On Measuring Available Bandwidth in Wireless
Networks
Andreas Johnsson
Research Area Packet Systems
Ericsson Research
Mats Björkman
The Department of Computer Science and Electronics
Mälardalen University
Abstract— BART is a state-of-the-art active end-to-end band-width measurement method that estimates not only the available bandwidth but also the link capacity of the bottleneck link. It uses a Kalman filter to give estimates in real time during a measurement session.
In this paper, we have studied the impact of 802.11 networks on the bandwidth estimates produced by BART. The Kalman filter used by BART is tunable, and one of the contributions of this paper is to show how the Kalman filter should be adjusted to improve real-time tracking and estimation accuracy when the bottleneck is an 802.11 link.
Further, the paper contributes by discussing how to interpret the estimates produced by BART and similar bandwidth esti-mation tools relying on self-induced congestion when used in wireless scenarios. An analysis show that the BART estimates produced are correct - but corresponds to a fair share of the wireless link rather than to the unused capacity. However, the estimates do indicate how much bandwidth an application or device in the wireless network can expect when sending and/or receiving network traffic.
I. INTRODUCTION
Since wireless networks often are used for nomadic access to the Internet from a laptop, it is important to study how methods for actively measuring available bandwidth behave when wireless links are part of the to-end path. If end-to-end available bandwidth measurement methods are to be widely accepted as performance measurement tools, it is important to ensure that they report correct values in wireless networks as well.
End-to-end available bandwidth methods relying on self-induced congestion that exist today are for example ABget [1], Pathchirp [2], Pathload [3], Spruce [4] and TOPP [5]. The principle is to inject so called probe packets, with some inter-packet separation, that traverse the network path to be measured. When a probe packet arrives at the receiver it is time stamped. The inter-packet separation has increased if the probe packets caused congestion on the path. By deploying different analysis methods to the sent and received time stamps the link capacity (a constant property of the bottleneck link) and/or the available bandwidth (the unused portion of the link capacity) can be estimated. The methods mentioned above differ in several ways, such as how the probe packets are
sent and how the analysis and estimation algorithms function. An overview of available bandwidth measurement methods, tools and theory can be found in [6]. More recent theoretical findings are reported in for example [7] [8].
BART [9] is a successor of the TOPP method and is used for actively estimating the end-to-end available bandwidth and link capacity on the IP layer. Assuming a fluid network model and FIFO queues for the selected traffic class, TOPP uses linear regression while BART deploys a Kalman filter to estimate the available bandwidth and link capacity. The advantage of using BART is that estimates are obtained in real time. To obtain fast-tracking and accurate bandwidth estimates using BART the Kalman filter can be tuned, this has been studied in several papers, for example in [10].
In this paper tuning of the Kalman filter used by BART
is examined in detail in scenarios where the bottleneck is an 802.11 link. For this study to be possible, a crucial observation is made in the paper: the estimated link capacity and available bandwidth are equal when using BART in scenarios where the bottleneck is an 802.11 link.
The second contribution of this paper is a discussion of
how to interpret the estimates produced by BART and similar tools when the bottleneck is an 802.11 link. An analysis show that the estimates produced are correct - but corresponds to a fair share of the wireless medium rather than to what was available in terms of bandwidth before initiating the probing. It should however be noted that the estimates do indicate what an application or device can expect to get in terms of bandwidth when sending and/or receiving network traffic.
The rest of this paper is organized as follows; in Section II the BART measurement model is described along with how BART actually estimates the available bandwidth and link capacity. The relation between estimated link capacity and available bandwidth using BART is also discussed. Section III presents the research questions addressed in this paper as well as the experimental setup. In Section IV a detailed presentation on how the BART Kalman filter can be tuned in order to enhance the estimation properties is given. In Section V the accuracy and interpretation of the estimates are investigated. Conclusions are located in Section VI.
II. MEASUREMENT MODEL
In this paper, BART [9] is used to estimate the available bandwidth and link capacity of an end-to-end path when the bottleneck is an 802.11 link. The BART tool is divided into two parts, one probe packet sender and one probe packet receiver. The BART sender injects UDP probe packets into the network at different input rates u, or with the mean packet separationΔin. The receiver, on the other end of the network, time stamps each incoming packet and calculates the received rate r, or the mean packet separation Δout. Then the inter-packet strain = Δout−Δin
Δin is calculated along with the
variance R. Assuming a fluid network model and FIFO queues, the strain is zero during network underload and increases linearly during overload (often related to as the TOPP model [5]). That is,
=
0 underload
αu+ β overload (1)
The available bandwidth B is then defined as the intersec-tion of the sloping line and the x-axis. That is B = −βα. The available bandwidth is the maximum rate u that can be used without saturating the network. Further, according to the TOPP model [5] the link capacity C is the inverse of α. That is C =α1.
A. The BART Kalman filter
BART [9] deploys a Kalman filter [11] in order to measure and track changes in α and β and thus the available bandwidth and the link capacity. BART injects probe packets into the network path and measures the strain at the receiver. For each measurement sample, where the probe rate u is larger than the current available bandwidth estimate, a new estimate is obtained, as described in [9].
The Kalman filter can be described as an iterative procedure where a system state xk = g(xk−1, uk−1, wk−1), that is not
directly observable, is predicted for a time step k. The function
g describes the evolution of the system state over time and must be linear in order to apply a Kalman filter, u is some input to the measured system and w is the process noise. For the prediction at time k a correction is made using a measurement sample zk = h(xk, uk, vk) where vk is the measurement noise. The weight of the new sample in the correction is given by the Kalman gain K, that depends on the accuracy of the measurement sample as well as on Q, the process noise covariance matrix. The estimate of the system state, ˆxk, obtained by predictions and corrections, will track changes in xk.
The system state xk in the BART Kalman filter is chosen as xk= α β (2) from which the available bandwidth and the link capacity is obtained.
Below, a short review of how the Kalman equations are applied in BART is given. The estimated prediction of the
system state ˆx−k and the predicted error covariance matrix Pk− are updated according to
ˆx−
k = Aˆxk−1 (3)
Pk−= APk−1AT + Q (4)
where A is a state transition matrix. A is chosen to predict the system state at time k given the estimated system state at time k− 1. In BART it is assumed that A = I which means no evolution of the system state.
When the predictions for time k are calculated a mea-surement sample zk is used as input in order to correct the predicted estimate of the system state ˆx−k. This is done in three steps according to the following Kalman equations
Kk= Pk−HkT(HPk−HkT+ R)−1 (5)
ˆxk = ˆx−k + Kk(zk− Hkˆx−k) (6)
Pk= (I − KkHk)Pk− (7)
where K is the Kalman gain. The new estimate of the system state ˆxk is calculated using the Kalman gain multiplied with the so called residual (zk − H ˆx−k). This is the difference
between the new sample and the prediction of that sample. Depending on the residual and the Kalman gain the adaptation of ˆx towards x will vary.
It is important to note that K increases with Q and decreases with the measurement sample variance R. Q is unknown, but it is possible to choose it to reflect the predicted stability of the system state. By varying Q the Kalman filter is tuned to weight the impact of the current sample on the prediction of the system state ˆx−k differently. The last step is that a new estimated error covariance matrix Pk is calculated.
In the Kalman filter, the measurement sample zk relates to the system state as
zk= Hkxk+ vk (8)
where vk is the measurement noise. In BART, the measure-ment sample zk equals the strain , which is linear during network overload as described by Equation 1. To create a linear relation between the strain and the system state, H is chosen as
Hk= uk 1 . (9)
Now Hkxk = αkuk + βk = k = zk. That is, a relation between the measurement sample zk and the system state xk is defined. Thus,ˆx can be updated for each new measurement sample z, that is BART is able to track the available bandwidth and link capacity in real time.
B. Tuning of the Kalman filter
It is possible to trade estimation stability for agility in the Kalman filter by tuning the Q matrix. In the BART Kalman filter the predicted process error covariance matrix Q has the following structure [10] Q= q11 q12 q21 q22 = V(Δα) C(Δα, Δβ) C(Δα, Δβ) V(Δβ) (10)
where V() is the variance and C() the covariance. A high value of the components in Q means that the measurement sample zk is weighted more heavily compared to the case with a low value. That is, the estimations may fluctuate more using a high Q. But on the other hand, the adaptation towards a new system state is faster using a high Q compared to a low
Q. Currently in BART, the covariance C() in Q is set to zero.
In Section IV later in this paper it is discussed how the
Q matrix can be tuned in order to enhance the estimation accuracy of the available bandwidth and link capacity in 802.11 networks, both when the system state (i.e. available bandwidth and link capacity) is stable but also when it varies over time.
C. The relation between estimates of the available bandwidth and link capacity in 802.11 networks
Using the measurement model described above it is in this paper argued for that the estimated link capacity should be equal to the estimated available bandwidth, when the bottleneck is an 802.11 link. The original TOPP model [5] states that in FIFO queue systems, the relation between the input rate u and the received rate r is
u r = 1 underload X C +Cu overload (11) where X is the cross-traffic rate transmitted through the FIFO queue (compare Equation 1). In [9] the conversion between u/r and is described and it is shown that + 1 =
u/r. Compare equations 1 and 11.
In earlier work it has been shown how Equation 11 should be modified to describe more details on how the properties of 802.11 links impact on the TOPP model [12]. In [12] + 1 =
u/r during overload was found to be
+ 1 = u r = nTk(X802.11) + Ts s X+ (nTk(X802.11) + Ts) 1 tu (12) where Tk() is a function of the cross traffic on the wireless
link X802.11. Tk() increases due to MAC link-layer contention
and retransmission caused by the cross traffic on the wireless link. Ts is the physical transmission time of s bits over the 802.11 link, n relates to the probe packet size s and tu is the inter-packet separation in time (i.e. related to u). In [12] there was no distinction made between the FIFO based cross traffic X, that flows through the same FIFO queue as the probe packets, and the cross traffic that originates from other nodes on the wireless network X802.11 (i.e. that affects the link layer). This distinction is however crucial in order to understand why the link capacity and available bandwidth estimates are equal in these types of networks when using BART for measuring available bandwidth and link capacity.
Since the cross traffic sharing the FIFO queue used by the probe-packet sender is zero (assuming that the probe-packet sender does not inject cross traffic during a measurement session), X = 0. Thus,
Fig. 1. The testbed.
+ 1 = u
r = (nTk(X802.11) + Ts)
1
tu (13)
during overload. For any such line the inverse of the slope equals the intersection of the line + 1 = u/r = 1. The intersection determines the available bandwidth while the inverse of the slope is proportional to the link capacity. That is, when using BART to obtain estimates in networks where the bottleneck is an 802.11 link, the available bandwidth and link capacity estimates will be the same.
III. RESEARCH QUESTION AND EXPERIMENTAL SETUP
This section describes in more detail what is studied in this paper and why. Further, the experimental setup used in order to perform the study of how the available bandwidth and link capacity estimates are affected by 802.11 bottleneck links is described.
A. Research questions
The research questions studied in this paper concern band-width measurements in wireless 802.11 networks. The TOPP model described above, that BART makes use of, relies on the fact that the forwarding mechanism in the routers is FIFO based. Thereby, the strain induced between probe packets is proportional to the amount of cross traffic sharing the same path. Using this fact the rate-response curve can be obtained by injecting probe packets at increasing rates. The rate-response curve is a segmented curve described by Equation 1 (or 11); first it is zero, then when the network is saturated the curve will deviate from zero and show a linear increase (point determining the available bandwidth). The available bandwidth and the link capacity of the bottleneck link can then be estimated either by using linear regression, used by TOPP, or a Kalman filter, applied by BART.
The first research question investigated in this paper is how
to set the Q matrix in the Kalman filter used by BART when the bottleneck is a wireless link. As described in Section II, a
large Q instructs the Kalman filter to anticipate large variations in the system state while a low Q does not. In the light of the discussion pointing out that the available bandwidth and link capacity estimates are equal it is not obvious how to set Q in BART to enhance the estimation properties. See Section IV.
The second research question is about trying to determine whether BART is estimating the available bandwidth in a correct manner assuming an 802.11 bottleneck link. The queues in each wireless node are FIFO based, but the layer-2 mechanism in 802.11 networks is approximately fair-queuing based. That is, is the TOPP model used by BART applicable?
What is actually measured? See Section V. B. Experimental setup
The wireline part of the testbed, see Figure 1, consists of 6 ordinary PC machines running Linux with a stable 2.4 kernel. Three of them are configured as routers. These machines are connected using wired single-access links that operate at 100 Mbps. In the wireless part of the testbed there are 4 laptops, 3 installed with Linux. The cross-traffic and probe-packet senders in the wireless part of the network are installed with Linux kernel 2.6. The administrator laptop is running Windows XP. The laptops connect to the wired part of the network using a standard 802.11b/g access point. The wireless cards in the laptops are Prism2 compatible and deploy the standard 802.11b drivers in Linux. The bottleneck in this network is the 802.11b access link.
Cross traffic can be generated from two of the laptops as well as from the cross-traffic machine in the wired part of the network. The cross-traffic receiver is the same in-dependent of source. The cross traffic used in the experi-ments that this paper reports on has been generated using tg (http://www.postel.org/tg/), from two cross-traffic nodes in the wireless part of the network. The cross traffic rate X802.11bis uniformly distributed in an interval(0.9X802.11b,1.1X802.11b)
and consists of 1400 byte UDP packets. This cross-traffic scenario may not be realistic, but it is sufficient for the study in this paper. No cross traffic is injected by the probe-packet sender.
IV. TUNING THEBART KALMAN FILTER FOR
QUALITATIVE ESTIMATION IN802.11NETWORKS
The Q matrix plays an important role when configuring the Kalman filter applied in BART. The Kalman gain K tells the filter how much weight a new measurement sample zk should have compared to the previous estimate of the system state ˆxk−1, and K depends on P which in turn is calculated using
Q. A high value of Q can be used when the system state to be measured is expected to change rapidly and a low Q is used when the measured system is predicted to be stable. That is, it is possible to trade estimation stability for agility when deploying the BART Kalman filter for estimating available bandwidth and link capacity.
In [10] tuning of the Q matrix was discussed. It was shown that Q can be used to trade estimation stability for agility. In [13] a description of a general change detection algorithm and how to utilize it together with the already existing BART Kalman filter was given. Using the change detection algorithm the Q matrix does not have to be fixed, rather it changes depending on whether BART guesses that the measured system is stable or not. 0 50 100 150 200 250 300 350 400 450 500 1 2 3 4 5 6x 10 6 Time (ticks) Estimation (Mbps) Q = (0.0001 0.0; 0.0 0.0001) 0 50 100 150 200 250 300 350 400 450 500 1 2 3 4 5 6x 10 6 Time (ticks) Estimation (Mbps) Q = (0.0001 0.0; 0.0 0.01)
Fig. 2. By varying the choice of Q the link capacity (dashed line) and available bandwidth (solid line) estimates vary. In the upper graphq11 =
q22= 0.0001 and in the lower q11= 0.0001, q22= 0.01
0 50 100 150 200 250 300 350 400 450 500 1 2 3 4 5 6x 10 6 Time (ticks) Estimate (Mbps) Q = (0.01 0.0; 0.0 0.01) 0 50 100 150 200 250 300 350 400 450 500 1 2 3 4 5 6x 10 6 Time (ticks) Estimate (Mbps) Q = (0.01 0.0; 0.0 0.0001)
Fig. 3. By varying the choice of Q the link capacity (dashed lines) and available bandwidth (solid lines) estimates vary. In the upper graphq11 =
q22= 0.01 and in the lower q11= 0.01, q22= 0.0001
In this paper the relation between the available bandwidth and the measured link capacity in 802.11 networks has been discussed. As argued for in Section II, these are the same using BART, if the probe-packet sender does not inject cross traffic into the network. That is, the cross traffic injected by other nodes in the wireless network causes a change in both the available bandwidth and the estimated link capacity.
The question this section tries to answer is what impact the properties of 802.11 networks have on the choice of Q. The general change detection algorithm described in [13] needs this information.
In Figure 2 and 3 the estimated available bandwidth (solid lines) and link capacity (dashed lines) are shown over time.
The graphs originate from the same measurement session, however the value of Q varies in the analysis. The measure-ment scenario is as follows; the probe packets are sent from the probe packet sender and cross traffic is generated from one laptop in the testbed. The cross traffic is zero during the first 250 time steps and then jumps up to 6 Mbps. Remember the previous discussion that showed that the available bandwidth estimate should be equal to the link capacity estimate produced by BART.
The Q matrix differ in the four graphs and as can be observed, the impact of the choice of Q is crucial to the stability of the estimates of the available bandwidth and link capacity.
To obtain the results shown in the top graph in Figure 2 both q11 and q22 are low which instructs the Kalman filter to expect low variance in both elements in the system state, thus the Kalman filter should give low weight to new samples compared to the case of having larger Q values. That is, the Kalman filter does not anticipate sudden changes in available bandwidth nor link capacity estimates. As seen, the estimate of the link capacity is stable and slowly reacts to the sudden change in cross traffic at time 250. The available bandwidth estimate is also stable but seems to overreact to the change in cross traffic at time 250. Later it moves towards the value of 3 Mbps.
In the lower graph in Figure 2 q22 is large compared to q11 and thus each sample has large impact on ˆβ, that is the estimate of β that is a part of the system state x. The link capacity is proportional to the inverse of α while the available bandwidth is computed as −αβ. This means that each new sample will have high impact on the available bandwidth estimate but low impact on the link capacity estimate. This is visible in the graph where it is clear that the link capacity estimate is stable and reacts slowly to the change in cross traffic while the available bandwidth estimate fluctuates and overreacts to the change in cross traffic on the wireless link.
In the top graph in Figure 3 both q11and q22 are large and then both bandwidth estimates fluctuate because each sample is weighted heavily on the estimates of α and β.
In the lower graph in Figure 3 q11 is large and q22 small. Now both the estimates of available bandwidth and link capacity seem to quickly react to the sudden change in cross-traffic rate while at the same time the values are not fluctuating as in previous examples.
As described previously in this paper the link capacity estimate and the available bandwidth estimate should be the same. Thus, the latter Q matrix configuration seems to be the best choice in this experiment scenario since the discrepancy between the two curves are small while at the same time both estimates react fast to the change in the system state.
A. Tuning of Q
To decide which Q to use in order to get high-quality estimates one could vary Q and then calculate the mean square error using the estimate and the true value of the available bandwidth as input. This is possible in a network where the
0 0.002 0.004 0.006 0.008 0.01 0 0.002 0.004 0.006 0.008 0.01 1 2 3 4 5 6 7 8 9 10 x 105 q11 q22 Difference (bit/s)
Fig. 4. The absolute difference between the estimated link capacity and available bandwidth on the z axis. The Q matrix varies in two dimensions on the x and y axes. The cross traffic is zero during half the experiment and then increases to 6 Mbps, that saturates the bottleneck.
0 0.002 0.004 0.006 0.008 0.01 0 0.002 0.004 0.006 0.008 0.01 3.5 4 4.5 5 5.5 6 6.5 7 7.5 x 105 q11 q22 Difference (Bit/s)
Fig. 5. The absolute difference between the estimated link capacity and available bandwidth on the z axis. The Q matrix varies in two dimensions on the x and y axes. The cross traffic is zero during the whole experiment.
true values of the available bandwidth and the link capacity are known, such as in a wireline network. However, in a wireless network the correct values are very hard to retrieve since they vary with the radio quality between the sender and the receiver. Therefore, in this paper we utilize the property of knowing that the bandwidth estimates obtained by BART are equal.
A good choice of the Q matrix can then be found by minimizing the difference between the available bandwidth and the link capacity estimates. In Figures 4-6 the x and y axes represent q11 and q22, respectively. Thus the two-dimensional value space of the Q matrix can be searched. The z axis is the absolute difference between the available bandwidth and the link capacity estimates during an entire measurement session
0 0.002 0.004 0.006 0.008 0.01 0 0.002 0.004 0.006 0.008 0.01 1 2 3 4 5 6 7 8 9 x 105 q11 q22 Difference (bit/s)
Fig. 6. The absolute difference between the estimated link capacity and available bandwidth on the z axis. The Q matrix varies in two dimensions on the x and y axes. The cross traffic is 3 Mbps during half the experiment and then increases to 3 + 3 Mbps send from two nodes, which saturates the bottleneck.
(i.e. 500 time ticks, compare Figure 2 or 3).
The graph in Figure 4 originate from a scenario where the cross-traffic rate was 0 during 250 time ticks and then 6 Mbps during the rest of the session (corresponding to the results shown in Figures 2 and 3). Figure 5 originate from a session where there was no cross traffic at all during 500 time ticks while the graph in Figure 6 is derived from when one cross-traffic sender is injecting 3 Mbps during the first 250 time ticks. Then two cross-traffic senders are injecting probe traffic at 3 Mbps each during the rest of the experiment (i.e. 250 additional time ticks).
The graphs illustrate that the difference between available bandwidth and link capacity estimates is minimized when using a low value of q22, independent of the cross-traffic scenario while the value of q11seems to depend on the cross-traffic scenario. If q11 is small, the Kalman filter does not anticipate sudden changes, thus a small value of q11minimizes the difference between available bandwidth and link capacity estimates if the cross-traffic rate is constant. On the other hand, a high value is better if the cross-traffic rate actually changes as in the scenarios corresponding to Figure 4 and 6.
B. Theoretical discussion of choice of Q
The following is a theoretical discussion on why the above values of Q should be used when measuring in 802.11 net-works.
As described in Section II the available bandwidth B and the link capacity C is derived from the system state vector xk by B =−βα and C =α1. Also, the available bandwidth and the link capacity are equal in 802.11 networks assuming that no cross traffic are sent from the probe-packet sender node. That is C = B which means that β = −1. Hence, β is constant and thus q22should be small since the expected variation in ˆβ
0.0e+000 2.0e+006 4.0e+006 6.0e+006 8.0e+006 1.0e+007 1.2e+007
−1 0 1 2 3 4 5
Probe rate [bit/s]
z
Fig. 7. Two distinct rate-response curves in one graph. During the first part of the measurement session the cross traffic is zero, then it increases to 6 Mbps.
0.0e+000 2.0e+006 4.0e+006 6.0e+006 8.0e+006 1.0e+007 1.2e+007
−1 0 1 2 3 4 5
Probe rate [bit/s]
z
Fig. 8. Two distinct rate-response curves in one graph. During the first part of the measurement session the cross traffic is 6 Mbps, then two sources are overloading the wireless link sending at 6 Mbps each.
will be small. On the other hand, if the estimated link capacity varies, that is the cross traffic from other nodes in the wireless network varies, q11 must be larger in order for the Kalman filter to adapt to changes in α.
This corroborates the results shown in the previous subsec-tion.
V. AREBARTESTIMATES CORRECT?
In the previous section it was investigated how to set Q in order to get stabile BART estimates while at the same time being able to track sudden changes in a wireless networks. But, how do we know that the BART estimates of the available bandwidth and link capacity are correct?
First, the assumed linear model used to describe the relation between the strain and the probe rate must be supported by experimental data. In this paper the approach is to study the rate-response curves obtained from using BART in different
scenarios. A rate-response curve is the visualization of Equa-tion 1.
In Figures 7 and 8 four curves are shown (i.e. two in each figure). The graph in Figure 7 originates from an experiment where the cross traffic is 0 during the first half and then jumps up to 6 Mbps during the second half of the experiment. As can be seen there are two distinct rate-response curves (compare Equation 1) from which the available bandwidth and link ca-pacity can be estimated. In Figure 8 results from an experiment where the cross traffic is 6 Mbps from one source during the first half and then jumps to 6 Mbps from two wireless sources during the second half of the experiment is depicted. As in the previous figure there are two rate-response curves from which BART estimates available bandwidth and link capacity. BART is assuming a piece-wise linear rate-response curve (as modeled in Equation 1) and observing the four curves we believe the experiments support the assumption of a linear model. Observe that the available bandwidth and link capacity estimates are updated by BART for each measurement sample, with strain above zero. A sample corresponds to a dot in the graphs. The actual BART estimates corresponding to the four rate-response curves are shown in Figures 9 and 10.
Cross traffic UDP BART AB
0 4 Mbps 3.75 - 4.4 Mbps
Uniform 6 Mbps x 1 3 Mbps 2.9 - 3.3 Mbps
Uniform 6 Mbps x 2 2.3 Mbps 2.1 - 2.6 Mbps
TABLE I
UDPTHROUGHPUT AND AVAILABLE BANDWIDTH ESTIMATES FOR THREE
SCENARIOS. THE NUMBERS ARE APPROXIMATE VALUES.
The next step in the validation of the BART estimates is to compare the true available bandwidth (the true value of the available bandwidth is what BART and other methods tries to estimate) and the available bandwidth estimate produced by BART. In a wireline testbed setting the true available bandwidth can be measured using tools such as tcpdump. Then the available bandwidth is computed as the fixed link capacity minus the cross-traffic load, obtained by tcpdump, during some time interval. However, in wireless 802.11 networks the capacity of the link at the IP layer is very hard to determine since it varies with the radio quality. Further, even if the radio quality was known there is no simple formula to calculate the cross-traffic impact on the capacity since it depends on the packet size, link-layer retransmission, backoff mechanisms and other MAC-layer properties. Instead, in this paper we use the maximum UDP throughput as a rough value of the available bandwidth.
In Table I the UDP throughput is summarized for three dif-ferent scenarios (approximate values) along with the estimates produced by BART. As can be seen from the table the BART estimates of the available bandwidth are more or less in line with the UDP throughput values. In the two scenarios where cross traffic is present on the wireless link each traffic flow gets a fair share of the capacity if sending at a rate above what
0 50 100 150 200 250 300 350 400 450 500 2.0e+006 2.5e+006 3.0e+006 3.5e+006 4.0e+006 4.5e+006 5.0e+006 Time Bandwidth (Mbps)
Fig. 9. The BART estimates of the available bandwidth (solid) and link capacity (dashed). During the first 250 time ticks the cross traffic is 0, then one cross-traffic source starts sending traffic at a rate of 6 Mbps.
0 50 100 150 200 250 300 350 400 450 500 2.0e+006 2.5e+006 3.0e+006 3.5e+006 4.0e+006 4.5e+006 5.0e+006 Time Bandwidth (Mbps)
Fig. 10. The BART estimates of the available bandwidth (solid) and link capacity (dashed). During the first 250 time ticks cross traffic is sent from one source at a rate of 6 Mbps. Then two cross-traffic sources generate 6 Mbps each.
is available. For example, when the UDP throughput test tool is competing with two cross-traffic sources sending traffic at 6 Mbps each flow get a throughput of approximately 2.3 Mbps. That is, their fair share of the wireless capacity.
In Figures 9 and 10 the BART estimates of the link capacity and the available bandwidth for the scenarios discussed above are shown in more detail. In this case the Q parameter has been fixed to Q= 0.01 0 0 0.00001 (14) as suggested in Section IV. Figure 9 describes a scenario where the cross traffic is zero at first and then jumps up to 6 Mbps sent from one cross-traffic source sharing the wireless
access network. The graph in Figure 10 corresponds to a scenario where the cross traffic first originates from one source sending at 6 Mbps and then changes to two nodes sending at 6 Mbps each. Observe the fast tracking of both bandwidth estimates when the cross traffic changes at time 250.
A. Discussion
There are several interesting observations to be made from the results presented in this section.
First, when BART, or the UDP throughput tool, is running in a scenario where no cross traffic is present the estimates are in line at 4 Mbps. When one cross-traffic source is active the sum of the cross-traffic rate and the available bandwidth estimate is 6 Mbps. Then, when two cross-traffic sources are active it seems that the total throughput is approximately 7 Mbps. It seems that the MAC layer used by 802.11 can achieve a higher total throughput when increasing the number of sending sources (asymptotically up to some limit).
As a second point, it seems that the available bandwidth and link capacity estimates corresponds to the fair share of the wireless capacity. If there are two nodes sharing the medium each node get approximately 3 Mbps, having three nodes each node reach approximately 2.3 Mbps. This is perhaps not a striking observation since the MAC layer used in 802.11 networks tries to be fair to each participating node. If all nodes are overloading the network each and every node gets1/n of the wireless capacity (where n is the number of nodes).
The above observations have implications on the interpre-tation of the estimates produced by BART and other similar tools that measures end-to-end available bandwidth utilizing self-induced congestion; it seems that the estimates correspond to a fair share of the medium rather than the unused capacity, which is the common definition of available bandwidth. On the other hand, the estimates do indicate what an application or device can expect to get in terms of bandwidth!
VI. CONCLUSIONS
In this paper a state-of-the-art active end-to-end available bandwidth measurement method called BART has been used to study the impact of wireless 802.11 bottleneck links on the produced bandwidth estimates.
It was reported on how to tune the Q matrix in the Kalman filter used by BART to get even better tracking properties and accurate bandwidth estimates when the bottleneck of an end-to-end network path is an 802.11 link.
The second contribution of this paper is the observation that methods and tools such as BART measure the fair share bandwidth when the bottleneck is an 802.11 link. This is not in line with the common definition of available bandwidth which is defined as the unused capacity. However, the estimates do indicate what an application or a device can expect to get in terms of bandwidth when sending and/or receiving traffic.
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