Observingtheeffectof TCP congestion controlon networktraffic

Observingtheeffectof TCP congestion controlon networktraffic YongminChoi 1 andjohna.silvester ElectricalEngineering-SystemsDept. UniversityofSouthernCalifornia LosAngeles,CA90089-2565 {yongminc,silvester}@usc.edu Abstract In this paper we quantitatively observe the relationship between packet loss rate and degree of traffic burstiness using ns-2 network simulations. We examine the traffic behavior of a single TCP connection in a lossy environment. The loss agent in the simulation uniformly drops incoming packets with a given probability. By changing the packet loss rate, we can vary the congestion level of network and influence the behavior of TCP s congestion control mechanism. We measure the variation of traffic burstiness as the packet loss rate is changed. We also observe different traffic behavior with respect to the types of traffic sources. It is observed that for exponential traffic source, the degree of traffic burstiness is influenced by the packet loss rate over some range. However, the degree of traffic burstiness for Pareto traffic source is almost the same regardless of the packet loss rate. While our simulation is similar to previous works [1][2], the observation is interesting since the relationship between packet loss rate and degree of traffic burstiness is measured quantitatively. Index Terms TCP congestion control, exponential back-off, heavy-tailed distribution, traffic characterization and modeling. I. INTRODUCTION Self-similarity is a well-known phenomenon in a number of measurements over a wide range of networks including Ethernet, wide area network, and WWW (world wide web). In networking area, self-similarity means qualitatively that when we aggregate a traffic process with respect to timescale, correlation structure of the aggregated process is similar to that of the original traffic process. In other words, bursty traffic remains bursty when we look at the traffic at large timescales. Self-similarity manifests itself mathematically in a number of equivalent ways. One example of those representations is long-range dependence in which the autocorrelation of traffic decays more slowly than that of a traditional Markovian (or memoryless) process does. While the autocorrelation function of a memoryless process decays exponentially, the autocorrelation function of a self-similar process decays hyperbolically fast and it implies strong correlation structure in such a process. We refer to [3][4][5] for exact definition and properties of self-similar processes. There have been diverse research efforts to investigate various aspects of traffic self-similarity, for example, modeling techniques, impact on network performance, and explanations 1 Yongmin Choi is a Ph.D. student at the University of Southern California. He is now with Service Development Laboratory at KT Corporation, Seoul 137-792, Korea. for the presence of self-similar traffic. To explain why selfsimilar traffic arises, many researchers have examined the traffic in two different perspectives: statistical properties of traffic source (especially with heavy-tailed distributions) and networking mechanisms (TCP flow/congestion control). It is shown that file sizes, flow (or session) durations with heavy-tailed distributions can induce self-similar traffic [6][7][8]. This perspective mainly deals with application/session layer quantities such as file size and session durations, or with user behaviors such as user think time. Regarding the networking mechanisms, we reviewed the following two works. In [1], the authors claim that the TCP congestion control mechanism generates heavy-tailed off periods in the traffic transmission pattern, which introduces long-range dependence in the traffic. They argue that the exponential backoff mechanism extends the packet inter-departure time distribution and that the traffic shows pseudo self-similarity in that scaling behaviors of traffic exist only over a finite range of timescales. In another work [2], the authors assert that not only the exponential back-off but the congestion avoidance mechanism is also responsible for the traffic self-similarity. They argue that at low packet loss probability, a sustained correlation appears due to congestion avoidance and at high probability the correlation appears due to the timeout mechanism. In this paper, we extend the previous research findings and observe effect of TCP congestion control mechanisms upon the degree of self-similarity in data network traffic. In our simulation, we observe traffic behavior of a single TCP connection in lossy environment. As we vary the packet loss rate of a TCP connection (i.e. network congestion level), TCP adaptively changes its congestion window size and packet transmission rate to cope with available bandwidth. The packet interdeparture time distribution for the resulting TCP traffic is affected by the packet loss rate and the degree of traffic burstiness varies in proportion as the distribution is changed. We carefully observe the relationship between packet loss rate and degree of self-similarity in traffic using ns-2 network simulation. Specifically, we observe the influence of TCP congestion control on the packet inter-arrival time distribution and the degree of traffic burstiness. For the traffic source, we use two types of packet inter-arrival distributions: exponential and Pareto. It is shown that the packet inter-departure time distribution at the TCP sender node is the same as the original inter-arrival distribution when the packet loss rate is low. 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ever, when the packet loss rate is high, the distribution becomes heavy-tailed and looks similar regardless of the type of traffic source. On the other hand, the degree of traffic burstiness depends on the type of traffic source. For the exponential source, the Hurst parameter is changed as the packet loss rate is increased. However, there is no apparent change in the Hurst parameter for the Pareto source over the range of packet loss rate we experimented. While our simulation is similar to the works in [1] [2], the relationship between packet loss rate (i.e. heavy-tailedness of packet inter-departure time distribution) and degree of selfsimilarity is examined quantitatively. The rest of this paper is organized as follows. In section 2, we briefly summarize the related mathematical concepts in selfsimilar traffic. Section 3 presents our simulation setup and scenario. Section 4 provides simulation results and discussions on the results. We summarize future research direction in section 5. II. BACKGROUNDS In this section, we briefly review some related concepts in self-similar traffic analysis. A more formal description can be found in [9] and references therein. A real-valued, discrete time random process X = {X t : t = 0, 1, 2,...}, is called a covariance stationary process if it has a finite mean µ, a finite variance R(0), and a time-homogeneous covariance function. The time-homogeneous covariance function R(k) is defined as R(k) = E{(X t µ)(x t+k µ)}, k = 0, ±1, ±2,... (1) where µ = E[X t ] < and r(0) <. For each m = 1, 2,..., we define the m-aggregated process X (m) = {X (m) t, t = 0, 1, 2,...} by summing the original time series over nonoverlapping, adjacent blocks of size m as follows: X (m) t = 1 m tm i=(t 1)m+1 X i (2) A discrete-time process X t is said to be exactly self-similar if for all m = 1, 2,..., the autocorrelation functions of the m- aggregated process and the original process are the same, i.e., R X (m)(k) = R X (k) (3) There is a weaker condition of self-similarity. A process is said to be asymptotically self-similar if the autocorrelation function of m-aggregated process is asymptotically the same as that of the original process for all m large enough R X (m)(k) R X (k) as m (4) We can interpret the aggregation of time series as compression of the timescale so that the original process X t has the highest resolution possible and the m-aggregated process is the same process reduced in resolution by a factor of m [10]. By averaging over each set of m points, we lose the fine details of the original process available at the highest resolution. With this definition of self-similarity, the autocorrelation of the aggregated process has the same form as that of the original process. This implies that the degree of variability, or burstiness in self-similar traffic would be the same at different timescales. Mathematically self-similarity is observed in a number of equivalent ways: slowly decaying variance, long-range dependence, and power-low behavior near the origin (1/f-noise) [3]. For a self-similar process, the variance of the time average does not go to zero as quickly as that of an ergodic process. The time average of an ergodic process should equal an ensemble average and the variance of the time average goes to zero relatively quickly as m becomes large. On the other hand, the variance of the time average for a self-similar process does so more slowly (slowly decaying variance). Thus, we have a self-similar process X with parameter β (0 < β < 1) if it satisfies for all m = ±1, ±2,..., V ar(x (m) ) = V ar(x) m β (5) An ergodic process has a parameter β = 1. For a self-similar process, the degree of burstiness (or selfsimilarity) is represented by a single parameter called the Hurst parameter, H. The Hurst parameter is related with the slope parameter β as follows: H = 1 β/2 (6) To measure the degree of burstiness for the synthetic traffic generated by the simulation, several estimation methods are used. In our simulation, we extensively use the wavelet-based tool [11]. The tool estimates the variance of wavelet coefficients of the packet series at particular timescales. This estimate is then plotted in a log-log scale diagram and the least square fit over all timescales is calculated. Then the slope of this asymptotic linear region gives an estimate of the Hurst parameter. Before performing the wavelet analysis, the synthetic traffic trace was aggregated into bins with size smaller than one RTT. The aggregated time series was analyzed using the publicly available tools. Lastly we review heavy-tailed distribution which is related to the self-similar traffic. As explained in the introduction, the traffic self-similarity can attributed to the application or session layer quantities with heavy-tailed distributions such as file sizes, flow (or session) durations [6][7][8]. Heavy-tailed distributions are introduced to explain the traffic self-similarity with TCP flow/congestion control [1][2]. The packet interarrival time distribution is classified as heavy-tailed over the finite range of timescales. A distribution is defined as heavytailed if the asymptotic behavior of the distribution follows the power-law with exponent less than 2, i.e., P [X x] x α, as x, 0 < α < 2 (7) When the packet inter-arrival time distribution is heavy-tailed, the resulting traffic is self-similar with the Hurst parameter given as follows: H = 3 α (8) 2 1-56555-276-8 64 Applied Telecommunications Symposium

Incoming traffic ( or Pareto) S Loss Agent R Complementary CDF of packet interarrival time Pareto (α=1.5) Fig. 1. Simulation setup III. SIMULATION SCENARIO AND SETUP This section describes our simulation setup and scenario. We use a simple experiment with the ns-2 simulator to observe the relationship between packet loss rate and traffic burstiness. As in other similar studies, we simulate the case in which TCP connections compete to send packets through a bottleneck link. Since we are interested in the behavior of a single TCP flow, we simulate only a single connection transmitting over a lossy link instead of simulating many TCP flows competing for the bottleneck resource. The interaction among competing TCP flows is modeled into a loss agent that uniformly drops packets with a given probability. The simulation topology is shown in Fig. 1. In this figure, node S is the sender, node R is the receiver. We put a loss module into the link connecting from node S to node R. Thus, only packets from the sender to the receivers experience losses. The packet size is fixed at 1000 bytes. The link capacity, the buffer size at the sender node, and the receiver window size are set to be large so that only the loss module affects TCP performance. The two-way propagation delay between the source S and the receiver R is set to 40 msec. TABLE I SIMULATION PARAMETERS Parameter Value Link bandwidth 128 kbps Link delay 20 msec Buffer size 100 Avg. inter-arrival time 1/10 seconds Total simulation time 108000 seconds The sender objects acts as an infinite source; thus it always wants to send as much data as possible. For the traffic source, we consider two different packet inter-arrival time distributions: exponential and Pareto. The packet arrivals in the exponential traffic source are independent while those arrivals in the Pareto traffic source are strongly correlated. We compare the degree of self-similarity to confirm how TCP modifies traffic self-similarity with respect to the source characteristics. We trace packet arrival events only at the downstream link of node D. IV. RESULTS The goal of this simulation study is to observe the influence of TCP congestion control upon the network traffic. The application generated traffic at the sender node is modulated by TCP flow control and thus the outgoing traffic observed at the link shows different statistics from the incoming traffic. Furthermore, packet losses at the link add more variability to TCP congestion control. We adjust the congestion level of the link Fig. 2. 10 1 10 2 Complimentary CDF of packet inter-arrival time for incoming traffic by changing the packet loss rate and observe the statistics of outgoing traffic at the link connecting the sender and receiver nodes. To measure the burstiness of TCP traffic, we will use such tools as histogram and complementary CDF of packet inter-departure time, coefficient of variation (c.o.v.), and degree of self-similarity for the traffic. We also find a linear relationship between packet loss rate and degree of self-similarity. A. Probabilistic distribution of incoming traffic In this simulation, we use two packet inter-arrival time distributions for the incoming traffic source at the TCP sender: exponential and Pareto distributions. The complementary distributions of two traffic sources are shown in Fig. 2. For the exponential source, the packet arrival rate is λ=10[packets/sec]. The parameters of Pareto traffic source is adjusted to have the same mean arrival rate as the exponential source has. For Pareto distribution, the mean arrival rate is given as: E[X] = α α 1 x 0 (9) Since we choose the shape parameter α=1.5 for the Pareto distribution, the minimum value x 0 of Pareto distribution should be 1/30 in order to give the same mean arrival rate as the exponential source. B. Packet inter-departure time distribution The inter-arrival time distribution of incoming packets is changed by TCP flow control. We observe the inter-departure time distribution of packets after the TCP sender node for both traffic sources. In addition to TCP flow control, packet losses at a link can change TCP status. When the network is highly congested, the exponential back-off mechanism of TCP works to relieve the network congestion. At this mode, packets are transmitted at the multiples of RTT estimate so that the packet inter-departure time can be increased up to 64 times the initial RTT estimate value. We observe this modification effect of TCP congestion control prominently at high packet loss rate. The complementary cumulative distribution functions for the original packet inter-arrival time and the inter-departure time of TCP traffic at high packet loss cases (p = 0.2) are shown in Fig. 3 for 1-56555-276-8 65 Applied Telecommunications Symposium

Complementary CDF of packet interarrival time (RTO=6 sec) Complementary CDF of packet interarrival time p=0 p=0.001 p=0.01 p=0.1 p=0.2 10 1 10 2 10 1 10 2 Complementary CDF of packet interarrival time (RTO=6 sec) Pareto Complementary CDF of packet interarrival time Pareto p=0 p=0.001 p=0.01 p=0.1 p=0.2 10 1 10 2 10 1 10 2 Fig. 3. Complementary CDFs of packet inter-departure time at the packet loss rate (p = 0.2) (a) exponential (b) Pareto. Fig. 4. Complimentary CDF of packet inter-arrival time for TCP traffic (Up) (Down) Pareto both traffic sources. In this figure, we see the modulation effect of TCP on the incoming traffic such that the packet inter-arrival time distribution is changed at the high packet loss rate. We also identify that the packet inter-departure time distributions are similar regardless of traffic sources. Thus we can conclude that the packet inter-departure time distribution is mainly determined by the TCP congestion control especially at the high packet loss rate. Next, we draw the complementary CDF s for both sources by changing the packet loss rate in Fig. 4. In this figure, we see that the packet inter-departure time distribution is similar to that of the original source at low packet loss rates. As the packet loss rate is increased, the complementary CDF of packet interdeparture time is changed from the original form. The CDF becomes heavy-tailed rather than exponential for the exponential source. For the Pareto source, the CDF is still heavy-tailed but the slope is changed a little. The more interesting phenomenon is that the complementary distributions for both traffic source are similar to each other at high packet loss rates (p= 0.1 and 0.2). This result is also confirmed from the Hurst parameter and the coefficient of variation. Next, we examine the characteristics of TCP modification effect with the histogram of packet inter-departure time. The histogram of packet inter-departure time for TCP traffic is characterized by some dominant values. This phenomenon is rather obvious from the TCP congestion control mechanism. When the network is highly congested, TCP congestion control is working so that the packet inter-departure time should be multiples of retransmission timeout value (RTO). Thus, the packet inter-departure time is not arbitrary and its distribution has some dominant values (Fig. 5). C. Degree of traffic burstiness We investigate the degree of burstiness in the TCP traffic with two measures, the coefficient of variation and the Hurst parameter. Firstly we consider the coefficient of variation (c.o.v.) for measuring the modulation effect of TCP congestion control. The c.o.v. is defined as the ratio of the standard deviation to the mean of the observed packet inter-departure time. The c.o.v. gives a normalized value for the spread of a distribution and allows for the comparison of spreads of packet inter-departure time distributions over varying packet loss rates. Since TCP traffic is self-similar over limited range of time scales (i.e. pseudo self-similar), we admit that the Hurst parameter alone is not appropriate to describe the burstiness of TCP traffic. For both traffic sources, the coefficients of variations are shown in II. The coefficient of variation for the exponential source is 1. For the exponential source, the c.o.v. for outgoing TCP traffic is decreased when the packet loss rate is relatively low. However, the c.o.v. is increased when the packet loss rate is high. We infer that TCP regulates the incoming traffic with little packet 1-56555-276-8 66 Applied Telecommunications Symposium

TABLE II COEFFICIENT OF VARIATION OF PACKET INTER-DEPARTURE TIME IN TCP TRAFFIC 0 0.001 0.01 0.1 0.2 0.7618 0.7618 0.7723 3.3770 8.9862 Pareto 9.3869 9.3864 9.3871 6.5006 9.1724 10 6 Histogram of packet interarrival time (RTO=6 sec) 0.95 Trend of Hurst parameter vs. Packet loss probability 10 5 0.9 10 4 0.85 Number of frequency 10 3 10 2 Hurst parameter 0.8 0.75 0.7 10 1 0.65 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 6 10 5 Interarrival time [sec] Histogram of packet interarrival time (RTO=6 sec) Pareto 0.6 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 Probability Fig. 6. Variation of the Hurst parameter with respect to the packet loss rate (0.01 < p < 0.1) for exponential source. Number of frequency 10 4 10 3 10 2 10 1 0 2 4 6 8 10 12 14 16 18 20 Interarrival time [sec] Fig. 5. Histogram of packet inter-departure time (p = 0.2) (Up) (Down) Pareto. loss so that the packet inter-departure time is constant if there are enough packets at the sender node. If the packet loss rate is high, then the packet inter-departure time has more variability by the exponential back-off mechanism. Like the complementary distribution of packet inter-departure time, there is an abrupt change in the c.o.v. between the packet loss rates 0.01 and 0.1 for the exponential source. We also note that for the Pareto source, the c.o.v. does not change much as in the case of complementary distribution. However, we observe a small decrease in the c.o.v. at p = 0.1. Next, we observe the Hurst parameter as a measure of selfsimilarity in TCP traffic. Although the TCP traffic is not strictly self-similar, it is still assumed to be pseudo self-similar or longrange dependent over a limited range of time-scales in which non-degenerate correlation structure exists. Hence, we use the Hurst parameter as a measure of traffic self-similarity over the range of time-scales. As shown in Table 2, the change in the degree of traffic self-similarity (i.e. the Hurst parameter in our experiment) with respect to the packet loss rate is different for both traffic sources. For the Pareto source, the Hurst parameter does not change a lot except a small increase at p = 0.1. For the exponential source, the Hurst parameter changes little at low packet loss rates. However, the degree of self-similarity is increased as the packet loss rate exceeds 0.1 and the traffic shows self-similarity like that of the Pareto source. We conclude that TCP induced self-similarity is apparent at high packet loss rate (i.e. in a highly congested network). For the exponential source, we investigate in depth the transition in value of the Hurst parameter between packet loss rates 0.01 and 0.1. The variation of the Hurst parameter with respect to the packet loss rate is shown in Fig. 6. There exists a quasilinear relationship between the Hurst parameter and packet loss rate. V. CONCLUSION This paper quantitatively observes the relationship between packet loss rate and the degree of burstiness in traffic using ns- 2 network simulations. By changing the packet loss rate of a link, we adjust the congestion level of the link and influence the behavior of TCP traffic. We observe the distribution of TCP traffic and measure the degree of burstiness with the coefficient of variation and the Hurst parameter. Using two traffic sources, exponential and Pareto distribution, we quantitatively measure TCP induced burstiness in addition to source induced burstiness. In addition, we find that there exists a relationship between the packet loss rate and the Hurst parameter for the exponential traffic source. It is interesting to observe the relationship over the more extensive range of packet loss rate. To explain this modification effect of TCP, we use Markovian 1-56555-276-8 67 Applied Telecommunications Symposium

models for TCP congestion control. Extensive results and detailed explanation of the relationship will be reported in another paper. REFERENCES [1] L. Guo, M. Crovella, and I. Matta, How does TCP generate pseudo-selfsimilarity?, in Proc. of Ninth International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, 2001, pp. 215 223. [2] D. R. Figueiredo, B. Liu, V. Misra, and D. Towsley, On the autocorrelation structure of TCP traffic, Tech. Rep., Computer Science Department, University of Massachusetts, 2000. [3] W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, On the self-similar nature of Ethernet traffic (Extended Version), IEEE/ACM Trans. Networking, vol. 2, pp. 1 15, February 1994. [4] B. Tsybakov and N. D. Georganas, On self-similar traffic in ATM queues: Definitions, overflow probability bound, and cell delay distribution, IEEE/ACM Trans. Networking, vol. 5, pp. 397 409, June 1997. [5] B. Tsybakov and N. D. Georganas, Self-similar processes in communications networks, IEEE Trans. Inform. Theory, vol. 44, pp. 1713 1725, September 1998. [6] V. Paxson and S. Floyd, Wide-area traffic: The failure of poisson modeling, IEEE/ACM Trans. Networking, vol. 3, pp. 226 244, June 1995. [7] M. Crovella and A. Bestavros, Self-similarity in world wide web traffic: Evidence and possible causes, IEEE/ACM Trans. Networking, vol. 5, pp. 835 846, December 1997. [8] W. Willinger, M. S. Taqqu, R. Sherman, and D. V. Wilson, Selfsimilarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM Trans. Networking, vol. 5, pp. 71 86, February 1997. [9] R. J. Adler, R. E. Feldman, and M. S. Taqqu, A practical guide to heavy tails: Statistical techniques and Applications, Birkhauser, 1998. [10] W. Stallings, High-speed networks: TCP/IP and ATM design principles, Prentice-Hall, 1997. [11] D. Veitch and P. Abry, A wavelet based joint estimator of the parameters of long-range dependence, IEEE Trans. Inform. Theory, vol. 45, pp. 878 897, April 1999. 1-56555-276-8 68 Applied Telecommunications Symposium