polynomial Congestion Control Algorithms MIMD-Poly and PIPD-Poly in TCP/IP Networks

Transcription

1 Improving Computational Efficiency using Polynomial Congestion Control Algorithms MIMD-Poly and PIPD-Poly in TCP/IP Networks M.Chandrasekaran, 1 and M.Kalpana 2 1 Assistant Professor, Department of ECE, Government College of Engineering, Salem , India. mcs123@rediffmail.com 2 Senior Lecturer, Department of ECE, Jayaram College of Engineering and Technology, Pagalavadi, Trichy , India. kalps_akila@yahoo.com Abstract - This paper proposes a technique for improving the computational efficiency using the congestion control algorithms. A class of nonlinear congestion control algorithms, called polynomial congestion control algorithms is introduced. This paper initially analyses the interaction between these algorithms and other Transmission Control Protocol (TCP) congestion control algorithms in TCP/IP networks. The proposed polynomial algorithms generalize the Additive Increase and Multiplicative Decrease (AIMD) algorithms used for the TCP/IP networks. These algorithms provide additive increase and multiplicative decrease using the polynomial of the current window size. Infinite numbers of TCP-friendly polynomial algorithms could be formulated by assuming polynomial of different order. By increasing the congestion window size faster, the proposed algorithms capture the channel bandwidth more. This additional bandwidth acquired, helps to improve the throughput and hence the overall efficiency of computations to be done on the information transferred using this additional bandwidth. A wired TCP network is simulated using ns2 to study the interaction between the various TCP algorithms. The results of simulation are compared with that of the TCP variants such as TCP/Tahoe, TCP/Reno, TCP/NewReno, and TCP/Vegas. The comparison shows that the proposed algorithms improve the long-term throughput. Keywords - Congestion control, TCP/IP, Polynomial algorithms, AIMD, ns2, Computational Efficiency. I. INTRODUCTION. During the last decade, computer networks have been growing very tremendously. Large number of computers gets connected to both private and public networks. In most of these networks the protocol stack used is TCP/IP. In spite of the rapid growth and explosive increase in traffic demand, computer networks in general, Internet in particular is still working without collapse. Also the growth of the Internet has sparked the demand of several applications, which require the stability of the Internet. For achieving such a success and to have the stability of Internet, mechanisms are developed to reduce transmission errors, to provide better bandwidth sharing of sources that use common bottleneck links, to reduce the round trip time (RTT) and mainly to provide the congestion control by the Transport layer protocol (TCP) in a TCP/IP network. TCP s end-to-end congestion control mechanism reacts to packet loss by adjusting the number of outstanding unacknowledged data segments allowed in the network [1] and [2]. Such algorithms are implemented in TCP. [3], [4] and [5]. 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 [11]. 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 [9]. These applications require more computations to be performed on large volumes of data. The data are to be transferred at a faster rate. This paper analyzes a new class of nonlinear congestion control algorithms for Internet Transport Protocols and applications. These proposed algorithms acquire more bandwidth and improve the efficiency of computation by increasing the throughput. [5], [6]. The authors analyze the proposed algorithms in a simulated wired TCP/IP network. The two models are proposed namely, MIMD-Poly and PIPD-Poly. They are compared with the TCP variants such as TCP/Tahoe (called as TCP), TCP/Reno, TCP/NewReno, and TCP/Vegas. The simulations are done in ns-2, the discrete event driven simulator that is used by most of the network researchers. This paper is structured as follows. Section 2 briefly describes the basic AIMD congestion control rules and the existing TCP congestion control algorithms. Section 3 discusses about the proposed generalized congestion control algorithms called Polynomial algorithms and the two models MIMD-Poly and PIPD-poly. Section 4 analyses the proposed algorithms. Section 5 simulates a wired TCP/IP network with Dumbbell topology and with different sources employing the various congestion control mechanisms. The results show an improved throughput and hence an improvement of computational efficiency.the paper finally concludes in section 6. II. WINDOW BASED CONGESTION CONTROL FOR TCP /IP NETWORKS. The state of art of the network congestion shows that it is a very difficult problem because there is no way to determine the network condition. The congestion occurs when there is a lot of traffic in the networks. Rapidly increasing bandwidth requirements and great variety of software applications have created a recognized need for

2 increased attention to TCP congestion control mechanisms [22]. TCP is a connection-oriented protocol that offers reliable data transfer as well as flow and congestion control. [5]. TCP maintains a congestion window that controls the number of outstanding unacknowledged data packets in the network. Sending data consumes slots in the window of the sender and the sender can send packets only as long as free slots are available [21]. On start-up, TCP performs slowstart, during which the rate roughly doubles each round-trip time to quickly gain its fair share of bandwidth [12]. 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 packet loss, indicated by a timeout, the congestion window is reduced to one slot and TCP reenters the slowstart phase. Packet loss indicated by three duplicate ACKs, results in a window reduction to half of its previous size. The AIMD algorithm may be expressed, as given in [9], [10] and [11], by the following rules. I: W t+r f W t + α ; α > 0 D: W t+δt f (1 - β ) W t ; ; 0< β < 1 (1) where I Increase in window as a result of the receipt of one window of acknowledgement in a round-triptime (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. There are many variations to these algorithms so as to quickly gain more bandwidth by adjusting the window size [22], [25]. The ns-2 simulator has implementations of many such variants [15]. The algorithm represented by (1) is implemented as TCP Congestion control algorithms [11]. The TCP variants implemented in ns-2 are TCP/Tahoe (simply denoted as TCP), TCP/Reno, TCP/NewReno, TCP/Vegas, TCP/SACK etc. These algorithms vary in slow-start and congestion avoidance phases [25]. III. POLYNOMIAL CONGESTION CONTROL ALGORITHMS This section presents the proposed polynomial congestion control algorithms. In theses algorithms the window adjustment policy is only one component of the congestion control protocol. Other mechanisms such as congestion detection (loss, ECN etc.), retransmissions (if required), estimation of Round-trip-time etc., remain the same as TCP [8]. The proposed algorithms mainly aim in increasing the window size faster to gain the bandwidth quicker. The authors generalized the AIMD rules into Polynomial rules in the following manner. They are given below: I : W t+r f W t + ( α / W t ) k + ( α / W t ) 2k + ( α / W t ) 3k ; α > 0 D: W t+δt f W t ( β W t ) l ( β W t ) 2l ( β W t ) 3l..... ; 0 < β < 1 (2) where k and l are two variables to define the order of the polynomial. These rules generalize the class of all congestion control algorithms based on window size adjustment. A. MIMD-Poly Now for the analysis of the algorithms, the rules in (2) are restricted into a model given below. I: W t+r f W t + ( α / W t ) k D: W t+δt f W t ( β W t ) l (3) The above rules are named as MIMD-Poly. For various values of k and l the above rules show the forms of various increase and decrease rules. (1) For k = 0, l = 1 the rules show AIMD. I: W t+r f W t + 1 D: W t+δt f W t β W t (4) (2) For k = -1, l = 1 the rules show Multiplicative Increase and Multiplicative Decrease (MIMD) I: W t+r f W t + W t / α D: W t+δt f W t β W t (5) (3) For k = -1, l = 0 the rules show Multiplicative Increase and Additive Decrease (MIAD) I: W t+r f W t + W t / α D: W t+δt f W t 1 (6) (4) For k = 0, l = 0 the rule show Additive Increase and Additive Decrease (AIAD) I: W t+r f W t + 1 D:W t+δt f W t 1 (7) B. PIPD-Poly By including the higher order terms polynomial algorithms of different orders are obtained. The following rules are obtained by considering the first two terms in (2). The rules are shown in (8). I: W t+r f W t + ( α / W t ) k + ( α / W t ) 2k ; α > 0 D: W t+δt f W t ( β W t ) l ( β W t ) 2l ; 0 < β < 1 (8) The above rules are named as PIPD-Poly. Using the above second order polynomial rules and assuming various values of k and l the following general polynomial algorithms are obtained. (1) For k = 0, l = 0 we get I: W t+r f W t + 2 D: W t+δt f W t 2 (9) These rules show AIAD. (2) For k = 1, l = 1 we get I: W t+r f W t + ( α / W t ) + ( α / W t ) 2 D: W t+δt f W t ( β W t ) ( β W t ) 2 (10) These rules show PIPD

3 (3) For k = 0, l = 1 the rules show Additive Increase and Polynomial Decrease (AIPD) and (4) For k = 1, 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. By including the higher order terms, polynomial increase and decrease algorithms of different orders are obtained that may be used for the window size adjustment for the congestion avoidance phase. IV. ANALYSIS OF THE ALGORITHMS: MIMD-POLY and PIPD- POLY. The polynomial algorithms, MIMD-Poly and PIPD- Poly are implemented as represented by equations (3) and (8). Both of 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 [12]. In this state, the congestion window size is doubled for every window of packets acknowledged. Upon the first congestion indication, the congestion window size is cut in half and the session enters into the polynomial congestion control state [11], [21] and [22]. In this state the congestion window size is increased by [( α / W t ) k + (α / W t ) 2k + ( α / W t ) 3k ] for each new acknowledgement 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) time-out. 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 1. The performance of these two algorithms are analysed by simulating selective packet drops [9], [21] and [25]. A. Simulation of Packet Drops The variations of window size with time for the MIMD-Poly and PIPD-Poly algorithms are studied by using the ns-2 simulations. The network topology, consisting of a TCP source node (n0) connected to a TCP receiver node (n3) through two IP routers (n1 and n2) as shown in figure 1, is used for analyzing the performance of the algorithms during packet drops. Figure 1. Topology to simulate the packet drops In figure 1 a TCP agent is attached to the source node and a TCP/Sink is attached to the receiver node. The links are assumed to be bidirectional with a bandwidth of 1Mbps. The link connecting the two IP routers is assumed with a buffer capacity of 20 and with Drop Tail buffer management algorithm. The data packets generated by an FTP Source is connected to the source node. The TCP agents are implemented with the MIMD- Poly and PIPD-Poly increase and decrease rules. These rules are implemented into the TCP agent program tcp.cc in ns-2. The program is modified such that the two algorithms are selected by choosing different values for the TCP/Agent variable windowoption_. If windowoption_ is 9, then MIMD-Poly is chosen and if it is 10, then PIPD-Poly is chosen. The selective packet drops is simulated and the effects of these drops on window size variations are recorded. Figure 2. Window size variation of MIMD-Poly Algorithm for the simulated packet drops Figure 3. Window size variation of PIPD-Poly Algorithm for the simulated packet drops The figures 2 and 3 show the window size vs. time plot for the simulated packet drops for MIMD-Poly and PIPD-Poly. The simulation is done for 5s. The simulation Program is written to drop the packets with sequence numbers 50, 150 and 700. The trace file generated by the simulator show that, in MIMD-Poly algorithm the packets are dropped at the time instances T 1 = 0.78s, T 2 = 1.205s and T 3 = 4.428s. In PIPD-Poly algorithm the packets are dropped at the time instances T 1 = 0.78s, T 2 = 1.205s and T 3 = 3.577s. The plots given in figures 3 and 4 shows that the two algorithms use the increase and decrease rules given by equations (3) and (8). The window size of the PIPD-Poly algorithm increases faster than the MIMD-Poly algorithm during the congestion avoidance phase. This is shown by the value of T 3 for PIPD-Poly, which is less than the value for MIMD-Poly. V. INTERACTION OF POLY ALGORITHMS IN WIRED TCP/IP NETWORKS This section presents the results of the ns-2 simulation of various polynomial algorithms in wired TCP/IP networks [15]. The authors start by investigating the connections running the polynomial algorithms MIMD-Poly

4 and PIPD-poly. The simulations use the topology shown in figure 4. It consists of 6 connections sharing a bottleneck link with bandwidth equal to 10 Mbps, 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. Each source always has data to send, modeled using the network simulators FTP application. On simulation the values of window size and throughput are observed and the figures display this information. Fig 5. (c) TCP/New Reno Figure 4. Dumbbell Topology used for wired TCP network Fig 5. (d) TCP/Vegas Fig. 5. (a) TCP Fig 5. (e) MIMD-Poly Fig 5. (b) TCP/Reno The results are obtained using the Drop Tail buffer management algorithm at the bottleneck gateway [16], [17]. Figure 5 (a) to (f) shows the variation of window size over a simulation period of 10 sec for TCP, TCP/Reno, TCP/NewReno, TCP/Vegas, MIMD-Poly and PIPD-Poly models. Fig 5. (f) PIPD-Poly Figure 5. (a) to (f). Window size vs. time (α =0.33 and β=0.2) The results show that both congestion control algorithms are TCP-compatible and MIMD-Poly consumes more bandwidth than PIPD-Poly. The vertical lines in the graph for TCP/Reno and TCP/NewReno show that, the congestion control results into oscillations of window size,

5 due to packet drops. The simulation is repeated for durations varying from 5 sec to 2000 sec. The results are used to evaluate the total throughput for each source. The throughput (λ ) is modeled by, c s λ = (11) R p where s is the segment size, R is the round trip time, p is the packet loss rate and c is a constant value commonly approximated as The evaluated throughput is plotted in figures 6 and 7. The results show that the throughput proportionately increases with the increased simulation duration, for all the TCP sources. But the rate of increase of total throughput of the proposed two models is very high compared to the other algorithms. Between the two models, MIMD-Poly performs better for durations above 490 sec, below which PIPD-Poly has larger throughput. Throughput in KB THROUGHPUT Vs. TOTAL DURATION Simulation Duration in Sec TCP Reno NewReno Vegas MIMD-Poly PIPD-Poly Fig 6. Total Throughput Vs. Time (Simulation Duration: 5 to 50 sec) Throughput in KB THROUGHPUT Vs. TOTAL DURATION Simulation Duration in Sec TCP Reno NewReno Vegas MIMD-Poly PIPD-Poly Fig 7. Total Throughput Vs. Time (Simulation Duration: 5 to 2000 sec) In applications like real time audio and video streaming, large volumes of information need to be processed and transferred between nodes. In distributed computing environment, the computations are shared among various nodes that require the data to be received in time. This necessitates that the channel throughput should be more. Hence increased throughput of both the Poly algorithms will increase the data transferred and hence will improve the efficiency of computation. VI. CONCLUSION This paper aimed at providing a technique for improving the computational efficiency by increasing the throughput offered to the nodes. This paper presents and evaluates a family of nonlinear congestion control algorithms, called polynomial algorithms for improving throughput. Two models, MIMD-Poly and PIPD-Poly are assumed for analyzing their interaction with other TCP variants. These polynomial algorithms generalize the familiar class of linear algorithms (AIMD). The Dumbbell topology with 6 TCP source-sink pairs connected through two IP routers is assumed for simulation. The simulation results showed good performance and interactions between polynomial algorithms (MIMD- Poly and PIPD-Poly) and TCP using standard algorithms in wired and mobile ad hoc networks. The algorithms MIMD- Poly and PIPD-Poly obtain higher long-term throughput than the standard algorithms for TCP, TCP/Reno, TCP/NewReno and TCP/Vegas. The figure 5 shows the variation of congestion window with respect to time for the TCP, TCP/Reno, TCP/NewReno, TCP/Vegas, TCP/MIMD-Poly and TCP/PIPD-Poly algorithms in the case of TCP/IP wired network topology shown in figure 4. Figure 6 and 7 displays the total throughput for the TCP variants in wired TCP/IP network for the simulation durations varying from 5 sec to 2000 sec. The authors believe that the results presented in this paper lead to an understanding of the issues involved in the increase and decrease phases of a congestion control algorithms. The results also show that both Poly algorithms can capture more bandwidth by adjusting the window size. The long-term throughput of both the algorithms are more and hence provide a way of improving the computational efficiency. REFERENCES [1]. Van Jacobson, "Congestion Avoidance and Control," ACM Computer Communication Review, vol.18, pp , Aug Proceedings of the Sigcomm '88 Symposium in Stanford, CA, August [2]. J. Widmer, R Denda, and M Mauve. A Survey on TCP-Friendly Congestion Control. IEEE Network Magazine, May [3 Douglas E. Comer, Internetworking with TCP/IP Volume I, Englewood Cliffs, New Jersey, Prentice Hall, [4]. W. R. Stevens, TCP/IP Illustrated, Volume 1, Addison-Wesley, Reading, MA, November [5]. M. Allman and V. Paxson, TCP Congestion Control, Internet Engineering Task Force, April 1999, RFC [6]. Sally Floyd and Kevin Fall, Promoting the use of end-to-end congestion control in the Internet, IEEE/ACM Transactions on Networking, vol. 7(4), pp , August [7]. 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 1999, vol. 3, pp [8]. Sally Floyd, "TCP and Explicit Congestion Notification," ACM Computer Communication Review, vol. 24, pp. 8-23, Oct

6 [9]. 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 2001, Available at [10]. Deepak Bansal and Hari Balakrishnan, Binomial congestion control algorithms, in Proceedings of IEEE INFOCOM, April [11]. Y. Richard Yang and Simon S. Lam, General AIMD congestion control, in Proceedings of ICNP, November [12]. Zheng Wang and Jon Crowcroft, "A New Congestion Control Scheme: Slow Start and Search (Tri-S)," ACM Computer Communication Review, vol. 21, pp 32-43, Jan 1991 [13]. Lawrence S. Brakmo 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 [14]. D. Bansal and H. Balakrishnan, TCP-friendly Congestion Control for Real-time Streaming Applications, Tech. Rep. MIT-LCS-TR-806, MIT Laboratory for Computer Science, May 2000 [15]. ns-2 Network Simulator, [16]. S. Floyd and V. Jacobson, Random Early Detection Gateways for Congestion Avoidance, IEEE/ACM Transactions on Networking, vol. 1, no. 4, Aug [17]. Tejas Kokje Vijay Kakadia, Analysis of Congestion Control Strategies For TCP Variants Using Droptail and RED Queuing Disciplines, Department of Computer Science University of Southern California, Los Angeles [18]. K.Sundaresan, V.Anantharaman, H-Y Hsieh, and R.Sivakumar. ATP: a reliable transport protocol for ad hoc networks, ACM Mobihoc, Jun [19]. G.Holland, and N.H.Vaidya, Analysis of TCP performance over mobile ad hoc networks, ACM MOBICOM 99, Seattle, August [20]. K.Chen, Y.Xue, and K.nahstedt, On setting TCP s congestion window limit in mobile ad hoc networks, IEEE ICC 03, Anchorage, Alaska, May [21]. Kevin Fall and Sally Floyd, Simulation-based Comparisons of Tahoe, Reno, and SACK TCP. Computer Communications Review, July 1996 [22]. Georgi Kirov, A Simulation Analysis of the TCP Control Algorithms,International Conference on Computer Systems and Technologies - CompSysTech [23]. K. Seada, S. Gupta, and A. Helmy. Systematic Evaluation of Multicast Congestion Control Mechanisms. SCS SPECTS, July [24]. K. Seada and A. Helmy. Fairness Evaluation Experiments for Multicast Congestion Control Protocols. Technical Report ,University of Southern California, CS Department, March 2002 [25]. Bogdan Moraru, Flavius Copaciu, Gabriel Lazar and Virgil Dobrota, Practical Analysis of TCP Implementations: Tahoe, Reno, NewReno, Technical University of Cluj-Napoca