Tcp

1026 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 18, NO. 4, AUGUST 2010

A Machine Learning Approach to TCP Throughput
Prediction
Mariyam Mirza, Joel Sommers, Member, IEEE, Paul Barford, and Xiaojin Zhu

Abstract—TCP throughput prediction is an important capability TCP sender’s behavior to path and end-host properties such as
for networks where multiple paths exist between data senders and RTT, packet loss rate, and receive window size. In this case,
receivers. In this paper, we describe a new lightweight method for different measurement tools can be used to gather the input
TCP throughput prediction. Our predictor uses Support Vector
data that is then plugged into the formula to generate a pre-
Regression (SVR); prediction is based on both prior file transfer
history and measurements of simple path properties. We evaluate diction. However, well-known network dynamics and limited
our predictor in a laboratory setting where ground truth can be instrumentation access complicate the basic task of gathering
measured with perfect accuracy. We report the performance of our timely and accurate path information, and the ever-evolving set
predictor for oracular and practical measurements of path proper- of TCP implementations means that a corresponding set of for-
ties over a wide range of traffic conditions and transfer sizes. For mula-based models must be maintained.
bulk transfers in heavy traffic using oracular measurements, TCP History-based TCP throughput prediction methods are con-
throughput is predicted within 10% of the actual value 87% of
the time, representing nearly a threefold improvement in accuracy
ceptually straightforward. They typically use some kind of
over prior history-based methods. For practical measurements of standard time series forecasting based on throughput measure-
path properties, predictions can be made within 10% of the actual ments derived from prior file transfers. In recent work, He et
value nearly 50% of the time, approximately a 60% improvement al. show convincingly that history-based methods are generally
over history-based methods, and with much lower measurement more accurate than formula-based methods. However, the au-
traffic overhead. We implement our predictor in a tool called Path- thors carefully outline the conditions under which history-based
Perf, test it in the wide area, and show that PathPerf predicts TCP prediction can be effective [11]. Also, history-based approaches
throughput accurately over diverse wide area paths.
described to date remain relatively inaccurate and potentially
Index Terms—Active measurements, machine learning, support heavyweight processes focused on bulk transfer throughput
vector regression, TCP throughput prediction. prediction.
Our goal is to develop an accurate, lightweight tool for pre-
dicting end-to-end TCP throughput for arbitrary file sizes. We
I. INTRODUCTION investigate the hypothesis that the accuracy of history-based pre-
dictors can be improved and their impact on a path reduced by
T HE availability of multiple paths between sources and re-
ceivers enabled by content distribution, multihoming, and
overlay or virtual networks suggests the need for the ability to
augmenting the predictor with periodic measurements of simple
path properties. The questions addressed in this paper include:
select the “best” path for a particular data transfer. A common 1) which path properties or combination of path properties in-
starting point for this problem is to define “best” in terms of the crease the accuracy of TCP throughput prediction the most? and
throughput that can be achieved over a particular path between 2) what is a minimum set of file sizes required to generate his-
two end-hosts for a given sized TCP transfer. In this case, the tory-based throughput predictors for arbitrary file sizes? Addi-
fundamental challenge is to develop a technique that provides tional goals for our TCP throughput prediction tool are: 1) to
an accurate TCP throughput forecast for arbitrary and possibly make it robust to “level shifts” (i.e., when path properties change
highly dynamic end-to-end paths. significantly), which He et al. show to be a challenge in his-
Prior work on the problem of TCP throughput prediction has tory-based predictors; and 2) to include a confidence value with
largely fallen into two categories: those that investigate formula- predictions—a metric with little treatment in prior history-based
based approaches and those that investigate history-based ap- throughput predictors.
proaches. Formula-based methods, as the name suggests, pre- We use Support Vector Regression (SVR), a powerful ma-
dict throughput using mathematical expressions that relate a chine learning technique that has shown good empirical perfor-
mance in many domains, for throughput prediction. SVR has
several properties that make it well suited for our study: 1) It can
Manuscript received December 02, 2008; revised July 15, 2009; approved accept multiple inputs (i.e., multivariate features) and will use
by IEEE/ACM TRANSACTIONS ON NETWORKING Editor C. Dovrolis. First
published January 12, 2010; current version published August 18, 2010. This all of these to generate the throughput prediction. 2) SVR does
work was supported in part by NSF grants CNS-0347252, CNS-0646256, not commit to any particular parametric form, unlike formula-
CNS-0627102, and CCR-0325653. Any opinions, findings, conclusions, or based approaches. Instead, SVR models are flexible based on
recommendations expressed in this material are those of the authors and do their use of so-called nonlinear kernels. This expressive power is
not necessarily reflect the views of the NSF. An earlier version of this paper
appeared in SIGMETRICS 2007. the reason why SVR has potential to be more accurate than prior
M. Mirza, P. Barford, and X. Zhu are with the Department of Computer Sci- methods. 3) SVR is computationally efficient, which makes it
ences, University of Wisconsin–Madison, Madison, WI 53706 USA (e-mail: attractive for inclusion in a tool that can be deployed and used
mirza@cs.wisc.edu; pb@cs.wisc.edu; jerryzhu@cs.wisc.edu).
J. Sommers is with the Department of Computer Science, Colgate University, in the wide area. For our application, we extend the basic SVR
Hamilton, NY 13346 USA (e-mail: jsommers@colgate.edu). predictor with a confidence interval estimator based on the as-
Digital Object Identifier 10.1109/TNET.2009.2037812 sumption that prediction errors are normally distributed, an as-
1063-6692/$26.00 © 2010 IEEE

MIRZA et al.: A MACHINE LEARNING APPROACH TO TCP THROUGHPUT PREDICTION 1027

sumption that we test in our laboratory experiments. Estimation been well known that many factors affect TCP throughput, such
of confidence intervals is critical for online prediction since re- as the TCP implementation, the underlying network structure,
training can be triggered if measured throughput falls outside a and the dynamics of the traffic sharing the links on the path be-
confidence interval computed through previous measurements. tween two hosts. A number of studies have taken steps toward
We begin by using laboratory-based experiments to inves- understanding TCP behavior, including [1] and [2], which de-
tigate the relationship between TCP throughput and measure- veloped stochastic models for TCP based on packet loss charac-
ments of path properties including available bandwidth , teristics. A series of studies develop increasingly detailed math-
queuing delays , and packet loss . The lab environment ematical expressions for TCP throughput based on modeling
enables us to gather highly accurate passive measurements of the details of the TCP congestion control algorithm and mea-
throughput and all path properties and develop and test our surements of path properties [4], [8], [10], [17], [18]. While
SVR-based predictor over a range of realistic traffic conditions. our predictor also relies on measurement of path properties, the
Our initial experiments focus on bulk transfers and compare SVR-based approach is completely distinguished from prior for-
actual throughput of TCP flows to predictions generated by our mula-based models.
SVR-based tool. Our results show that throughput predictions A large number of empirical studies of TCP file transfer and
can be improved by as much as a factor of 3 when including throughput behavior have provided valuable insight into TCP
path properties in the SVR-based tool versus a history-based performance. Paxson conducted one of the most comprehensive
predictor. For example, our results show that the SVR-based studies of TCP behavior [19], [20]. While that work exposed a
predictions are within 10% of actual 87% of the time for bulk plethora of issues, it provided some of the first empirical data on
transfers under heavy traffic conditions (90% average utiliza- the characteristics of packet delay, queuing, and loss within TCP
tion on the bottleneck link). Interestingly, we find that the path file transfers. Barford and Crovella’s application of critical path
properties that provide the most improvement to the SVR-based analysis to TCP file transfers provides an even more detailed
predictor are and , respectively, and that including perspective on how delay, queuing, and loss relate to TCP per-
provides almost no improvement to the predictor. formance [6]. In [5], Balakrishnan et al. studied throughput from
Next, we expand the core SVR-based tool in three ways. the perspective of a large Web server and showed how it varied
First, the initial tests were based entirely on passive traffic depending on end-host and time-of-day characteristics. Finally,
measurements, which are unavailable in the wide area, so we detailed studies of throughput variability over time and corre-
tested our SVR-based approach using measurements of lations between throughput and flow size can be found in [31]
and provided by the BADABING tool [25]. The reduction in and [32], respectively. These studies inform our work in terms
accuracy of active versus passive measurements resulted in a of the basic characteristics of throughput that must be consid-
corresponding reduction in accuracy of SVR-based throughput ered when building our predictor.
predictions for bulk transfers under heavy traffic conditions Past studies of history-based methods for TCP throughput
on the order of about 35%—still a significant improvement prediction are based on standard time series forecasting
on history-based estimates. Also, throughput prediction based methods. Vazhkudia et al. compare several different simple
on training plus lightweight active measurements results in a forecasting methods to estimate TCP throughput for transfers of
dramatically lower network probe load than prior history-based large files and find similar performance across predictors [30].
methods using long-lived TCP transfers and heavyweight A well-known system for throughput prediction is the Net-
probe-based estimates of available bandwidth such as de- work Weather Service [28]. That system makes bulk transfer
scribed in [11]. We quantify this difference in Section VII. forecasts by attempting to correlate measurements of prior
Second, unlike prior work that focuses only on bulk transfers, large TCP file transfers with periodic small (64 kB) TCP file
we enabled SVR to predict throughput accurately for a wide transfers (referred to as “bandwidth probes”). The DualPats
range of file sizes. We found that a training set of only three system for TCP throughput prediction is described in [16].
file sizes results in accurate throughput predictions for a wide That system makes throughput estimates based on an expo-
range of file sizes. Third, He et al. showed that “level shifts” nentially weighted moving average of larger size bandwidth
in path conditions pose difficulties for throughput prediction probes (1.2 MB total). Similar to our work, Lu et al. found that
[11], suggesting the need for adaptivity. To accomplish this, we prediction errors generally followed a normal distribution. As
augmented the basic SVR predictor with a confidence interval mentioned earlier, He et al. extensively studied history-based
estimator as a mechanism for triggering a retraining process. predictors using three different time series forecasts [11]. Our
We show in Section VI-C1 that our technique is able to adapt SVR-based method includes information from prior transfers
to level shifts quickly and to maintain high accuracy on paths for training, but otherwise only requires measurements from
where level shifts occur. We implement these capabilities in a lightweight probes and is generalized for all files sizes, not just
tool called PathPerf1 that we tested in the wide area. We present bulk transfers.
results from 18 diverse wide area paths in the RON testbed [3] Many techniques have been developed to measure path prop-
and show that PathPerf predicts throughput accurately under a erties (see CAIDA’s excellent summary page for examples [9]).
broad range of conditions in real networks. Prior work on path property measurement directs our selection
of lightweight probe tools to collect data for our predictor. Re-
II. RELATED WORK
cent studies have focused on measuring available bandwidth on
Since seminal work by Jacobson and Karels established the a path. AB is defined informally as the minimum unused ca-
basic mechanisms for modern TCP implementations [13], it has pacity on an end-to-end path, which is a conceptually appealing
1PathPerf will be openly available for download at http://www.wail.cs.wisc. property with respect to throughput prediction. A number of
edu/waildownload.py. studies have described techniques for measuring AB including


[14], [26], and [27]. We investigate the ability of AB measure- freedom in by selecting a subset of features, thus reducing .
ment as well as other path properties to enhance TCP throughput An implicit but more convenient alternative is to require to be
predictions. smooth,2 defined as having a small parameter norm . Com-
Finally, machine learning techniques have not been widely bining loss and smoothness, we estimate the parameters
applied to network measurement. One notable exception is in by solving the following optimization problem:
network intrusion detection (e.g., [12]). The only other appli-
cation of SVR that we know of is to the problem of using IP
address structure to predict round-trip time latency [7]. (2)

III. A MULTIVARIATE MACHINE LEARNING TOOL where is a weight parameter to balance the two terms. The
The main hypothesis of this work is that history-based TCP value of is usually selected by a procedure called cross val-
throughput prediction can be improved by incorporating mea- idation, where the training set is randomly split into two parts,
surements of end-to-end path properties. The task of throughput then regression functions with different are trained on one
prediction can be formulated as a regression problem, i.e., pre- part and their performance measured on the other part, and fi-
dicting a real-valued number based on multiple real-valued nally one selects the value with the best performance. In our
input features. Each file transfer is represented by a feature experiments, we used using cross validation. The
vector of dimension . Each dimension is an observed optimization problem can be solved using a quadratic program.
feature, e.g., the file size, proximal measurements of path Nonetheless, a linear function is fairly restrictive and
properties such as queuing delay, loss, available bandwidth, may not be able to describe the true function . A standard math-
etc. Given , we want to predict the throughput . This ematical trick is to augment the feature vector with nonlinear
is achieved by training a regression function , bases derived from . For example, if , one can
and applying to . The function is trained using training augment it with . The linear re-
data, i.e., historical file transfers with known features and the gressor in the augmented feature space
corresponding measured throughput. then produces a nonlinear fit in the original feature space. Note
The analytical framework that we apply to this problem is has more dimensions than before. The more dimensions
Support Vector Regression (SVR), a state-of-the-art machine has, the more expressive becomes.
learning tool for multivariate regression. SVR is the regression In the extreme (and often beneficial) case, can even have
version of the popular Support Vector Machines [29]. It has a infinite dimensions. It seems computationally impossible to esti-
solid theoretical foundation and is favored in practice for its mate the corresponding infinite-dimensional parameter . How-
good empirical performance. We briefly describe SVR below ever, if we convert the primal optimization problem (2) into its
and refer readers to [21] and [23] for details and to [15] as an dual form, one can show that the number of dual parameters is
example of an SVR software package. actually instead of the dimension of . Furthermore, the
To understand SVR, we start from a linear regression function dual problem never uses the augmented feature explicitly.
. Assume we have a training set of file It only uses the inner product between pairs of augmented fea-
transfers . Training involves estimating tures . The function is known as
the -dimensional weight vector and offset so that is the kernel and can be computed from the original feature vec-
close to the truth for all training examples . There tors . For instance, the Radial Basis Function (RBF) kernel
are many ways to measure “closeness”. The traditional measure implicitly corresponds to an
used in SVR is the -insensitive loss, defined as infinite-dimensional feature space. In our experiments, we used
a RBF kernel with , again selected by cross vali-
dation. The dual problem can still be efficiently solved using a
if quadratic program.
(1) SVR therefore works as follows. For training, one collects a
otherwise.
training set and specifies a kernel .
This loss function measures the absolute error between predic- SVR solves the dual optimization problem, which equivalently
tion and truth, but with a tolerance of . The value is applica- finds the potentially very high-dimensional parameter and
tion-dependent in general, and in our experiments we set it to in the augmented feature space defined by . This produces a
zero. Other loss functions (e.g., the squared loss) are possible, potentially highly nonlinear prediction function . The func-
too, and often give similar performance. They are not explored tion can then be applied to arbitrary test cases and pro-
in this paper. duces a prediction. In our case, test cases are the file size for
It might seem that the appropriate way to estimate the pa- which a prediction is to be made and current path properties
rameters is to minimize the overall loss on the training based on active measurements.
set . However if is large compared to the
number of training examples , one can often fit the training IV. EXPERIMENTAL ENVIRONMENT AND METHODOLOGY
data perfectly. This is dangerous because the truth in training
data actually contain random fluctuations, and is partly fit- This section describes the laboratory environment and exper-
ting the noise. Such will generalize poorly, i.e., causing bad iments that we used to evaluate our throughput predictor.
predictions on future test data. This phenomenon is known as 2If

are the coefficients of a polynomial function, the function will tend to
overfitting. To prevent overfitting, one can reduce the degree of be smooth (changes slowly) if k


Fig. 1. Laboratory testbed. Cross traffic flowed across one of two routers at hop B, while probe traffic flowed through the other. Optical splitters connected Endace
DAG 3.5 and 3.8 passive packet capture cards to the testbed between hops B and C and hops C and D. Measurement traffic (file transfers, loss probes, and available
bandwidth probes) flowed from left to right. Congestion in the testbed occurred at hop C.

A. Experimental Environment B. Experimental Protocol
We generated background traffic by running the Harpoon IP
The laboratory testbed used in our experiments is shown traffic generator [24] between up to four pairs of traffic gen-
in Fig. 1. It consisted of commodity end-hosts connected eration hosts as illustrated in Fig. 1. Harpoon produced open-
to a dumbbell-like topology of Cisco GSR 12000 routers. loop self-similar traffic using a heavy-tailed file size distribu-
Both measurement and background traffic was generated and tion, mimicking a mix of application traffic such as Web and
received by the end-hosts. Traffic flowed from the sending peer-to-peer applications common in today’s Internet. Harpoon
hosts on separate paths via Gigabit Ethernet to separate Cisco was configured to produce average offered loads ranging from
GSRs (hop B in the figure) where it was forwarded on OC12 approximately 60% to 105% on the bottleneck link (the OC3
(622 Mb/s) links. This configuration was created in order to between hops C and D).
accommodate a precision passive measurement system. Traffic As illustrated in Fig. 2, measurement traffic in the testbed con-
from the OC12 links was then multiplexed onto a single OC3 sisted of file transfers and active measurements of AB, L, and Q.
(155 Mb/s) link (hop C in the figure), which formed the bottle- We also measured all three metrics passively using packet traces.
neck where congestion took place. We used an AdTech SX-14 All measurements are aggregates for all flows on the path. Mea-
hardware-based propagation delay emulator on the OC3 link surements were separated by 30-s intervals. For the measurement
to add 25 ms delay in each direction for all experiments and traffic hosts, we increased the TCP receive window size to 128 kB
configured the bottleneck queue to hold approximately 50 ms (with the window scaling option turned on). In receive window
of packets. Packets exited the OC3 link via another Cisco GSR limited transfers, file transfer throughput was approximately 21
12000 (hop D in the figure) and passed to receiving hosts via Mb/s. That is, if the available bandwidth on the bottleneck link
Gigabit Ethernet. was 21 Mb/s or more, the flow was receive window lim-
The measurement hosts and traffic generation hosts were ited; otherwise, it was congestion window limited. We
identically configured workstations running FreeBSD 5.4. increased the receive window size because we wanted file trans-
The workstations had 2-GHz Intel Pentium 4 processors fers to be -limited so we could evaluate our predictor thor-
with 2 GB of RAM and Intel Pro/1000 network cards. They oughly; -limited transfers have constant throughput for a
were also dual-homed, so all management traffic was on a given size, so any reasonable predictor performs well on
separate network than that depicted in Fig. 1. We disabled -limited transfers. For this reason, we do not report any re-
the TCP throughput history caching feature in FreeBSD 5.4, sults for -limited flows.
controlled by the variable net.inet.tcp.inflight.enable, to allow Series of measurements were collected and then split up into
TCP throughput to be determined by current path properties mutually exclusive training and test sets for SVR. Notions of
rather than throughput history. separate training and test sets are not required for history-based
A key aspect of our testbed was the measurement system methods; rather, predictions are made over the continuous no-
used to establish the true path properties for our evaluation. tion of distant and recent history. In our evaluation of history-
Optical splitters were attached to both the ingress and egress based methods, we use the final prediction of the training set as
links at hop C, and Endace DAG 3.5 and 3.8 passive moni- the starting point for the test set.
toring cards were used to capture traces of all packets entering Fig. 2 shows that we gather three types of measurements
and leaving the bottleneck node. By comparing packet headers, for each experiment: Oracular Passive Measurements (OPM),
we were able to identify which packets were lost at the con- Practical Passive Measurements (PPM), and Active Measure-
gested output queue during experiments and accurately mea- ments (AM). Oracular measurements, taken during the file
sure available bandwidth on the congested link. Furthermore, transfer, give us perfect information about network conditions,
the fact that the measurements of packets entering and leaving so we can establish the best possible accuracy of our prediction
hop C were synchronized at a very fine granularity (i.e., a single mechanism. In practice, this oracular information is not avail-
microsecond) enabled us to precisely measure queuing delays able for making predictions. AM, taken before the file transfer,
through the congested router. are available in practice and can thus be used for prediction.


introduced in [11] to evaluate the accuracy of an individual
throughput prediction. Relative prediction error is defined
as In what follows, we use the
distribution of the absolute value of to compare different
prediction methods.

V. BUILDING A ROBUST PREDICTOR
This section describes how we developed, calibrated, and
evaluated our prediction mechanism through an extensive set
of tests conducted in our lab testbed.

A. Calibration and Evaluation in the High-Traffic Scenario
The first step in developing our SVR-based throughput pre-
dictor is to find the combination of training features that lead to
the most accurate predictions over a wide variety of path con-
ditions. We trained the predictor using a feature vector for each
Fig. 2. Measurement traffic protocol and oracular and practical path measure-
ments used for SVR-based throughput prediction.
test that contained a different combination of our set of target
path measurements (AB, Q, L) and the measured throughput.
The trained SVR model is then used to predict throughput for
PPM, passive measurements taken at the same time AM are a feature vector containing the corresponding sets of network
taken, show the best possible accuracy of our prediction mech- measurements, and we compare the prediction accuracy for the
anism with practical measurements, or show how much better different combinations.
SVR would perform if the active measurements had perfect We also compare the accuracy of SVR to the exponentially
accuracy. weighted moving average (EWMA) History-Based Predictor
AB is defined as the spare capacity on the end-to-end path. (HB) described in [11], . We use
YAZ estimates available bandwidth using a relatively low-over- an value of 0.3 because it is used in [11].
head, iterative method similar to PATHLOAD [14]. The time re- For most of the results reported, we generated an average of
quired to produce a single AB estimate can vary from a few 140 Mb/s of background traffic to create high utilization on our
seconds to tens of seconds. The passive measurement value of OC3 (155 Mb/s) bottleneck link. We used one set of 100 ex-
AB is computed by subtracting the observed traffic rate on the periments for training and another set of 100 experiments for
link from the realizable OC3 link bandwidth. testing. An 8-MB file was transferred in each experiment.
We use BADABING for active measurements of L and Q. Fig. 3(a)–(h) show scatter plots comparing the actual and
BADABING requires the sender and receiver to be time-syn- predicted throughput using different prediction methods as dis-
chronized. To accommodate our wide area experiments, the cussed below. A point on the diagonal represents perfect pre-
BADABING receiver was modified to reflect probes back to the diction accuracy; the farther a point is from the diagonal, the
sender, where they were timestamped and logged as on the greater the prediction error.
original receiver. Thus, the sender clock was used for all probe 1) Using Path Measurements From an Oracle: Fig. 3(a)
timestamps. BADABING reports loss in terms of loss episode shows the prediction accuracy scatter plot for the HB method.
frequency and loss episode duration, defined in [25]. Although Fig. 3(b)-(g) show the prediction error with SVR using Orac-
we refer to loss frequency and loss duration together as L or ular Passive Measurements (OPM) for different combinations
loss for expositional ease, these two metrics are two different of path measurements in the feature vector. For example,
features for SVR. Q is defined as the difference between the SVR-OPM-Queue means that only queuing delay measure-
RTT of the current BADABING probe and the minimum probe ments were used to train and test, while SVR-OPM-Loss-Queue
RTT seen on the path. We set the BADABING probe probability means that both loss and queuing delay measurements were
parameter to 0.3. Other parameters were set according to used to train and test.
[25]. Passive values of Q and L are computed using the same Table I shows relative prediction errors for HB forecasting
definitions as above, except that they are applied to all TCP and for SVM-OPM-based predictions. Values in the table in-
traffic on the bottleneck link instead of BADABING probes. dicate the fraction of predictions for a given method within a
For experiments in the wide area, we created a tool, PathPerf. given accuracy level. For example, the first two columns of the
This tool, designed to run between a pair of end-hosts, initiates first row in Table I mean that 32% of HB predictions have rel-
TCP file transfers and path property measurements (using our ative prediction errors of 10% or smaller, while 79% of SVR-
modified version of BADABING) and produces throughput esti- OPM-AB predictions have relative prediction errors of 10% or
mates using our SVR-based method. It can be configured to gen- smaller. We present scatter plots in addition to tabular data to
erate arbitrary file size transfers for both training and testing and provide insight into how different path properties contribute to
initiates retraining when level shifts are identified as described throughput prediction in the SVR method.
in Section VII. From Fig. 3(a), we can see that the predictions for the HB
predictor are rather diffusely scattered around the diagonal, and
C. Evaluating Prediction Accuracy that predictions in low-throughput conditions tend to have large
We denote the actual throughput by and the predicted relative error. Fig. 3(b)-(d) show the behavior of the SVR pre-
throughput by . We use the metric relative prediction error dictor using a single measure of path properties in the feature


Fig. 3. Comparison of prediction accuracy of HB, SVR-OPM, and SVR-AM in high background traffic conditions. (a) HB. (b) SVR-OPM-AB. (c) SVR-OPM-
loss. (d) SVR-OPM-queue. (e) SVR-OPM-AB-loss. (f) SVR-OPM-loss-queue. (g) SVR-OPM-AB-loss-queue. (h) SVR-AM-loss-queue.

TABLE I
RELATIVE ACCURACY OF HISTORY-BASED (HB) THROUGHPUT PREDICTION AND SVR-BASED PREDICTORS USING DIFFERENT TYPES OF ORACULAR PASSIVE
PATH MEASUREMENTS (SVR-OPM) IN THE FEATURE VECTOR. TABLE VALUES INDICATE THE FRACTION OF PREDICTIONS WITHIN A GIVEN ACCURACY LEVEL

vector—AB, L, and Q, respectively. The AB and Q graphs have dictive power, while AB and Q are able to predict throughput
a similar overall trend: Predictions are accurate (i.e., points are quite accurately.
close to the diagonal) for high actual throughput values, but far Fig. 3(e) and (f) show improvements in prediction accuracy
from the diagonal, almost in a horizontal line, for lower values obtained by using more than one path property in the SVR fea-
of actual throughput. The L graph has the opposite trend: Points ture vector. We can see that when L is combined with AB or
are close to the diagonal for lower values of actual throughput Q, the horizontal lines on the graphs are replaced by points
and form a horizontal line for higher values of actual throughput. much closer to the diagonal. Combining AB or Q with L allows
The explanation for these trends lies in the fact that file trans- SVR to predict accurately in both lossy and lossless conditions.
fers with low actual throughput experience loss, while file trans- Since both AB and Q help predict throughput in lossless condi-
fers with high actual throughput do not experience any loss. tions, do we really need both AB and Q, or can we use just one
When loss occurs, the values of AB and Q for the path are nearly of the two and still achieve the same prediction accuracy? To
constant. AB is almost zero, and Q is the maximum possible answer this question, we compared AB-Loss and Loss-Queue
value (which depends on the amount of buffering available at predictions with each other and with AB-Loss-Queue predic-
the bottleneck link in the path). In this case, throughput depends tions [i.e., Figs. 3(e)–(g)]. The general trend in all three cases
on the value of L. Hence, L appears to be a good predictor when is the same: The horizontal line of points is reduced or elimi-
there is loss on the path, and AB and Q, being constants in this nated, suggesting that prediction from nonconstant-value mea-
case, have no predictive power, resulting in horizontal lines, i.e., surements is occurring for both lossy and lossless network con-
a single value of predicted throughput. On the other hand, when ditions. If we compare the AB-Loss and Loss-Queue graphs
there is no loss, L is a constant with value zero, so L has no pre- more closely, we observe two things. First, in the lossless predic-


TABLE II examine three issues: first, whether our finding that Loss-Queue
RELATIVE ACCURACY OF HISTORY-BASED (HB) THROUGHPUT PREDICTION has the same prediction accuracy as AB-Loss-Queue from the
AND SVR-BASED PREDICTORS USING TRACE-BASED PASSIVE PATH
SVR-OPM case holds for the SVR-PPM and SVR-AM case;
MEASUREMENTS (PPM) OR ACTIVE PATH MEASUREMENTS (AM).
TABLE VALUES INDICATE THE FRACTION OF PREDICTIONS second, whether SVR-PPM and SVR-AM have the same ac-
WITHIN A GIVEN ACCURACY LEVEL curacy; and third, how SVR-AM accuracy compares with HB
prediction accuracy.
All prediction accuracy results in the SVR-PPM and SVR-AM
columns in Table II are very similar. AB-Loss-Queue has ap-
proximately the same accuracy as Loss-Queue for both
SVR-PPM and SVR-AM. This is encouraging because it is con-
sistent with the observation from SVR-OPM, i.e., that we can
achieve good prediction accuracy without having to measure
AB. SVR-AM has accuracy similar to SVR-PPM, i.e., using
active measurement tools to estimate path properties yields
predictions almost as accurate as having ground-truth passive
measurements. This is important because in real wide-area
paths, instrumentation is generally not available for collecting
tion case, the points are closer to the diagonal in the Loss-Queue accurate passive measurements.
case than in the AB-Loss case. Second, in the Loss-Queue case, Finally, we compare HB with SVR-AM. Although
the transition in the prediction from the lossless to the lossy case Fig. 3(a) and 3(h) are qualitatively similar, SVR-AM has a
is smooth, i.e., there is no horizontal line of points, while in the tighter cluster of points around the diagonal for high actual
AB-Loss case there is still a horizontal line of points in the actual throughput than HB. Thus, SVR-AM appears to have higher
throughput range of 11–14 Mb/s. This suggests that Q is a more accuracy than HB. As Table II shows, SVR-AM-Loss-Queue
accurate predictor than AB in the lossless case. The relative pre- predicts throughput within 10% of actual accuracy 49% of
diction error data of Table I supports this: SVR with a feature the time, while HB does so only 32% of the time. Hence, for
vector containing Loss-Queue information predicts throughput high-traffic scenarios, SVR-AM-Loss-Queue, the practically
within 10% of actual for 87% of transfers, while a feature vector deployable lightweight version of the SVR-based prediction
containing AB-Loss measurements predicts with the same ac- mechanism, significantly outperforms HB prediction.
curacy level for 78% of transfers. Finally, there is no differ- The above observations raise the question of why SVR
ence in accuracy (either qualitatively or quantitatively) between performs so much better than HB at high accuracy levels. HB is
Loss-Queue and AB-Loss-Queue. a weighted average that works on the assumption that transfers
The above discussion suggests that AB measurements are not close to each other in time will have similar throughputs.
required for highly accurate throughput prediction and that a HB loses accuracy when there are rapid and large changes
combination of L and Q is sufficient. This observation is not in throughput because in that case there is a large difference
only surprising, but rather good news. Prior work has shown between the weighted average and individual throughputs.
that accurate measurements of AB require at least moderate SVR predicts throughput by constructing a function mapping
amounts of probe traffic [22], [26], and some formula-based path properties to throughput values. This function is able
TCP throughput estimation schemes take as a given that AB to capture complex nonlinear relationships between the path
measurements are necessary for accurate throughput prediction properties and throughput. As long as the mapping between
[11]. In contrast, measurements of L and Q can be very light- path properties and resulting throughput is consistent, SVR
weight probe processes [25]. We discuss measurement overhead can predict throughput accurately, regardless of the variation
further in Section VII. between the throughput of neighboring transfers. SVR accuracy
2) Using Practical Passive and Active Path Measurements: breaks down only when the mapping between path properties
So far, we have considered the prediction accuracy of SVR and throughput becomes inconsistent, e.g., when path condi-
based on only Oracular Passive Measurements (OPM). This tions are so volatile that they change between the active path
gives us the best-case accuracy achievable with SVR and also measurement and the file transfer, or when an aggregate path
provides insight into how SVR uses different path properties measure does not hold for the transfer, such as when there is
for prediction. Table I shows that HB predicts 32% of transfers loss on the bottleneck link, but the file transfer experiences
within 10% of actual, while SVR-OPM-Loss-Queue predicts more or less loss than the aggregate traffic. Thus, SVR outper-
87%, an almost threefold improvement. In practice, however, forms HB because: 1) it has access to additional information,
perfect measurements of path properties are not available, so in in the form of path properties such as AB, L, and Q, while HB
what follows we assess SVR using measurements that can be has access only to past throughputs; and 2) it constructs a much
obtained in practice in the wide area. more sophisticated functional mapping of path properties to
Table II presents relative prediction error data for HB, throughput compared to the simple time-series analysis that
SVR-PPM, and SVR-AM. Due to space limitations, we present HB uses. The fact that SVR’s supremacy over HB is limited to
only Loss-Queue and AB-Loss-Queue results for SVR. We high accuracy levels, and HB catches up with SVR for lower
choose these because we expect AB-Loss-Queue to have the accuracy levels (predicted throughput within 40%–90% of
highest accuracy as it has the most information about path prop- actual, Table II), is a feature of the distribution of throughputs
erties, and Loss-Queue because it is very lightweight and has in our test set. We can see from the graphs in Fig. 3(a)–(h)
accuracy equal to AB-Loss-Queue for SVR-OPM. We wish to that the average throughput of the test set is between 10 and


TABLE III
RELATIVE ACCURACY OF SVR-BASED PREDICTOR USING ORACULAR PASSIVE
MEASUREMENTS (OPM) AND TRAINING SETS CONSISTING OF ONE, TWO,
THREE, SIX, OR EIGHT DISTINCT FILE SIZES

Fig. 4. Normal Q-Q plots for prediction errors with (a) oracular measurements
(SVR-OPM) and (b) active measurements (SVR-AM) of Loss-Queue.

15 Mb/s. We expect the HB prediction to be around the average
throughput. Fig. 3(a) shows that this is indeed the case: All HB file sizes, not just bulk transfers, so in this section we evaluate
predictions are between 10 and 15 Mb/s. All but one transfers prediction accuracy for a broad range of file sizes, something
have actual throughput between 5 and 18 Mb/s, so the relative not considered in prior HB prediction studies.
error is 100% or less for low We conducted experiments using background traffic at an av-
throughputs (all predictions within a factor of two of actual) erage offered load of 135 Mb/s. We used nine different training
and 80% or less for high through- sets, each of size 100, consisting of between one and nine unique
puts. If the range of actual throughputs had been wider but the file sizes. The file sizes for the training sets were between 32 kB
average had been the same, HB would have been less able to bytes and 8 MB bytes . The first training set con-
match SVR accuracy for relative error values of 40%–90%. sisted of 100 8-MB files; the second of 50 32-kB files and 50
A remaining question is why Q is a better predictor of 8-MB files; the third of 33 each of 32-kB bytes , 512-kB
throughput than AB. When we compare AB and Q predic- bytes , and 8-MB bytes files; the fourth of 25 each of
tion behavior in Fig. 3(b) and (d), we see that as throughput -, -, -, and -byte files; and so on, dividing the
decreases, i.e., as the network moves from lossless to lossy range of the exponent, 15 to 23, into more numerous but smaller
conditions, AB loses its predictive power sooner than Q does, intervals for each subsequent training set.
around 15 Mb/s instead of 11 Mb/s for Q. As soon as the Test sets for our experiments consist of 100 file sizes between
link experiences loss, AB is zero. While Q eventually reaches 2 kB bytes and 8 MB bytes . To generate file sizes for
a maximum value under sufficiently high congestion, under the test set, uniformly distributed random numbers between 11
light loss it retains its resolution because Q will be different and 23 were generated. The file size was set to bytes, rounded
depending on the percentage of packets that experience the to the closest integer; note that kB, and MB.
maximum possible queuing delay and those that experience less This log-based distribution of file sizes contains a much greater
than the maximum. Hence, Q is a better predictor of throughput number of smaller files than a uniform linear distribution of
than AB most likely because it can be measured with better file sizes from 2 kB to 8 MB would. The bias toward smaller
resolution for a wider range of network conditions. file sizes is important for proper evaluation of predictor perfor-
3) The Nature of Prediction Error: Lu et al. [16] observed mance for small files because it generates a more even distribu-
in their study that throughput prediction errors were approxi- tion between files that spend all their transfer time in slow-start,
mately normal in distribution. As the authors noted, normality those that spend some time in slow-start and some in congestion
would justify standard computations of confidence intervals. We avoidance, and those that spend a negligible amount of time in
examined the distribution of errors in our experiments and also slow-start. If the uniform linear distribution had been used, most
found evidence suggestive of normality. of the file sizes generated would have spent a negligible amount
Fig. 4 shows two normal quantile-quantile (Q-Q) plots for of time in slow-start. We also use a wider range of small files
SVR-OPM-Loss-Queue [Fig. 4(a)] and SVR-AM-Loss-Queue in the test set compared to the training set—the test set starts
[Fig. 4(b)]. Samples that are consistent with a normal distribu- with 2-kB files, while the training set starts with 32 kB—be-
tion form approximately a straight line in the graph, particularly cause we want to see how well our predictor extrapolates for
toward the center. In Fig. 4(a) and (b), we see that the throughput unseen ranges of small file sizes.
prediction samples in each case form approximately straight Tables III and IV present prediction accuracy for training sets
lines. These observations are consistent with normality in the consisting of one, two, three, six, or eight distinct file sizes for
distribution of prediction errors. Error distributions from other SVR-OPM and SVR-AM. Graphs in Fig. 5 present SVR-AM re-
experiments were also consistent with the normal distribution sults for one, two, and three file sizes in the training set. We do
but are not shown due to space limitations. We further discuss not include graphs for remaining training sets due to space lim-
the issues of retraining and of detecting estimation problems in itations: They are similar to those for two and three file sizes
Section VII. in the training set. The first observation is that for the single
file size in training, the prediction error is very high. This in-
B. Evaluation of Prediction Accuracy for Different File Sizes accuracy is expected because the predictor has been given no
Thus far, we have predicted throughput only for bulk transfers information about the relationship between size and throughput
of 8 MB. However, our goal is accurate prediction for a range of for small files. The second observation is that for more than one


Fig. 5. Scatter plots for the SVR-based predictor using one, two, or three distinct file sizes in the training set. All results shown use active measurements to train
the predictor. Testing is done using a range of 100 file sizes from 2 kB to 8 MB. (a) SVR-AM with file size of 8 MB in training set. (b) SVR-AM with file sizes of
32 kB and 8 MB in training set. (c) SVR-AM with file sizes of 32 kB, 512 kB, and 8 MB in training set.

TABLE IV ples for a single file size. We would not see maximum accuracy
RELATIVE ACCURACY OF SVR-BASED PREDICTOR USING ACTIVE
MEASUREMENTS (AM) AND TRAINING SETS CONSISTING OF ONE,
occurring at three file sizes and would instead see an increase in
TWO, THREE, SIX, OR EIGHT DISTINCT FILE SIZES accuracy with increasing number of file sizes in the training set
if we kept the number of samples of a single file size constant at
100 in the training set and allowed the size of the training set to
increase from 100 to 200, 300, etc., as we increase the number
of file sizes in the training set.
VI. WIDE AREA EXPERIMENTS
To further evaluate our SVR-based TCP throughput predic-
tion method, we created a prototype tool called PathPerf that
can generate measurements and make forecasts on wide area
paths. We used PathPerf to conduct experiments over a set of
paths in the RON testbed [3]. This section presents the results
of our wide area experiments.
file size, prediction becomes dramatically more accurate, i.e.,
the predictor is able to successfully extrapolate from a handful A. The RON Experimental Environment
of sizes in training to a large number of sizes in testing. The The RON wide area experiments were conducted in January
third observation is that relative error is low for large file sizes 2007 over 18 paths between seven different node locations. Two
(corresponding to high actual throughput), while it is higher for nodes were in Europe (in Amsterdam, The Netherlands, and
small files (low actual throughput), or in other words, predicting London, U.K.), and the remainder were located at universities
throughput accurately for small files is more difficult than for in the continental United States (Cornell University, Ithaca,
large files. For small files, throughput increases rapidly with file NY; University of Maryland, College Park; University of New
size during TCP’s slow-start phase due to the doubling of the Mexico, Albuquerque; New York University, New York; and
window every RTT. Also, packet loss during the transfer of a University of Utah, Salt Lake City). Of the 18 paths, two are
small file has a larger relative impact on throughput. Due to trans-European, nine are trans-Atlantic, and seven are transcon-
the greater variability of throughput for small files, predicting tinental U.S. The RON testbed has a significantly larger number
throughput accurately is more difficult. The fourth observation of available nodes and paths, but two considerations limited the
is that for small file sizes (i.e., small actual throughput), the error number of nodes and paths that we could use. The first consid-
is always that of overprediction. The smallest file in the training eration was that the nodes should have little or no other CPU
set is 32 kB, while the smallest file in the test set is 2 kB. This or network load while our experiments were running; this is
difference is the cause of overprediction errors: Given the high required for BADABING to measure loss accurately. The second
variability of throughput for small file sizes due to slow-start ef- issue was that we could not use any nodes running FreeBSD 5.x
fects and losses having a greater relative impact on throughput, because the TCP throughput history caching feature in FreeBSD
without a broader training set, the SVR mechanism is unable to 5.x, controlled by the variable net.inet.tcp.inflight.enable, is on
extrapolate accurately for unseen ranges of small file sizes. by default and interfered with our experiments. Consequently,
A final observation is that prediction accuracy reaches a max- we were restricted to using nodes running FreeBSD 4.7, which
imum at three file sizes in the training set, and there is no clear does not have the throughput history caching feature.
trend for four to nine file sizes in the training set. The number We use the following convention for path names: A–B means
of transfers in our training set is always constant at 100, so for that A is the TCP sender and B is the receiver, i.e., the TCP
the single training size, there are 100 8-MB transfers for the two data flow direction is from A to B, and TCP ack flow is in the
training sizes, there are 50 32-kB transfers and 50 8-MB trans- reverse direction. A–B and B–A are considered two different
fers, and so on. We believe that accuracy is maximum at three paths because routing and background traffic level asymmetry
training sizes in our experiments because there is a tradeoff be- between the forward and reverse directions can lead to major
tween capturing a diversity of file sizes and the number of sam- differences in throughput.


Fig. 6. Wide area results for HB and SVR predictions. The HB and SVR columns present the fraction of predictions with relative error of 10% or less. Training
and test sets consisted of 100 samples each. Two megabytes of data were transferred. Labels use node initials; see Section V for complete node names.

TABLE V
MINIMUM RTTS FOR THE 18 RON PATHS USED FOR WIDE-AREA EXPERIMENTS obtained by dividing the 200 measurements gathered for each
path into two consecutive sets of 100, using the first 100 as the
training set and the second 100 as the test set. Some paths feature
more than once because node availability allowed us to repeat
experiments on those paths.
We observe two major trends from Fig. 6. First, for the
majority of experiments, prediction accuracy is very high
for both HB and SVR: Most paths have greater than 85%
of predictions within 10% of actual throughput. Second,
for five out of the 26 experiments—Cornell–Amsterdam,
London–Maryland–1, London–Utah–2, London–Utah–5, and
NYU–Amsterdam—the SVR prediction accuracy is quite low,
as low as 25% for London–Utah–2. The reasons for this poor
accuracy will be analyzed in detail in Section VI-C.
Next, we take a more detailed approach to assessing predic-
The wide area measurement protocol was the following: tion accuracy. We divide the 200 samples into sets of and
1) run BADABING for 30 s; 2) transfer a 2-MB file; 3) sleep 30 s; for values of from 1 to 199. The first samples are
and 4) repeat the above 200 times. used for training, and the remaining samples are used
In Section V, we showed that available bandwidth measure- for testing. This allows us to understand the tradeoff between
ments are not required for accurate TCP throughput predic- training set size and prediction accuracy, which is important for
tion, so we omit running YAZ in the wide area. Thus, the wide a practical online prediction system where it is desirable to start
area prediction mechanism is the SVR-AM-Loss-Queue protocol generating predictions as soon as possible. This analysis also
from Section V. We reduced the size of the file transfers from 8 allows us to identify the points in a trace where an event that
MB in the lab experiments to 2 MB in the wide area experiments has an impact on prediction accuracy, such as a level shift, oc-
because the typical throughput in the wide area was an order of curs and whether retraining helps maintain prediction accuracy
magnitude lower compared to the typical throughput in the lab in the face of changing network conditions. We present this data
(1–2 Mb/s versus 10–15 Mb/s). for SVR only; for HB, there is no division of data into training
The measurements were carried out at different times of the and test sets because retraining occurs after every measurement.
day for different paths depending upon when the nodes were Fig. 7 presents the SVR prediction accuracy for , 5,
available, i.e., when the nodes had little or no other CPU and and 10 for those experiments in Fig. 6 that had high predic-
network activity in progress. Depending again on node avail- tion accuracy for . For all but three of the experiments
ability, we ran a single set of experiments on some paths and in Fig. 7, there is little difference between prediction accuracy
multiple sets on others. We can only conduct active measure- for training set sizes of 1, 5, 10, and 100. This is because there
ments in the wide area because the infrastructure required for is little variation in the throughput observed during the experi-
passive measurements is not present. ments. A path with little or no variation in observed throughput
Table V lists the minimum round-trip times observed on the over the course of an experimental run is the easy case for both
wide area paths over all BADABING measurements taken on each SVR and HB throughput predictors, so these experiments will
path. The shortest paths have a minimum RTT of 8 ms, and the not be discussed any further in this paper. For three experiments
longest a minimum RTT of 145 ms. In Table V, we ignore path in Fig. 7, Amsterdam–London, London–Utah–1, and Utah–Cor-
directions, e.g., we list Amsterdam–London and London–Ams- nell, the prediction accuracy for values of 1, 5, and 10 is sig-
terdam as a single entry because minimum RTT is the same in nificantly lower compared to that for . The reason for
both directions. this poor accuracy will be discussed in detail in Section VI-C.

B. Wide Area Results C. Detailed Analysis of Wide Area Results
Fig. 6 compares the accuracy of the SVR and HB throughput In this section, we analyze the reasons for poor SVR predic-
predictions for the 18 wide area paths. The results in Fig. 6 are tion accuracy for five paths from Fig. 6 (Cornell–Amsterdam,


Fig. 7. Effect of training set size on SVR prediction accuracy in the wide area. For paths with high prediction accuracy in Fig. 6, this table shows how large a
training set size was needed to achieve high accuracy. Labels use node initials; see Section V for complete node names.

shift from a throughput of 1.4 to 0.6 Mb/s occurs after 144 file
transfers, and a level shift from 0.6 back to 1.4 Mb/s occurs
after 176 transfers. Fig. 8(b) shows that prediction accuracy de-
creases from 0.84 at one file transfer to a global minimum of
0.40 at 144 file transfers, and then increases very rapidly to 1.00
at 145 file transfers. This result can be explained by the fact
that the level shift is not included in the training data. Thus, the
prediction function will generate samples at the first throughput
level accurately and those at the second throughput level inac-
curately. Prediction accuracy decreases from 1 to 144 because
Fig. 8. London–Utah–5: An example of a wide area path with level shifts. Time there are relatively fewer samples at the first level and more
on the x-axis is represented in terms of file transfer number. (a) Throughput
profile. (b) Prediction accuracy. at the second level in the test set as the value of x increases,
so there are relatively more inaccurate predictions, leading to
a decreasing trend in prediction accuracy. If the division into
London–Maryland–1, London–Utah–2, London–Utah–5, training and test sets is at the level shift boundary, in this case the
and NYU–Amsterdam) and three paths from Fig. 7 (Ams- first 144 file transfers, the training set consists only of measure-
terdam–London, London–Utah–1, and Utah–Cornell). We find ment samples before the level shift and the test set of samples
that there are two dominant reasons for poor SVR prediction after the level shift. All predictions will be inaccurate (assuming
accuracy: background traffic level shifts and changes in back- the level shift changes the throughput by more than 10%, our
ground traffic on small timescales. We find that retraining can threshold) because the prediction function has never encoun-
improve prediction accuracy for level shifts but not for changes tered the new throughput level. Hence, we observe minimum
in network conditions on small timescales. prediction accuracy at the level shift boundary, i.e., 144 trans-
In the analysis that follows, we use a pair of graphs per fers. If the division into training and test set includes a level
experiment to illustrate the details of each experiment. Con- shift, some samples with the new network conditions and resul-
sider Fig. 8(a) and (b) for London–Utah–5. The first graph, the tant new throughput are included in the training set. The predic-
throughput profile, is a time series representation of the actual tion function is now aware of the new network conditions and
throughput observed during the experiment. The second graph, is able to make better predictions in the new conditions. In our
prediction accuracy, is a more detailed version of the bar graphs example, including only one sample from after the level shift
of Fig. 7, incorporating all possible values of . At an x value of in the training set, the 145th sample, is sufficient to allow all
, the first of the 200 samples are used as the training set, and throughputs at the lower levels to be predicted accurately. That
the remaining samples as the test set. The y value is the is, the SVR predictor needs the minimum possible training set
fraction of samples in the test set of whose predicted size (one single sample) for the new network conditions before
throughput is within 10% of the actual throughput. As the value it can generate accurate predictions.
of increases, the training set becomes larger compared to the Fig. 9(a) and (b) compare the behavior of SVR and HB
test set because the total number of samples is fixed at 200. For predictors for a level shift. The training set for SVR consisted
values of close to 200, the test set is very small, and thus the of the first 145 samples, i.e., 144 samples at the first throughput
prediction accuracy values, whether they are high or low, are level and one sample at the second throughput level. The test
not as meaningful. set consisted of the remaining 55 samples. For HB, recall
1) Level Shifts: Level shifts were responsible for poor that there is no separation into training and test sets, and re-
prediction accuracy in four experiments: Utah–Cornell, training occurs after every measurement sample. Comparing
London–Utah, London–Utah–2, and London–Utah–5. We Fig. 9(a) (SVR) and (b) (HB), we see that the SVR-predicted
discuss London–Utah–5 in detail as a representative example. throughput follows the actual throughput very closely, while
Fig. 8(a) and (b) are the throughput profile and prediction ac- the HB-predicted throughput takes some time to catch up with
curacy graphs for London–Utah–5. Fig. 8(a) shows that a level actual throughput after a level shift. If the SVR predictor has

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