Bandwidth-based congestion control for TCP:
measurement noise-aware parameter settings andself-induced oscillation
Mizuho Kodama

Go Hasegawa

Masayuki Murata

Graduate School of Information
Cybermedia Center,
Graduate School of Information
Science and Technology, Osaka University
Osaka University
Science and Technology, Osaka University
1-5 Yamadaoka, Suita,
1-32 Machikaneyama, Toyonaka,
1-5 Yamadaoka, Suita,
Osaka, 565-0871, Japan
Osaka, 560-0043, Japan
Osaka, 565-0871, Japan
Email: m-kodama@ist.osaka-u.ac.jp
Email: hasegawa@cmc.osaka-u.ac.jp
Email: murata@ist.osaka-u.ac.jp

Abstract—With increase in the heterogeneity and complexity of
the Internet, many problems have emerged in the traditional TCP
Reno. Against the problem, we have proposed a new bandwidthbased TCP congestion control mechanism, TCP Symbiosis. Unlike
the recent works on delay-based and hybrid congestion control,
TCP Symbiosis relies on the bandwidth measurement to control the congestion window size. Although we have conﬁrmedthat TCP Symbiosis has the effectiveness in terms of averagethroughput, stability, and scalability to the bandwidth-delay
product, the throughput of TCP Symbiosis highly depends onthe measurement results of available bandwidth. In this paper,
we redesign TCP Symbiosis to deal with the measurement error
and noise of the available bandwidth. First, we propose thedynamic parameter setting algorithm based on the variance ofthe measured available bandwidth. Second, for the purpose ofabsorbing the ill-effect of environmental change, we propose to
add self-induced oscillation to the congestion window size of TCP
connection. We conﬁrm the effectiveness of the proposed methods
through ns-2 simulation experiments.
Index Terms—TCP, congestion control, network measurement,
available bandwidth, measurement error, Lotka-Volterra competition model

I. I NTRODUCTION
Recent research results have revealed that there are many
problems in TCP Reno’s congestion control mechanism [15] with increase in the heterogeneity and complexity of theInternet. The main reasons for those problems are that the
network congestion is indicated only by packet losses andthat TCP Reno uses ﬁxed Additive Increase and Multiplicative
Decrease (AIMD) parameter values to increase and decrease
the congestion window size, whereas those parameters should
be changed according to the network environments.
Many solutions have been proposed for the above problems [5-11]. In general, they are classiﬁed into 3 types in termsof congestion indication: loss-based [5-7], delay-based [8, 9]
and hybrid [10, 11] approaches. Loss-based approaches utilize
packet losses for network congestion indication as TCP Reno,
but employ the modiﬁed functions to regulate the congestion
window size. Delay-based approaches utilize RTT values forthe congestion indication to deal with the incipient network

congestion. Hybrid approaches combine loss-based and delaybased approaches to alleviate their unfairness problems.
However, these studies have not focused on the bandwidth
information. Since a window size indicates the maximum
amount of packets that TCP can transmit for one Round Trip
Time (RTT), an adequate window size for a TCP connection
is equal to the product of the available bandwidth and theround-trip propagation delay of the network path between thesender and receiver hosts. TCP measures RTT by checking thedeparture times of data packets and the arrival times of the corresponding ACK packets. However, TCP Reno and its variants
do not have an effective mechanism to recognize bandwidthrelated information of the network path. We believe, therefore,that if a TCP sender recognizes the bandwidth information of
the network path quickly and accurately, we can create a bettermechanism for congestion control for TCP that can resolve
various problems such as self-induced periodical packet losses.
We have proposed a new congestion control mechanism,
TCP Symbiosis in [12]. TCP Symbiosis employs bandwidthbased congestion control mechanisms. That is, it controls thecongestion window size based on the bandwidth information
obtained from the measurement mechanism. Note that TCP
Symbiosis can be utilized with any bandwidth measurement
mechanisms. One possible solution is to combine TCP Symbiosis with ImTCP [13], which estimates the physical capacity
and available bandwidth of the network path in an inline fashion, by using data and ACK packets transmitted by an active
TCP connection. Since the ImTCP sender obtains bandwidth
information every 3-4 RTTs, it is well able to follow the trafﬁc
ﬂuctuation of the underlying IP network.
In TCP Symbiosis, we employ congestion control mechanisms based on the algorithms borrowed from biophysics.
We utilize from the logistic growth model and the LotkaVolterra competition model [14], both of which are used inbiophysics to describe changes in the population of species.
The biophysics models were chosen based on their intrinsic
stability and robustness, which is achieved even when they behave without any interaction in an autonomous and distributed

fashion. This is the case for the congestion control of TCP:
each TCP connection behaves independently, but still we want
to improve the bandwidth utilization and the throughput of theconnection.
In the previous study, we have investigated the performanceof TCP Symbiosis by ns-2 [15] simulation and implementation
experiments under the public Internet environment [12, 16].
As a result, we have conﬁrmed that TCP Symbiosis has theeffectiveness in terms of average throughput, stability, andscalability to the bandwidth-delay product. However, we havealso revealed that the throughput of TCP Symbiosis highly
depends on the measurement results of available bandwidthby ImTCP. When the measurement result is larger than true
value, overlarge window size causes the buffer overﬂow. On
the other hand, when the measurement result is smaller thantrue value, the window size of TCP Symbiosis is not large
enough to utilize the available bandwidth to the full. That is,
the performance of TCP Symbiosis would degrade when themeasurement results of the bandwidth information have someerrors and noises.
In this paper, therefore, we redesign TCP Symbiosis to deal
with the measurement error and noise of the available bandwidth. First, we give mathematical explanation of the effect oferror and noise in the available bandwidth measurement, andreveal that they affect the parameter settings in Lotka-Volterracompetition model for fair share of the bottleneck bandwidthamong competing TCP connections. We then propose thedynamic parameter setting algorithm based on the variance ofthe measured available bandwidth. Second, we show that TCP
Symbiosis degrades its throughput against the sudden changes
in the network environment (e.g. the amount of the available
bandwidth). Against this problem, we propose to add selfinduced oscillation to the congestion window size of a TCP
connection to absorb the effect of the environmental change.
We conﬁrm the effectiveness of the proposed methods throughns-2 simulation experiments. We believe that the proposed
methods against measurement error and noise can be applied
not only to bandwidth-based approaches like TCP Symbiosis
but also to delay-based and hybrid approaches.
The rest of this paper is organized as follows. In Section II,
we brieﬂy introduce TCP Symbiosis. Then, we introduce two
approaches and demonstrate them by the simulation results in
Sections III and IV. We ﬁnally conclude this paper and offer
future work in Section V.
II. TCP S YMBIOSISTCP Symbiosis utilizes the information of physical capacity
and available bandwidth obtained from an inline measurement
technique [13], and the window updating algorithm is borrowed from biophysics models; the logistic growth and LotkaVolterra competition models. In many biological systems, theactions of the entity (e.g., living organism) are not determinedbased on the results of direct interactions among entities,
but rather on information obtained through the environment,
which is a fundamental necessary condition for the system
to be robust. Furthermore, the species which have the samecharacteristic (e.g., the carrying capacity of the environment,
the intrinsic growth and the ratio of the competition coefﬁcientof other species) can keep fairness. Therefore, we expect TCP
Symbiosis can achieve stability, robustness and fairness.
The logistic equation is a formula that represents theevolution of the population of a single species over time.
Generally, the per capita birth rate of a species increases
as the population of the species becomes larger. However,since there are various restrictions on living environments, theenvironment has a carrying capacity (upper limit of the total
population size), which is usually determined by the available
sustaining resources. The Lotka-Volterra competition model
is a well known model for examining the population growthof two or more species that are engaged in inter-speciﬁccompetition. It makes a change to the logistic growth model,
as it includes the effects of both inter-speciﬁc competition andintra-speciﬁc competition.
The basic two species Lotka-Volterra competition modelwith both species N1 and N2 having logistic growth in the absence of the other is comprised of the following equations [14]:()
dN1 + γ12 N2
N1 = ϵ1 1 −
N1 ,
(1)
dt
K1
(
)
d
N2 + γ21 N1
N2 = ϵ2 1 −
N2
(2)
dt
K2
where Ni , Ki , and ϵi are the population of the species, thecarrying capacity of the environment, and the intrinsic growthrate of the species i, respectively. γij is the ratio of thecompetition coefﬁcient of species i with respect of species
j, and t is time. Furthermore, we can easily extend Equations(1) and (2) for n species as follows:()∑nNi + γ j=1,i̸=j NjdNi = ϵ 1 −
Ni .
(3)
dt
K
To convert the changes in the population of species into
the changes in congestion window sizes, the population of a
species can be viewed as the window size of a TCP connection,
the carrying capacity of the environment as the physicalcapacity of the network path, and inter-speciﬁc competition
among species as bandwidth sharing among competing TCP
connections. We estimate the sum of the window size of allof the other connections by using the physical capacity andavailable bandwidth of a network path. It gives the following
equation:()
dwi + γ(K − Ai )τi
wi = ϵ 1 −
wi
(4)
dt
Kτi
where wi , Ai and τi are the congestion window size, theavailable bandwidth and the minimum value of the RTTs of
TCP connection i, respectively. K is physical capacity. Finally,
we integrate Equation (4) as follows:n“”oAϵt 1−γ 1− iKw (0)e{K − γ(K − Ai )}τi„i n«wi (t) =“”oAiϵt 1−γ 1− K
wi (0) e− 1 + {K − γ(K − Ai )}τi }(5)

III. M EASUREMENT ERROR - AWARE PARAMETER SETTINGS
bwi [Mbps]

Ntcp

5 [msec]

BW [Mbps]
τ [msec]

A. Mathematical explanation and simulation results

bwi [Mbps]
5 [msec]

TCP Traffic
SenderFig. 1.

ReceiverNetwork topology in simulation experiments

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Time [sec]0Fig. 2.

Bandwidth (Mbps)

cwnd [pkts]

Connection 1
Connection 2

Basic behavior of TCP Symbiosis

In [16], we have revealed that the measurement error andnoise of the available bandwidth degrade the throughput of
TCP Symbiosis. In this section, we give the mathematicalexplanation of the effect of the measurement noise and propose the dynamic parameter setting algorithm to alleviate theproblem.
In general, the measured value of the available bandwidth,
which is denoted as A′ (t) where t is time, includes themeasurement error. On the other hand, we assume that thephysical capacity, K, remains constant and can be accurately
measured, since the measurement error of the physical capacity is relatively small compared with that of the available
bandwidth. Equation (4) can be written as follows:()dw(t) + γ(K − A′ (t))τ
w(t) = ϵ 1 −w(t). (6)dt
Kτ
Given that the noise ratio of (K − A′ (t)) is n(t). Then,
K − A′ (t) = (1 + n(t))(K − A(t)),(7)

where A(t) is the true value of the available bandwidth at timet. Hence Equation (6) can be written as follows:()dw(t) + (1 + n(t))γ(K − A(t))τ
w(t) = ϵ 1 −
w(t).
dt
Kτ

In Equation (5), when we set the initial value of the window
size (wi (0)) and the current time to 0 (t = 0), we can directly
obtain window size wi (t) for any time t. We use the above
equation for the control algorithm of the window size of TCP
connections.

Now, Equation (7) can be written as follows:

Since Equation (5) requires the measurements of the physical capacity and available bandwidth of an end-to-end network
path, we use the same algorithm as TCP Reno for window
updating algorithm until the measurement results are obtained
through ImTCP. In case of detecting packet losses by receiving
three duplicated ACKs, a window size is halved in an identical
way to TCP Reno. Similarly, when a timeout occurs, the sender
TCP discards all measurement results, the window size is reset
to one packet, and the slow-start phase begins. With obtained
bandwidth information of the network path, we can calculate
the window size from Equation (5) by regarding the arrival
interval between the latest two ACK packets as t.

By comparing Equations (4) and (9), we can observe that themeasurement noise in the available bandwidth can be viewed
as the noise in the control parameter γ.
As shown in Section II, γ has to satisfy 0 < γ < 1 for stablebehavior in Lotka-Volterra competition model. When γ > 1,
some species (corresponding to the competing TCP connections) become extinct, meaning that some TCP connections
suffer from very low throughput. Therefore, the noise in γ
degrades the performance of TCP Symbiosis because it sometimes makes γ be larger than 1. Setting γ to the safe side (farsmaller than 1) enables to avoid the extinct situation. However,
we can recognize from the Equation (4) that the small valueof γ would increase the queue length at the bottleneck linkin the convergence states. We exhibit the above property bysimulation results. The simulation topology is the same as in
Figure 2. The bottleneck link bandwidth is 50 Mbps and theminimum RTT is 120 msec. We ran 2 TCP Symbiosis ﬂows attime 0. We intentionally add a white noise to the measurement
results of the available bandwidth to investigate the effectof the measurement noise. We start the simulation with thesmall noise, and double the noise size every 100 sec. The
results are summarized in Figure 3 (γ = 0.95) and Figure 4(γ = 0.5). When γ closed to 1 (γ = 0.95), we can see that thecongestion window size of the two connections becomes more

We show the typical behavior of TCP Symbiosis by using
the results of the simple simulation experiment. The simulation
topology is a dumbbell topology as shown in Figure 1. The
bottleneck link bandwidth is 100 Mbps and the minimum
RTT is 120 msec. We run 2 TCP Symbiosis connections andthe second connection joins the network at 50 sec. Figure 2
illustrates the change in the congestion window size of the
two TCP Symbiosis connections. This ﬁgure shows that TCP
Symbiosis quickly converges the window size without packet
losses and the two connections fairly share the bandwidth.
Refer to [12, 16] for more performance evaluation results.

γ ′ (t) = (1 + n(t))γ,()dw(t) + γ ′ (t)(K − A(t))τ
w(t) = ϵ 1 −
w(t).
dt
Kτ

(8)
(9)

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Against the above problem, we propose the dynamic setting
algorithm of γ according to the measurement results of theavailable bandwidth. We determine γ based on the varianceof the measured bandwidth values over time.
From Equation (8), we can dynamically determine γ asfollows:γt,(10)γ(t) =
1 + lCv

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(c) Queue length of bottleneck link

Available Bandwidth
cwnd

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Time [sec]200300Time [sec]

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where γt is the target value for γ, which is the ideal value.
Since n(t) in Equation (8) is the noise ratio of (K − A′ (t)),
we replace n(t) with Cv , which is the coefﬁcient of variationof the measurement values of (K − A′ (t)). In addition, we
introduce the parameter l to control the degree of noise
awareness.
We obtain the deviation of the measurement results of theavailable bandwidth as RTO calculation in TCP [17]:(d) Bottleneck link utilization

400

cwnd [pkts]

50

0

100

Simulation results with γ = 0.95

Fig. 3.

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cwnd

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(a) Available bandwidth andcwnd of connection 1

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(c) Queue length of bottleneck link
Fig. 4.

0

100

200
300
Time [sec]Figure 4(c), the queue length of the bottleneck link remains
larger value as compared with Figure 3(c) with γ=0.95. Thislarge queue length would increase the queueing delay at thebottleneck link buffer and the probability of buffer overﬂow
also increases with sudden change of the background trafﬁc.
From the above results, we conclude that the constant valueof γ can not perform well in noise-prone environments.
B. Dynamic parameter setting(b) Available bandwidth andcwnd of connection 2

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Bandwidth [Mbps]

400(a) Available bandwidth andcwnd of connection 1

Queueing Packet [pkts]

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Available Bandwidth
cwnd

cwnd [pkts]

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Available Bandwidth
cwnd

cwnd [pkts]

Bandwidth [Mbps]

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500

(d) Bottleneck link utilization

Err = x − µ,µ ← µ + gErr,σ ← σ + h(|Err| − σ),where x, µ and σ are the latest measured value, the moving
average value and the average deviation. g and h are theweighting factor. Then we can calculate Cv = σ/µIn Figure 5, we show the simulation results with the same
simulation setting as in Figures 3 and 4, where we set g=0.125,
h=0.25 [17], l=4 and γt =0.95. Figure 5(e) exhibits the changein γ(t) in the proposed mechanism. We can see from Figure 5that the congestion window sizes of the two connections
remain stable regardless of the degree of the noise ratio(Figures 5(a) and 5(b)) and that the utilization of the bottleneck
link keeps 100% (Figure 5(d)). In addition, the queue lengthof the bottleneck link is regulated properly and is smaller thanin Figure 4(c) especially when the degree of the noise ratio issmall.

Simulation results with γ = 0.5

IV. S ELF - INDUCED OSCILLATION FOR ABSORBINGENVIRONMENTAL CHANGE

unstable with larger noise. This is because the larger noise in
the available bandwidth makes γ ′ (t) in Equation (9) to belarger than 1 frequently. This results in unfairness between
the two connections and unstable queue length (Figure 3(c))
and lower utilization of the bottleneck link (Figure 3(d)). On
the other hand, when γ is far from 1 (γ = 0.5), the congestion
window size of the two connections remain stable regardless ofthe noise ratio (Figures 4(a) and 4(b)), and the bottleneck link
utilization remains 100% (Figure 4(d)). However, as shown in

A. Effect of environmental change
TCP Symbiosis highly depends on the measurement resultsof available bandwidth of a network path. In Section III,
we discussed the dynamic parameter setting according to thedegree of the measurement noise, while the true value ofthe available bandwidth remains unchanged. Here, we focus
on the behavior of TCP Symbiosis when the true valueof the available bandwidth suddenly changes due to someenvironmental change.

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Fig. 6. Change in the congestion window size without self-induced oscillation

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10Connection1
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Fig. 7.

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Change in the congestion window size with self-induced oscillation

0.4
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100 150 200 250 300 350 400 450 500
Time [sec](e) Change in the value of γ
Fig. 5.

Simulation results with proposed method

Generally, the end-to-end available bandwidth is measured
by repeating the exchange of probe packets between endhosts.
For example, in ImTCP, the sender TCP transmits TCP data
packets with pre-deﬁned transmission intervals, and calculates
the available bandwidth from arrival intervals of the corresponding ACK packets. ImTCP gives estimation results every
3-4 RTTs. This means that when the true value of the available
bandwidth changes, it takes several RTTs for the sender-side
TCP to recognize the change. Furthermore, TCP symbiosis requires additional RTTs to converge its congestion window size
according to the new value of the available bandwidth. These
delayed behaviors of TCP Symbiosis affect the performanceof the congestion control against the environmental change.
We show an example of the performance degradation bysimulation experiments. Figure 6 shows the change in thecongestion window size when the available bandwidth changes
as 80 Mbps in 0-20 sec, 20 Mbps in 20-40 sec, and 80 Mbps
in 40-60 sec. Note that the buffer size of the bottleneck link
is set to 1000 packets, the background trafﬁc is composed by
an UDP ﬂow, and there is one TCP Symbiosis connection.
The bottleneck link bandwidth is 100 Mbps and the minimum
RTT is 120 msec. When the available bandwidth suddenly
decreases at 20sec, TCP’s retransmission timeout occurs andthe congestion window size is reset to one packet, whichsigniﬁcantly degrades the throughput. This is caused by the
packet losses at the buffer of the bottleneck link. On theother hand, when the available bandwidth suddenly increases
at 40sec, TCP Symbiosis requires some delay to ﬁll-up theincreased bandwidth.
This delayed behavior of TCP Symbiosis is caused since it
relies on the measurement results of the available bandwidth.
When the network environment is stable, this mechanism
gives good results in terms of stable and high throughput.
However, when facing the environmental change, it degrades
the performance due to its delayed behavior.
B. Self-induced oscillation
To solve the above problem, we propose to add self-induced
oscillation to the congestion window size. This means that thecongestion window size remains ﬂuctuating even when theavailable bandwidth remains unchanged. Note that the averagethroughput does not change since the oscillation is equally
injected in both of increase and decrease directions. By thismechanism, we expect that the effect of the environmental
change can be absorbed probabilistically.
In [18], the authors deﬁne the two-species Lotka-Volterra
model in the presence of a noise as follows:dx= µ1 x(α1 − x − β1 (t)y) + xξx (t),dtdy= µ2 y(α2 − y − β2 (t)x) + yξy (t),(11)
dtwhere x and y are the population of the species, α1 and α2 are
the intrinsic growth rate, β1 (t) and β2 (t) are the coefﬁcient ofProbability of Occuring Retransmission Timeout

1.2
1
0.8
0.6
0.4
80Mbps->20Mbps
80Mbps->30Mbps
80Mbps->40Mbps
80Mbps->50Mbps

0.2
0
0

0.05

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0.15
0.2
Noise Rate (m)0.25

Fig. 8.

Probability of retransmission timeout

0.3

the congestion window size. Another one is to add the selfinduced oscillation to the congestion window size to absorb
the effect of the sudden environmental change. By applying
these two methods, we have provided a new advantage to
TCP Symbiosis: robustness to the measurement errors andenvironmental changes, which is important to deploy TCP
Symbiosis to the actual Internet environment.
To the best of our knowledge, TCP Symbiosis is the ﬁrst
proposal of bandwidth-based congestion control mechanisms
for TCP. However, we believe that the proposed methods
in this paper can be applied to any other bandwidth-basedcongestion control mechanisms. In addition, we can also saythat the proposed methods are effective to delay-based andhybrid approaches.
R EFERENCES

intra-speciﬁc competition. ξx (t) and ξy (t) denotes Gaussian
white noise. These equations represent the change in the
population of two species with the presence of the noise andsome other deterministic periodical drive force present in theecosystems such as the temperature. We refer to these equations for adding self-induced oscillation to TCP Symbiosis
mechanisms, by converting the noise in Equation (11) into theself-induced oscillation. We then obtain the following equation
to control the congestion window size as follows:()dw(t) + γ(K − A(t))τ
w(t) = ϵ 1 −w(t) + mw(t)ξ(t),
dt
Kτ
(12)
where ξ(t) denotes Gaussian white noise and m is a parameterto determine the degree of the self-induced oscillation.
Figure 7 shows the simulation results of the proposed
method with m = 0.3 in the same simulation settings as
in Figure 6. We can observe that the congestion window
size continues ﬂuctuating even when the available bandwidth
remains stable. Note that at 20 sec, the proposed method
experiences no packet loss and retransmission timeout. Afterthe sudden increase of the available bandwidth at 40 sec,
the congestion window size increases in shorter time than in
Figure 6.
In Figure 8, we show the probability of occurring retransmission timeout when the available bandwidth suddenly
decreases, as a function of m. Note that m=0 corresponds
to TCP Symbiosis without self-induced oscillation. In thegraph, we show the results of the three cases of the decrease
degree of the available bandwidth. We can observe from thisﬁgure that by adding the oscillation to the congestion window
size, we can avoid the retransmission timeout with signiﬁcantprobability, regardless of the degree of the bandwidth decrease.
V. C ONCLUSION
In this paper, we have proposed two methods to improve the performance of TCP Symbiosis, a bandwidth-basedcongestion control mechanism. The ﬁrst one is a dynamic
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