TOPP Probing of Network Links with Large Independent Latencies

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1 TOPP Probing of Network Links with Large Indeendent Latencies M. Hosseinour, M. J. Tunnicliffe Faculty of Comuting, Information ystems and Mathematics, Kingston University, Kingston-on-Thames, urrey, KT1 2EE Abstract - The TOPP robing algorithm gauges the bandwidth of a network ath in terms of the disersion between ackets transmitted in closely-saced airs. Its alication to wireless networks has been frustrated by the large latency associated with the re-transmission contention hase. This aer examines the mechanisms involved, and rooses an extended TOPP algorithm to rovide consistent estimates of link and available bandwidth in the resence of a large latency. I. INTRODUCTION The Train-of-Packet-Pairs (TOPP) robing algorithm, first develoed by Melander et al. [1,2], uses the bottleneck-sacing effect to gauge the link caacity and available bandwidth of each ho in a network ath. By measuring the mean disersion between closely saced ackets it is theoretically ossible to estimate the characteristics of each hidden bottleneck in the ath. A simlified version DieTo develoed by Johnsson et al. [3], which assumes a single congestible link er ath, roved successful in all-wired networks but roblematic in networks containing a wireless link. In the latter case, results were shown to deend on the robe acket size and the cross-traffic intensity [4]. This effect was attributed to the large indeendent latency (i.e. a latency indeendent of acket size) associated with the contention hase rior to acket transmission [4]. This aer work resents a quantitative investigation of this theory, and demonstrates a TOPP-based algorithm to rovide consistent estimates of bandwidth and latency. II. BANDWIDTH PROBING AND TOPP If a network node with outgoing link caacity l bits/s rocesses ackets of size bits, each acket exeriences a minimum latency of /l seconds (lus an additional overhead delay which will for the moment be ignored). Under this assumtion, finite acket-size can be ignored and traffic-flows aroximated as continuous fluids. Thus if a traffic rate r bits/s is offered to the link, the outut rate should be: r ; m = l; r l. (1) r > l In the former case, arriving ackets are carried frictionlessly. In the latter case, incoming ackets are queued until the outut ort becomes free. Now suose that a second cross-traffic stream c bits/s is alied to the same network node. If a olicy of roortional fair queuing imlemented then r ; r + c l m = r l ; r + c > l r + c i.e. the node behaves frictionlessly until the combined inut rate exceeds the link caacity, at which oint, the bandwidth is shared roortionally between the two cometing streams. The value r=l-c at which the frictionless behavior ceases is termed the available bandwidth a. If the ath asses through n nodes, the available bandwidth is set by the node with the smallest value of a: i ( ) i { 1.. n} (2) a tot = min a. (3) This is the tight-link of the ath (which is not necessarily the narrow-link, the node with the smallest link caacity [5]). The resent aer is concerned only with the tight-link. To illustrate this, a urose-built simulation of a storeand-forward network was imlemented in C++. The software could suort any arbitrary node toology and traffic configuration, but the exeriments reorted here are based on two simle scenarios: Figure 1 shows a single-ho network, in which 5% of the 2Mbit/s link bandwidth is used by a 1Mbit/s cross-traffic stream. (Throughout this IBN: PGNet

2 aer, cross-traffic is assumed to be Poisson.) The node can also be given an indeendent latency, but this was initially set to zero. Figure 2 shows a two-node network reresenting a wired-cum-wireless scenario. The u-stream node (the wireless link) carries data at a 1Mbit/s, while Node B (wired) runs at 1Mbit/s. For acket sequences (including acket-airs), traffic rate is interreted as the acket size (in bits) divided by the mean acket searation (seconds). Thus the acket disersion ratio D (outut searation/inut searation) is equal to the ratio of the offered rate r to the measured outut rate m. Rearranging Eqn.(2) we obtain: Disersion Ratio byte robe acket data 5byte robe acket data 5byte robe acket regression line 5byte robe acket regression line D = r m 1 ; r m = 1 > m +. r 1 ; r m l l By collecting a set of results for r > m, the values of m and l can be comuted using least-square analysis. Figure 3 shows some tyical results for the one-ho network scenario (Fig.1). The transition between the two linear domains is clearly not abrut as Eqn.(4) would suggest; the disersion ratios observed in the region r m are considerably higher than their theoretical redictions. (This is due to the robing bias, theoretically redicted by Liu et al. [6]). However, this effect is less ronounced if the robe ackets are much larger than the cross-traffic ackets (2bytes), and decays raidly as the offered rate increases. The 5byte data yields very accurate estimates of the available and link bandwidths (1 and 2Mbit/s resectively). Figure 1. ingle-ho network. The available bandwidth should theoretically be 1Mbit/s. Probe In Cross Traffic In: 1Mbit/s, 2byte acket, Poisson Probe In Cross Traffic Out.5Mbit/s, 2byte 1Mbit/s Wireless Link Probe Out 2Mbit/s, 1,, byte buffer Zero fixed latency 8Mbit/s, 2byte 1Mbit/s Wired Link Figure 2. Two-ho wired-cum-wireless scenario. Available bandwidth is 5kbit/s. (4) Probe Out Offered Bit Rate (bits/s) Figure 3. Tyical disersion results obtained from single-ho simulation using 5 and 5byte robe ackets. III. INDEPENDENT NODE LATENCY In addition to the time taken to transmit the acket (acket size transmission rate), the node imoses an additional overhead latency, indeendent of acket size. This aears on all links (wired and wireless) and includes the header-rocessing and roagation delays. However, a wireless link imoses an unusually long delay due to the inter-frame sacing and contention times. Thus the latency imosed on a acket of size bits should be modeled as (/l + t), where l is the link bandwidth and t is the indeendent delay. (For the moment we assume that t is constant; variable t will be considered later.) If a source offers traffic at a rate r bit/s with a acket size bits, then the effective quantity of link bandwidth used by the transmission must be r(1+lt/ ) bits/s. Thus the erceived link bandwidth l is related to the actual link caacity by the formulae: lt l = l 1 + or l l =. (5) + lt Also if a robe source transmits data at a rate equal to the available bandwidth a bits/s (for the articular acket size ), and the cross-traffic rate is c bits/s with a acket size c bits, then the following relationshi must also hold: lt lt a c = l 1+. (6) c

3 This yields the following exression for the available bandwidth: ( l c ) eff a = (7) + lt where c eff is the effective cross traffic rate, given by Available Bandwidth (bits/s) lt c = + eff c 1. (8) c Tight-link caacity: 1Mbit/s Cross traffic at tight-link: 5kbit/s, 2 byte ackets, Poisson arrival. Model: 1byte ackets Model: 3byte ackets Model: 1byte ackets Data: 1byte ackets Data: 3byte ackets Data, 1byte ackets Additional Latency (er acket) at Tight-Link (microseconds) Figure 4. Comarison of exerimental and theoretical available bandwidth as a function of fixed indeendent latency. (Available bandwidth was defined as the highest rate at which no acket losses were observed.) Link Bandwidth (bits/s) Model: 1byte ackets Model: 3byte ackets Model: 1byte ackets Data: 1byte ackets Data: 3byte ackets Data, 1byte ackets Additional Latency (er acket) at Tight-Link (microseconds) Figure 5. Comarison of the exerimental and theoretical link bandwidth as a function of fixed indeendent latency. Measured Bandwidth (bits/s) Probe Packet ize (bytes) Figure 6. Measured bandwidth comared with theoretical redictions for zero (broken lines) and constant 4µs (solid lines) indeendent latency. Data oints: =Available bandwidth, zero additional latency, =Available bandwidth, 4µs additional latency, =link caacity, zero additional latency, =link caacity, 4µs additional latency. Figures 4 and 5 comare the comuted bandwidths with those observed for a deterministic stream with three different acket sizes. The two-node scenario of Figure 2 was used, with the additional delay aearing only on the 1Mbit/s (wireless) tight-link. Offered traffic was incremented in 1,bits/s stes, and available bandwidth was defined as the highest rate at which acket-loss was zero. (Link bandwidth was obtained by reeating the exeriment with the cross-traffic removed.) In all cases, the model redictions are in close agreement with the exerimental results. Figure 6 shows the results of a TOPP robing exeriment on the same network model. The available and link bandwidths were measured using the acket-disersion method, with fixed additional latencies of zero and 4µs with the theoretical values obtained from Eqns. (5) and (7). In the case of zero additional latency, there is an observed tendency to underestimate link caacity when the robe acket size is small, but this can be exlained in terms of the robing bias reviously discussed. Otherwise the model fits the data extremely well. For the urose of bandwidth robing, it is more imortant to be able to go the other way: Namely to obtain values for the link caacity, available bandwidth and indeendent latency from the raw data alone. Rearranging Eqn.(5) yields: l 1 = l + t Thus /l can be lotted against and the values of l and t can be comuted by least-square analysis. (9)

4 Table I Measured and estimated arameters for a 1Mbit/s narrow link with a fixed indeendent latency of 4µs er acket. Probe acket sizes varied in the range 1-1 bytes, with a cross-traffic rate of 5kbit/s, acket size 2 bytes. Parameter Measured Actual Link Bandwidth 1.58 Mbit/s 1. Mbit/s Effective Cross Traffic 6.77 kbit/s 625 kbit/s Additional Latency 492 µs 4 µs Obtaining the recise cross traffic arameters (rate and acket-size) is roblematic, but it is ossible to estimate the effective cross-traffic rate c. Eqns.(5) and (6) can be combined to roduce: lt c' = c 1 + (1) where c is the erceived cross traffic rate, given by (l eff - a), which can be calculated using the estimated values of l and t, averaged across the entire range of acket sizes (1-1 bytes). The resulting value can in rincile be used to obtain the available bandwidth for any required value of using Eqn.(3). Table I shows some tyical results for a 4µs fixed indeendent latency. o far some fairly simlistic conditions have been assumed; namely that the additional node latency is constant, and that the cross traffic is comosed of ackets of one size only. The former assumtion may be valid in a lightly loaded wireless network, where a transmitting node nearly always gains access to the transmission medium once the minimum inter-frame sacing time (e.g. DIF) has elased. In a more heavily loaded network, a node may frequently enter a contention hase, causing the latency to vary stochastically between ackets-transmissions. The exeriment was therefore reeated using randomly-selected additional latencies, governed by a uniform (mean ± 1%) and a Poisson random distribution, and a range of different mean latencies. Figure 7 shows the comuted link bandwidth and the effective cross-traffic lotted against the set mean additional latency. While some random variation exists, the estimates are generally within about 5% of their true values (indicated by the solid and broken lines). Figure 8 shows the estimated mean additional latencies: Although some redictions are very close to their true values, there is (as was reviously seen in Table I) a tendency to overestimate the mean latency, and to underestimate the effective cross traffic. Data Rates (bits/s) 1.1E+6 1.E+6 9.E+5 8.E+5 7.E+5 6.E+5 5.E+5 4.E Link Bandwidth (Actual) Measured Link Bandwidth (Constant) Measured Link Bandwidth (Uniform) Measured Link Bandwidth (Poisson) Actual Mean Additional Latency (s) Effective Cross Traffic (Actual) Measured Effective Cross Traffic (Constant) Measured Effective Cross Traffic (Uniform) Measured Effective Cross Traffic (Poisson) Figure 7. Measured link bandwidth and effective cross-traffic intensities obtained using constant, uniform random (±1%) and Poisson additional node latencies, comared with their true values. Measured Mean Additional Latency (s) Actual Mean Additional Latency (s) Actual Value Constant Uniform Poisson Figure 8. Measured mean additional latency obtained using constant, uniform random (±1%) and Poisson additional node latencies, comared with their true values. o far it has been assumed that the cross-traffic is comosed entirely of Poisson-distributed 2 byte ackets. Further exeriments used a mixture of acket sizes, based on the distribution used by Johnsson et al. [4], while the total rates of 5kbit/s and 8Mbit/s (aearing at the 1Mbit/s and 1Mbit/s nodes resectively) were reserved. Table 2 shows the distribution of cross traffic.

5 Available Bandwidth (bits/s) Packet ize (bytes) Table II Comosition of cross-traffic (based on [4]). % of Total Packets % of Total Traffic Rate Tight-link caacity: 1Mbit/s 5kbit/s mixed Poisson cross traffic, effective acket size bytes Model: 1byte ackets Model: 3byte ackets Model: 1byte ackets Data: 1byte ackets Data: 3byte ackets Data, 1byte ackets Mean Additional Latency (microseconds) Figure 9. Comarison of actual and measured available bandwidth for different additional mean latencies (±1% uniform random distribution) with values obtained using deterministic streams of 1, 3 and 1, byte ackets. Measured Bandwidth (bits/s) 1.E+6 8.E+5 6.E+5 4.E+5 2.E+5 LC, t= AB, t= LC t=4us AB, t=4us Model LC, t= Model AB, t= Model LC, t=4us Model AB, t=4us.e+ Probe Packet ize (bytes) Figure 1. Measured available bandwidth (AB) and link caacity (LC) for 5kbit/s mixed-acket-size cross traffic, comared with theoretical redictions for zero and uniform random (4±4µs) additional latency at the 1Mbit/s tight-link. In order to quantify the combined imact of n different acket sizes, c in Eqn.(8) must be relaced by an effective value: c( eff ) = n α i = 1 ( ) i c i 1 (11) where α i reresents the roortion of the total cross traffic transmitted using ackets of size c(i) bits. For the data shown in Table II, c(eff) equals 578.8bytes (463.5 bits). Figure 9 comares available bandwidths redicted from this value with results obtained from a simulation exeriment, showing that the equations still hold under mixed-traffic conditions. The next challenge is to see whether or not acket-air robing can still be used to estimate the available bandwidth under mixed cross-traffic. Figure 1 comares the available and link bandwidths obtained from regression analysis with their theoretically redicted values. The data shows general agreement with theory, although there is a greater degree of scattering than was observed in Figure 6. As before, there is a slight tendency to underestimate the link caacity when the additional latency is zero. IV: CONCLUION AND FUTURE WORK In this aer we have examined the behavior of the TOPP robing algorithm in a network which imoses large latencies indeendent of acket size. The algorithm has been extended to include trains of different sized ackets, ermitting these latencies to be eliminated. The results we, on the whole otimistic, but were obtained using a simulation tool based on simlistic assumtions: Firstly the cross-traffic was governed by a temorally uniform Poisson rocess, which may not reresent tyical network loading behavior. econdly, the statistical rocess generating the latency in a real wireless node is likely to be more comlex than the uniform and Poisson models assumed here. We are therefore currently working on extending the study to a more realistic simulation, based on the commercial network simulation ackage OPNET. Figures 11 and 12 illustrate some tyical OPNET scenarios: Figure 11 shows a single-ho wireless network, while Figure 12 shows a wired-cum-wireless scenario akin to the network reresented in Figure 2. REFERENCE [1] B.Melander, M.Björkman, P.Gunningberg, A New End-to- End Probing and Analysis Method for Estimating Bandwidth Bottlenecks, Proc. IEEE Glogecom, an Francisco, CA, UA, Nov. 2.

6 [2] B.Melander, M.Björkman, P.Gunningberg, Regression- Based Available Bandwidth Measurements, Proc. 22 Int. ym. on Performance Evaluation of Comuter and Telecommunication ystems, 22. [3] A.Johnsson, B.Melander, M.Björkman,M, DietTo: A First Imlementation and Evaluation of a imlified Bandwidth Measurement Method, 2 nd wedish National Comuter Network Worksho,.5, Karlstad, Nov. 24. [4] A.Johnsson, B.Melander, M.Björkman, Bandwidth Measurement in Wireless Networks, Proc. Mediterranean Ad Hoc Networking Worksho, Porquerolles, France, June 25. [5] M.Jain, C.Dovrolis, Ten Fallacies and Pitfalls on End-to- End Available Bandwidth Estimation, Proc. 4 th ACM IGCOMM, Taormina, icily, Italy,.272-7, 24. [6] X.Liu, K.Ravindran, B.Liu, D.Loguinov, ingle-ho Probing Asymtotics in Available Bandwidth Estimation: amle-path Analysis, Proc. ACM Internet Measurement Conference, 24. Figure 11. OPNET model of a one-ho wireless network scenario. Mobile nodes 1 and 2 communicate with the wireless server. Figure 12. OPNET model of a wired-cum wireless network scenario. The mobile nodes communicates with the fixed server host via the intermediate suervisor host.