Approaches to Congestion Control in Packet Networks

Abstract

We discuss congestion control algorithms, using network awareness as a criterion to categorize different approaches. The first category ("the box is black") consists of a group of algorithms that consider the network as black box, assuming no knowledge of its state, other than the binary feedback upon congestion. The second category ("the box is grey") groups approaches that use measurements to estimate available bandwidth, level of contention or even the temporary characteristics of congestion. Due to the possibility of wrong estimations and measurements, the network is considered a grey box. The third category ("the box is green") contains the bimodal congestion control, which calculates explicitly the fair-share, as well as the network-assisted control, where the network communicates its state to the transport layer; the box now is becoming green.

Full text

22 JOURNAL OF INTERNET ENGINEERING, VOL. 1, NO. 1, JANUARY 2007
Approaches to Congestion Control in Packet
Networks
Lefteris Mamatas, Tobias Harks, and Vassilis Tsaoussidis
Abstract— We discuss congestion control algorithms, using
network awareness as a criterion to categorize different ap-
proaches. The first category (”the box is black”) consists of
a group of algorithms that consider the network as a black
box, assuming no knowledge of its state, other than the binary
feedback upon congestion. The second category (”the box is
grey”) groups approaches that use measurements to estimate
available bandwidth, level of contention or even the temporary
characteristics of congestion. Due to the possibility of wrong
estimations and measurements, the network is considered a
grey box. The third category (”the box is green”) contains the
bimodal congestion control, which calculates explicitly the fair-
share, as well as the network-assisted control, where the network
communicates its state to the transport layer; the box now is
becoming green.
We go beyond a description of the different approaches
to discuss the tradeoffs of network parameters, the accuracy
of congestion control models and the impact of network and
application heterogeneity on congestion itself.
I. INTRODUCTION
A network is considered congested when too many packets
try to access the same router’s buffer, resulting in an amount
of packets being dropped. In this state, the load exceeds
the network capacity. During congestion, actions need to be
taken by both the transmission protocols and the network
routers in order to avoid a congestion collapse and furthermore
to ensure network stability, throughput efficiency and fair
resource allocation to network users. Indeed, during a collapse,
only a fraction of the existing bandwidth is utilized by traffic
useful for the receiver.
Congestion collapse is considered, in general, as a catas-
trophic event. However, congestion itself is associated with
different properties, depending on the characteristics of the
underlying networks, the mechanisms of the transmission
protocols, the traffic characteristics of the contenting flows,
the level of flow contention, and the functionality of network
routers. Therefore, the impact of congestion may be temporary
and easily controllable; or it may be catastrophic. Consider,
for example, a high speed network which hosts a number of
competing flows that increases or decreases. The window of
each flow also increases and decreases. However, unlike the
traditional networks, the time it takes for the flows to exploit
the available bandwidth is certainly longer; the amount of
loss upon congestion is certainly higher; and the duration of
congestion itself throughout the overall communication time
may be relatively smaller.
Since the nature of acceptable congestion cannot be pre-
scribed or even accurately defined in general, congestion
control becomes a complex task. Furthermore, complexity
Manuscript received November 13, 2006; revised January 16, 2007.
Lefteris Mamatas and Vassilis Tsaoussidis are with the Department of
Electrical and Computer Engineering, Demokritos University of Thrace,
Xanthi 67100, Greece (E-mails: {emamatas, vtsaousi}@ee.duth.gr).
Tobias Harks is with the Zuse Institute Berlin (ZIB), Berlin 14195, Germany
(E-mail: harks@zib.de).
increases due to the multipurpose-task of congestion con-
trol algorithms. They need to control congestion and avoid
collapses, maximize bandwidth utilization, guarantee network
stability, and ensure fair resource allocation.
Considering the network as a black box that only provides
a binary feedback to network flows upon congestion, shifts
all the burden to end users and calls for solutions that are
more generic and perhaps less responsive. That is, a binary
congestion signal does not reflect the particular network state.
Each sender operates independently and goals to adjust its
rate (or window) in a manner that the total bandwidth of
the network will be expended fairly and effectively. From
its algorithmic perspective the above problem is challenging
because the distributed entities (sources) do not have any
prior or present knowledge of the other entities’ states; nor
do they know the system’s capacity and the number of
competitors. Hence, the goal of fairness and efficiency appears
initially difficult to attain. However, if the system is entitled
to a prescribed behavior and the entities agree on common
transmission tactics, convergence1to fairness becomes feasible
[38]. AIMD, the traditional congestion control algorithm of the
Internet, operates within that scope: it increases additively the
rate of the senders (by a value α) until the system reaches
congestion. Upon congestion, all senders decrease their rate
multiplicatively using a decrease ratio β.
On the other hand, one can measure network conditions,
estimate the available bandwidth or even flow contention,
and obtain some knowledge about the network. However,
measurements are taken at time-instances which may not
necessarily represent current network dynamics, or may not
correspond to the overall conditions; consequently, protocols
may not manage to accurately estimate the load and predict
its duration, resulting in either wrong estimations or wrong re-
covery strategies. Furthermore, some generic questions cannot
really be addressed with certainty: How frequently should we
measure the network? How far can we trust our measurements?
How responsive should the recovery strategy be? How shall
we associate the instantaneous measurements of congestion
with the network load over some sufficiently long but also
sufficiently recent time period? Consequently, the network
may not be a black box but it is certainly not better than
grey, involving occasionally a considerable risk.
One can go beyond the blind algorithms or the high risk of
estimations and actually ask the network2for help. Of course,
precision comes at some cost. Besides the practical difficulty
of layer collaboration and the issue of convincing people to add
functionality (and invest money) to their network, the issue of
recovery strategies remains. That is, even when the network is
really a green box (which practically is very difficult), changes
1Convergence to fairness should be perceived in this paper as the procedure
which enables different flows that consume different amount of resources each,
to balance their resource usage.
2An approach to calculate the fair-share without any network support was
published in [5]

MAMATAS et al.: APPROACHES TO CONGESTION CONTROL IN PACKET NETWORKS 23
may be so rapid and unpredictable that our costly and painful
effort to obtain some information may go wasted.
Beyond our attempt to provide a categorized description
of different congestion control strategies, we also attempt to
introduce a manner to characterize them comparatively. Hence,
we discuss an evaluation framework, which we use to highlight
the advantages of different approaches, exploit the way they
handle the tradeoffs of network parameters, and understand
their impact on the network itself or the network applications.
In order for us to explore the complexity of the issue, we
discuss the nature of congestion itself along with other open
issues. We devote considerable attention to pricing models.
Finally, we discuss the open issues that arise mainly from the
diversity of applications, the heterogeneity of internetworks,
and the interrelation of network parameters.
More specifically, we define congestion-related terms, goals
and metrics in Section II. In Section III we introduce the
control models for congestion. In Section IV we discuss
end-to-end congestion avoidance and control algorithms that
belong in the first category, including the blind AIMD and
AIMD-FC algorithms and other generalizations of AIMD. In
Section V we detail measurement-based congestion avoidance.
In Section VI, we present the explicit calculation of the fair-
share along with network-assisted schemes. Having discussed
the major approaches, we highlight in Section VII some issues
which are yet to be solved. In Section VIII, we conclude our
paper.
II. GOAL S AND ME TRI CS
The congestion window determines the number of packets
that can be outstanding at any time. That is, the number of
packets that can be sent without having received the corre-
sponding ACK packets. It is incorporated into the transport
layer and controls the number of packets put into the network.
The rate describes packets per second or bits per second. The
window or rate can be dynamically adjusted as the total load
on the system changes, however, the former is strictly based
on ACKs.
Acycle is the phase between two seriate feedbacks of
1 (indicating congestion). Hence, a cycle consists of one
decrease step triggered by congestion and a number of additive
increase steps. A step describes a single window adjustment
in response to a single feedback (either 0 or 1).
The system is in an equilibrium state, when resource usage
of all flows in a bottleneck is balanced. AIMD-based conges-
tion control algorithms guarantee convergence to equilibrium
[11]. In congestion avoidance algorithms this is not always
guaranteed.
A non-TCP protocol is called TCP-friendly when it yields
the same throughput as traditional TCP. TCP-friendly proto-
cols are generally used for multimedia/real-time applications.
Although the sources might discover their fair-share early
on, the dynamics of real systems in practice prohibit a straight-
forward adjustment, but instead, they call for continuous
oscillations as a means of discovering the available bandwidth.
Our metrics for the system performance are as follows:
•Efficiency: Efficiency is the average flows throughput per
step (or per RTT), when the system is in equilibrium.
•Fairness: Fairness characterizes the fair distribution of
resources between flows in a shared bottleneck link. A
m
P
i=1
wi
User 1
User 2
·
·
·
User m
Network
y/n
m
P
i=1
wi≥XGoal?
Fig. 1. Synchronous control system model of m users sharing a network.
well-known metric is [11]:
F(x) = P(xi)2
nP(x2
i)(1)
This index is bounded between 0 and 1.
•Convergence Speed: Convergence speed describes time
passed till the equilibrium state.
•Smoothness: Smoothness is reflected by the magnitude
of the oscillations during multiplicative decrease. It de-
pends on the oscillations size.
•Responsiveness: Responsiveness is measured by the
number of steps (or RTTs) to reach an equilibrium (i.e.,
to equate the windows in order to be in a fair state).
The difference between Responsiveness and Convergence
Speed is that the former is related to a single flow and
the latter to the System.
Goals we set in the evaluation process of a congestion
avoidance/control algorithm are:
•To achieve high bandwidth utilization.
•To converge to fairness quickly.
•To minimize the amplitude of oscillations.
•To maintain high responsiveness.
•To coexist fairly and be compatible with traditional
widely-used (AIMD based) protocols.
III. MOD ELS F OR CONGESTION CONTROL
A. Binary Feedback Models
A synchronous-feedback control system model is shown in
Fig. 1. In congestion control literature, the load change is the
response to one occurred event (e.g., a packet drop). The syn-
chronous model is characterized by a synchronous generation
of responses, in congruity with [11]. The system response
is 1 when bandwidth is available and 0 when bandwidth is
exhausted. The instruction to the system entities (sources) is
to increase or decrease their data rate, respectively. Note that
in real networks, the responsive behavior of the system is
not administered by any centralized authority with additional
knowledge of the network dynamics - it is simply a packet
drop due to congestion that naturally happens when bandwidth
is exceeded.
To illustrate the concept, consider a system with m users
(flows) and instantaneous throughput (window size) for the
ith flow, Wi. The system’s goal is to operate at an optimal
point Xgoal. Note that this point is not necessarily bandwidth
B, since throughput might decrease before we reach B. We

24 JOURNAL OF INTERNET ENGINEERING, VOL. 1, NO. 1, JANUARY 2007
assume that responses are synchronous and consequently the
duration of RTTs is common for all flows. Hence, the sources
respond uniformly by decreasing their windows in response to
a 0 signal; they increase their windows by one in response to
a signal of 1 (in case of traditional AIMD).
The limitations of the system are derived from the dynamics
of packet networks:
•Bandwidth B is limited.
•Each flow is not aware of the throughput rates (window
sizes) of other flows.
•Each flow is not aware of the number of competitors in
the channel.
•No flow is aware of the size of bandwidth B.
Although the synchronous model is widely adopted, it is as-
sociated with a number of assumptions and/or simplifications,
which may not really hold in real networks. Gorinsky et al. in
[23] shows that the choice of the model has a direct impact
on the results and extends further the model of Chiu and
Jain to include different RTTs and consequently asynchronous
feedback. MIMD (Multiplicative Increase Multiplicative De-
crease), which is not stable in Chiu-Jain model, does converge
to fair-states under the more realistic assumption of propor-
tional negative feedback.
In [39] Lahanas and Tsaoussidis describe an asynchronous-
feedback model, which corresponds to the diverse round-trip
times (RTTs) of competing flows within the same communi-
cation channel. In this system, authors show that congestion
epoch, which equals3to the RTT of a flow times the number
of additive increases, is a common knowledge among all
competing flows. Based on this relation, they proposed a new
algorithm that increases the consumption rate proportionally
to the RTT of the flow using a mechanism which adjusts the
sizes of the windows of the competing flows at the end of
each congestion epoch. Flows with long RTT’s are relatively
favored (in terms of resources exploitation) because their win-
dow is increased faster than in traditional AIMD scheme. The
system reaches a window-based equilibrium. This mechanism,
named τ-AIMD, uses an extra adjustive component τalong
with the additive increase formula of AIMD.
In paper [22], authors compare AIMD and MAIMD (Mul-
tiplicative additive increase and multiplicative decrease). They
show that the convergence speeds to fair states of AIMD
and MAIMD are close to each other. Furthermore, MAIMD
has some advantages. For example, its speed to use available
network bandwidth can be much faster than AIMD. Authors
have also investigated a more realistic asynchronous system
model, where round-trip-times differ.
B. Price Based Models
We review a price-based congestion control framework that
relies on convex optimization theory. The original model was
initially proposed by Kelly et al. in [35] and has been extended
in the last few years by several research groups (see [20],
[44], [57] and references therein). The crucial assumption of
these works is that every link computes a price, based on load
measurements and communicates it to the senders using that
link. In turn, senders adapt their rates according to the sum of
received link prices along the used path.
3This is not an exact equality because the RTT is variable [28] and increases
with the load of the system. However, the definition gives an intuition of the
relation between congestion epoch and the number of additive increases
1) Fluid Flow Model: A network is modeled by a set L
of links (resources) with finite capacities c= (cl, l ∈L). The
resources are shared by a set Sof sources indexed by s. Each
source suses a set Ls⊂Lof links. Equivalently, each link
is used by a subset Sl⊂Sof senders s. The sets Lsor Sl
define a routing matrix:
Rls =(1if l∈Ls,
0else.(2)
A transmission rate xs(t)at time tin packets per second
is associated with each source s. With each link l, a scalar
positive congestion-measure pl(t), called price, is associated.
In current implementations, the congestion measure or price is
based upon information about either loss (Drop-Tail), queuing
length (RED) [19], or marks (REM) [4], which requires an
ECN [62] bit. Let
yl(t) = X
s∈S
Rlsxs(t−τf
ls)
be the aggregate flowrate of link l(i.e., the sum over all rates
using that link) and let
qs(t) = X
l∈L
Rlspl(t−τb
ls)
be the end-to-end congestion measure of source s, where τf
ls
and τb
ls are the forward- and backward-delay. Note that taking
the sum of congestion measures of a used path is essential to
maintain the interpretation of pl(t)as dual variables. Source
scan observe its own rate xs(t)and the end-to-end conges-
tion measure qs(t)of its path. Link lcan observe its local
congestion measure pl(t)and the aggregate flow rate yl(t).
The source rate is adjusted each time period according to a
function which depends only on xs(t)and qs(t):
xs(t+ 1) = Fs(xs(t), qs(t)).(3)
The link congestion measure pl(t+ 1) is adjusted based on
information about pl(t)and yl(t):
pl(t+ 1) = Gl(yl(t), pl(t)).(4)
Here Fsmodels a TCP-like algorithm and Glan AQM
algorithm.
Assume (3) and (4) have a set of equilibria (x∗, p∗). The
implicit function theorem yields a relation: x∗
s=fs(q∗
s),
where fs(.)is a positive, strictly monotone decreasing function
(increasing congestion qsresults in decreasing rate xs). We
define the utility-function for each source as:
Us(xs) = Zf−1
s(xs)dxs, xs≥0
Again f−1
sis assumed to be monotonically decreasing and
therefore its integral is monotonically increasing and strictly
concave. An increasing utility function implies a greedy
source and concavity implies diminishing return. According
to Shenker [66] this is exactly the appropriate type of utility
for elastic traffic. The problem becomes:
max
xsX
s∈S
Us(xs)s.t. Rx ≤c(5)
An optimal solution exists because the feasible set is compact
and the Uiare strictly concave. As the sources are coupled
through the shared links, a coordination among all sources
using that link is required to solve this problem directly. The
key to solving this problem is to regard xsas primal variables,

MAMATAS et al.: APPROACHES TO CONGESTION CONTROL IN PACKET NETWORKS 25
plas dual variables and to look at the dual problem with
Lagrangian L(x, p):
min
p≥0max
xs≥0L(x, p) = min
p≥0max
xs≥0X
s∈S
Us(xs)−p(Rx −c)
= min
p≥0max
xs≥0X
s∈S
(Us(xs)−xsX
l∈L(s)
pl) + X
l∈L
plcl
= min
p≥0max
xs≥0X
s∈S
(Us(xs)−xsqs) + X
l∈L
plcl(6)
With a given vector p∗, the first term of (6) can be divided
into Sseparable subproblems
max
xs≥0Us(xs)−xsqs(7)
which can be solved separately by the sources knowing the
congestion measure qsof the used path. The source law for a
sender ssolving (7) becomes:
x∗
s=d
dxs
U−1
s(qs).(8)
The term xsqsin (7) can be interpreted as the cost or price the
network imposes when sending at rate xs. The role of prices
pl(t)that are Lagrange-Multipliers is to coordinate the actions
of individual sources in order to align individual optimality
with social optimality (i.e., to solve (5)). The simplest link
algorithm to yield equilibrium prices is the gradient-projection
algorithm applied to the dual:
pl(t+ 1) = (pl(t) + γ(yl(t)−cl)if pl(t)>0
pl(t) + γ[yl(t)−cl]+if pl(t) = 0 ,
where [z] = max{0, z}. This algorithm can be implemented
in a distributed environment, since the information needed at
the links is the link bandwidth cland the aggregate flow rate
yl(t)which are available. In equilibrium, the prices satisfy
the complementary slackness condition (i.e., pl(t)are zero
for non-saturated links and non-zero for bottleneck links). In
compact form the gradient projection algorithm representing
a source law and an AQM algorithm can be written as:
xs=Fs(xs(t), qs(t)) = d
dxs
U−1
s(qs), s ∈S(9)
˙pl=Gl(yl(t), pl(t)) = γ(yl(t)−cl), l ∈L(10)
In [45] it is shown that this algorithm converges to the unique
solution of (5) in an asynchronous environment, where delays
can be substantially different and sources and links can update
and communicate at different times with different frequencies.
In the context of TCP/AQM, the source algorithm Fsis
carried out by TCP-Tahoe [28], TCP-Reno [29] and TCP-
Vegas [8], and the link algorithm Glis carried out by Drop-
Tail, RED [19] or REM [4]. Various TCP/AQM protocols can
be interpreted as different distributed primal-dual algorithms
to solve the problem (5) in real time with different utility
functions. Thus the optimization framework allows us to
predict the equilibrium rates (windows) and the marking- or
dropping probabilities of these congestion control schemes in
a large network and to assess the fairness in a homogeneous
network where the same scheme is adopted by all sources, as
well as the friendliness of different interacting schemes in a
heterogeneous network.
2) Fairness Issues, Real-time Traffic, and Nonconvex Util-
ities: The fundamental assumption in the previous section
concerned the choice of utility functions describing elastic
traffic. This choice affects the resulting resource allocation in
terms of fairness. Following [53], we can associate a class
of concave utility functions with corresponding bandwidth
fairness-criteria as follows:
Us(xs, ηs) = (−wsx1−ηs
1−ηs, ηs>0, ηs6= 1,
wslog(xs), ηs= 1.(11)
Then, in the case ηs= 1, we have weighted proportional
fairness [35]. In the case ηs= 2, we have minimum potential
delay fairness, and for ηs→ ∞, we have max-min fairness.
If real-time traffic is considered, the concavity assumption
for utility functions does not hold. For instance, the utility
function for a VoIP application encoded into a set of layers
would be a step function, where the steps correspond to the
respective layers.
We can classify the work in this area into two categories.
The first category covers approaches that aim at maximizing
aggregate (nonconvex) utility subject to capacity constraints:
due to the possible duality gap of this type of problem,
stable decentralized algorithms are only in special cases to
be derived. Lee, Mazumdar and Shroff show in [41] that
the canonical distributed algorithms (9) and (10) may fail
to converge to a feasible rate allocation and may lead to
instability and congestion. To overcome these problems they
propose a ’self regulating’ heuristic for the special type of
sigmoidal utilities in combination with a subgradient method
to generate prices. Chiang, Zhang and Hande [10] examine
the conditions under which the canonical algorithms converge
to the globally optimal rate despite the nonconcavity of utility
functions.
In the second category belong approaches that are concerned
with a different fairness definition rather than maximizing
aggregate utility: an equilibrium point should result in roughly
equal utility values for different applications [64], [25], [42],
[9]. In [64], only mild assumptions on the feasible utility func-
tions are required (non-decreasing, not necessarily continuous,
min. bandwidth exists for a given utility value). The drawbacks
of this approach are that the links have to maintain per-flow
states in order to allocate bandwidth utility fair, and that there
are no stability results given in the presence of communication
delay. Cao and Zegura present in [9] a link algorithm that
achieves a utility max-min fair bandwidth allocation, where
for each link the utility functions of all flows sharing that
link is maintained. Hyang and Song [40] present a distributed
algorithm without per-flow states that converges to a utility
max-min fair operating point. However, they prove stability
under bounded communication delay only in the single link
case.
More recently, Harks et al. [25], [26] present a distributed
utility fair congestion control framework. By transforming
possibly non-concave bandwidth utility functions Us(·)into
strictly concave functions Fs(·), they rely on the concave op-
timization framework described before. The previous fairness
characterizations are extended by including a second order
utility function:
Fs(xs):=Zf−1
s(Us(xs))dxs,(12)
where fs(·)is a strictly decreasing transformation function.
If all users s∈Suse the same transformation function fs=

26 JOURNAL OF INTERNET ENGINEERING, VOL. 1, NO. 1, JANUARY 2007
Fig. 2. Vectorial representation of two-flow convergence to fairness. Figure
is based on [11].
f, ∀s∈S,utility proportional fairness as defined in [25] is
achieved. If a certain class of transformation functions is used
fs(qs, κ) = q−1
κ
s,s∈Swhich leads to
Fs(xs, κ) = Z(Us(xs)−κdxs,(13)
we get in the limiting case κ→ ∞ utility max-min fairness.
IV. THE BOX IS BLAC K: BL IND CONGESTION CONTRO L
The Additive Increase Multiplicative Decrease (AIMD)
algorithm is used to implement TCP window adjustments;
based on the analysis of Chiu and Jain the algorithm achieves
stability and converges to fairness in situations where the
demand (of competing flows) exceeds the channel’s bandwidth
[11].
The congestion control in the traditional TCP, is based on
the basic idea of AIMD. In TCP-Tahoe [28], TCP-NewReno
[15] and TCP-Sack [50], the additive increase phase is adopted
exactly as in AIMD, when the protocols are in the Congestion
Avoidance phase. In case of a packet drop, instead of the
multiplicative decrease a more conservative tactic is used in
TCP-Tahoe. The congestion window resets and the protocol
enters again the slow-start phase. On the other hand, in TCP-
NewReno and TCP-Sack, when the sender receives 3 DACKs,
a multiplicative decrease is used in both window and slow-start
threshold. In such case, the protocols remain at the Congestion
Avoidance phase. When the retransmission timeout expires,
they enter the slow-start phase as in TCP-Tahoe.
A. AIMD-FC
A recent improvement of AIMD, Additive Increase Mul-
tiplicative Decrease with Fast Convergence (AIMD-FC) was
proposed in [37]. AIMD-FC impacts positively both efficiency
and fairness. It is not based on a new algorithm, but rather on
an optimization of AIMD during the convergence procedure
that enables the algorithm to converge faster and achieve
higher efficiency. AIMD-FC increases the bandwidth utiliza-
tion of AIMD from 3/4 to 5/6.
Authors highlighted the following four observations which
were the basis of that work:
1) During the additive increase phase, equal amount of
system resources is being allocated to the flows. This
amount (’k’) is a public or common knowledge (i.e., it
is known to every flow in the system).
2) AIMD affects both the initial windows and the amount
of system resources (k), that has been fairly allocated,
during the multiplicative decrease phase. Note that the
manipulation of the initial (and unknown) windows is
the real target for achieving fairness.
3) The distance between the Bandwidth Limit Line and
the Efficiency Line when the system is in equilibrium
depends only on the multiplicative decrease factor [11]
(see Figure 2).
4) Two algorithms may need the same number of cycles
to converge to fairness: for example, two variants of
AIMD with different additive increase rate but the
same multiplicative decrease ratio. The number of steps
determines the relative efficiency of the algorithm to
converge to fairness.
Practically, fairness is achieved in AIMD-FC by releasing
(through multiplicative adjustments of the windows) the (un-
known to other flows) initial resources of the flows, because
during the additive increase phase the flows increase their
resource consumption uniformly. So, it is becoming apparent
that the distinctive difference of AIMD and AIMD-FC is
centered on the portion of the congestion window that is
affected by multiplicative decrease (this portion is called
decrease window).
Furthermore, there are some open issues related with
AIMD-FC:
•The efficiency boundaries of AIMD have not yet been
exploited.
•Further modifications can be made in order for AIMD-FC
to favor responsiveness or smoothness.
The same authors improved in [37] furthermore the effi-
ciency, smoothness and fairness of AIMD-FC and proposed a
new algorithm named AIMD-FC+.
B. Binomial Mechanisms
Bansal and Balakrishnan presented in [7] a new class
of nonlinear congestion control algorithms named Binomial
Congestion Control Algorithms. These algorithms are called
binomial because their control is based on the involvement of
two additional algebraic terms with different exponents.
While an AIMD control algorithm may be expressed as:
Increase :Wt+R←Wt+a;a > 0(14)
Decrease :Wt+δt ←(1 −β)Wt; 0 < β < 1(15)
authors generalized the AIMD rules in the following way:
Increase :Wt+R←Wt+a
Wk
t
;a > 0(16)
Decrease :Wt+δt ←Wt−βW l
t; 0 < β < 1(17)
where ”Increase” refers to the increase in window as a result
of the receipt of one window of ACKs within a single RTT,
”Decrease” refers to the decrease in window upon detection
of congestion by the sender, Wtthe window size at time t, R
the flow’s RTT, and a, b, k, l are constants.
For example, for k=0, l=1 we get AIMD. Authors proposed,
in the (k, l) space, two AIMD variations (which are also TCP-
compatible). IIAD (with k=1 and l=0) and SQRT (with k=1/2
and l=1/2) algorithms. The first is called Inverse Increase
Additive Decrease (IIAD) because its increase rule is in inverse
proportion to the current window. The second is called SQRT
because both its increase is inversely proportional and decrease
proportional to the square-root of the current window. Note
that a binomial algorithm is TCP-compatible if and only if
k+l= 1 and l61for suitable αand β.

MAMATAS et al.: APPROACHES TO CONGESTION CONTROL IN PACKET NETWORKS 27
C. SIMD
Another TCP-friendly nonlinear congestion control algo-
rithm is SIMD [32]. SIMD is the first congestion control
algorithm which utilizes history information.
The control rules of SIMD is defined as:
Increase :Wt+R←Wt+apWt−W0;a > 0(18)
Decrease :Wt+δt ←Wt−βWt; 0 < β < 1(19)
where w0is the window size after the last decrease and Wt
is the continuous approximation of the window size at time t
(in RTTs) that elapsed since the window started to increase.
Authors show that:
w(t) = w0+a2t2
4(20)
SIMD uses the same multiplicative decrease but a different
increase rule from those used by AIMD and binomial algo-
rithms; this rule is based on history information.
If two SIMD flows are competing, the flow with the
smaller window size is more aggressive due to the nonlinear
nature of SIMD. This results in better convergence behavior.
Authors show also that SIMD converges faster than memory-
less AIMD and binomial controls. Authors evaluated in [32]
the TCP-friendliness of SIMD and showed that SIMD can
maintain smoothness in steady state.
D. HIGHSPEED-TCP
It is well known that standard TCP does not perform well
in high-speed and long-distance networks. Since standard TCP
increases its congestion window by one at every round trip
time (RTT) and reduces the window by half upon each loss
event, it takes more than 83,333 RTT’s to fully utilize a
10Gbps link with 1500-byte packet size. This limitation has
triggered the proposal of HighSpeed-TCP (HS-TCP) [17]. The
idea of HS-TCP is to modify the TCP response function in en-
vironments with large Delay-Bandwidth product and increase
the congestion window more aggressively upon receiving an
ACK and decreases the window more gently upon a loss event.
In [54], [76], however, is shown that HS-TCP does not cope
well with fast convergence and RTT fairness. First, when a new
HS-TCP flow starts provided there are already large HS-TCP
flows active it takes a long time for the new flow to achieve its
fair-share. Second, flows with different RTT’s consume unfair
bandwidth shares.
E. BIC-TCP
To remedy the round trip time unfairness of HS-TCP
the Binary Increase Congestion Control Protocol (BIC-TCP)
has been proposed in [76]. The BIC-TCP protocol can be
characterized by three major concepts: multiplicative decrease,
binary search increase and additive increase. Upon a packet
loss event, BIC-TCP reduces its window by a multiplicative
factor. The window size before the reduction is set to the
maximum value and the window size just after the reduction is
set to the minimum value. Then, BIC-TCP performs a binary
search using these two values by jumping to the midpoint.
However, if jumping to the midpoint is too much increase
within one RTT, BIC-TCP increments linearly the current
window size. If BIC-TCP does not experience packet losses
within the updated window size, that window size becomes the
new minimum. Otherwise, that window size becomes the new
maximum. This process continues until the window increment
is less than some small constant and the window is set to the
current maximum.
F. Other Generalizations of AIMD
General AIMD Congestion Control (GAIMD) generalizes
AIMD congestion control by parameterizing the additive in-
crease value αand multiplicative decrease ratio β. Authors of
[77], [13] extended the throughput equation for standard TCP,
proposed in [56], to include parameters α,β:
Tα,β (p, RT T , T0, b) = 1
RT T r2b(1−β)
α(1+β)p+T0min(1,3r(1−β2)b
2αp)p(1 + 32p2)
(21)
where p is the loss rate; T0is the retransmission timeout
value; b is the number of packets acknowledged by each ACK.
The overall throughput of TCP-Friendly (α,β) protocols is
bounded by the average throughput of standard TCP (α= 1,
β= 0.5), which means that equation (23), which is derived
from (22) (see [77], [13]) could provide a rough guide to
achieve friendliness.
Ta,b(p, RT T , T0, b) = T1,0.5(p, R T T, T0, b)(22)
Authors of [77] derive from (1) and (2) a simple relationship
for αand β:
α=4(1 −β2)
3(23)
Based on experiments, they proposed a β= 7/8as the
appropriate value for the reduced the window (i.e., less rapidly
than TCP does). For β= 7/8, (3) gives an increase value
α= 0.31.
V. TH E BOX IS GREY: MEASUREMENT-BAS ED
CONGESTION CON TROL
Standard TCP relies on packet losses as an implicit con-
gestion signal from overloaded links. However, packet loss is
not a sufficient indication of congestion, in its own right, for
a number of reasons:
1) Packet loss can be caused by random bit corruption when
bandwidth is still available.
2) Acknowledgement-based loss detection at the sender
side can be affected by the cross-traffic on the reverse
path.
3) Packet loss, as a binary feedback, cannot indicate the
level of contention before the occurrence of congestion.
Therefore, an efficient window adjustment tactic should re-
flect various network conditions, which cannot all be captured
simply by packet drops. Several measurement-based transport
protocols gather information on current network conditions.
A. TCP-VEGAS
A well-designed, measurement-based congestion avoidance
mechanism is TCP-Vegas [8]. TCP-Vegas defines BaseRTT
to be the minimum of all measured RTTs, and ExpectedRate
to be the ratio of the congestion window to BaseRTT. The
sender measures the ActualRate based on the sample RTTs.
If the difference between the ExpectedRate and ActualRate is
below a lower bound, the congestion window increases linearly
during the next RTT; if the difference exceeds an upper bound,

28 JOURNAL OF INTERNET ENGINEERING, VOL. 1, NO. 1, JANUARY 2007
TCP-Vegas decreases the congestion window linearly during
the next RTT. According to [8], TCP-Vegas achieves better
transmission rates than TCP-Reno and TCP-Tahoe. However,
[27] shows that TCP-Vegas can not guarantee fairness or
distinguish the nature of errors. From the research perspective
of the present work it is important to consider that the authors
of TCP-Vegas demonstrated effectively that measurement-
based window adjustment is a viable mechanism.
B. FAST-TCP
Fast-TCP is a congestion control protocol that reacts to
queuing delay and packet loss [73]. It exhibits the same
equilibrium properties as TCP-Vegas but its convergence and
stability properties are improved. In Fast-TCP, the congestion
window wi(t)for source ievolves according to:
wi(t+ 1) = γdiwi(t)
di+qi(t)+αi+1−γwi(t),(24)
where qi(t)is the measured queuing delay, diis the round-trip
propagation delay of source i,αiis a parameter estimating
the buffered packets along the used path, and γ∈(0,1) is
a positive protocol parameter. The equilibrium properties of
the above control system, such as throughput, fairness, and
delay, can be characterized by the solution of an associated
optimization problem (c.f., [35], [46], [44] and references
therein. Let l∈Ldenote the links of a given network
with corresponding capacity cl. If the total round-trip time
is denoted by Ti(t) = di+qi(t)than the sending rates are
given by xi=wi(t)
Ti(t). Let the individual queuing delay of link
lbe pl(t). The equilibrium values (w∗, p∗)are given by the
solution of:
max
x≥0X
i
αilog(xi),s.t.: Rx ≤c,
where Ris the routing matrix and x, c are in vector notation.
Using the dual of the above problem and interpreting the
individual queuing delays pl(t)as Langrange multipliers for
the corresponding capacity constraint the solution to the above
problem is given by:
xi=αi
qi
.(25)
Relation (25) implies that in equilibrium αipackets are
buffered along source i’s path. Furthermore, (24) has the
appealing property that it is provably locally stable in the
absence of delay. For a delayed version of (24) only limited
results are known: for the single link and bounded delay, (24)
is locally stable.
C. TCP-REAL
TCP-Real [78], [72] employs a receiver-oriented and
measurement-based congestion control mechanism that sig-
nificantly improves TCP performance over heterogeneous
(wired/wireless) networks and over asymmetric paths. TCP-
Real goes beyond the limitation of ack-based binary feedback.
It estimates the level of contention and distinguishes the reason
of packet losses. TCP-Real relies on:
•Receiver-oriented congestion detection that abrogates the
impact of false assessments at the sender due to lost or
delayed acknowledgments on a lossy reverse path. The
receiver measures the network condition and attaches the
results to the ACKs sent back to the sender.
•Measurements based on wave patterns that distinguish the
nature of a packet loss (due to congestion or transient
wireless errors
A wave [71] consists of a number of fixed-sized data seg-
ments sent back-to-back, matching the inherent characteristic
of TCP to send packets back-to-back. The receiver computes
the data-receiving rate of a wave, which reflects the level of
contention at the bottleneck link. If a packet drop is due to a
wireless error, the data-receiving rate shall not be affected by
the gap of missing packets, since the wave size is published
to the receiver. The congestion window is multiplicatively
reduced only when a drop is associated with congestion.
D. TCP-WESTWOOD
In TCP-Westwood [48] (TCPW), the sender continuously
measures the rate of the connection by monitoring the rate
of returning ACKs. Upon three duplicate acknowledgments or
timeout, the slow start threshold and the congestion window
are set in consistence with the effective bandwidth used at the
time packet loss is experienced. No specific mechanism exists
to support error classification and the corresponding recovery
tactics for wired/wireless networks, albeit the proposed mech-
anism appears to be effective over symmetric wireless links
due to its efficient congestion control. An optimized version
of TCP-Westwood is TCP-Westwood+ [49].
E. TFRC
TFRC [24] is a TCP-Friendly, rate-based congestion control
protocol, which intends to compete fairly for bandwidth with
TCP flows. The sending data rate is adjusted in response to
the level of congestion as it is indicated by the loss rate. This
adjustment is ”gentle”; that is, its instantaneous throughput
has, in general, a much lower variation over time, compared
with TCP. The smoothing of the transmission gaps makes
TFRC suitable indeed for streaming media, telephony or
other applications requiring a smooth sending rate. However,
smoothness has its own price: the protocol becomes less
responsive to bandwidth availability [79].
Furthermore, TFRC is designed for applications that use
fixed sized packets. In case of applications with a variance in
their packet size (e.g., some audio applications), TRFC’s con-
gestion control mechanism cannot be used. A TFRC variant
named TFRC-SP (TFRC Small-Packet) can be used instead
(see [16]).
TFRC introduces the ”loss event” instead of the traditional
packet loss. A loss event is defined as one or more lost or
marked packets from a window of data (a marked packet
refers to a congestion indication from Explicit Congestion
Notification). TFRC uses a receiver-based mechanism for the
calculation of loss event rate. Such a mechanism is suitable
for multicast congestion control and also fits in the case of a
large server handling many concurrent requests from clients
with more memory and the CPU cycles available. The receiver
measures the loss event rate and then passes this information
to the sender. The sender calculates its sending rate using
a throughput equation that incorporates the loss event rate,
round-trip time and packet size.
In summary, TFRC’s congestion control mechanism works
as follows:
•The receiver measures the loss event rate (based on lost
or marked packets from ECN [62], in a single window)
and then feeds this information back, to the sender.

MAMATAS et al.: APPROACHES TO CONGESTION CONTROL IN PACKET NETWORKS 29
•The sender measures the round-trip time (RTT).
•The loss event rate, round-trip time and packet size are
used in the throughput calculation function (26). The
sender adjusts its sending data rate to match the calculated
rate.
X=s
R·q2·β·p
3+ (t RT O ·(3 ·q3·β·p
8)·p·(1 + 32 ·p2))
(26)
Where:
X is the transmit rate in bytes/second.
s is the packet size in bytes.
R is the round trip time in seconds.
p is the loss event rate, between 0 and 1.0, of the number of
loss events as a fraction of the number of packets transmitted.
t RTO is the TCP retransmission timeout value in seconds.
βis the number of packets acknowledged by a single TCP
acknowledgement.
It may be useful to associate each information fed back
to the sender with a statistical figure, which indicates the
possibility of a potential wrong decision. Then, based on this
data either an aggressive or a conservative strategy can be
chosen.
F. TCP-JERSEY
Authors of [75] proposed a new TCP scheme, called
TCP-Jersey. They focused on the capability of the transport
mechanism to distinguish the wireless from congestion packet
losses. TCP-Jersey introduces an Available Bandwidth Esti-
mation (ABE) algorithm and the Congestion Warning (CW)
router configuration. ABE continuously estimates the available
bandwidth and directs the sender to adjust the transmission
rate according to the estimation. The CW-configured-routers
mark packets when there is a sign of an incipient congestion
to notify the sender, who in turn, classifies errors accordingly.
The performance of the above transport mechanisms is
tightly coupled with the robustness of their estimators. Several
investigations (such as [30]) have been carried out regarding
the accuracy of the proposed estimators.
VI. THE BOX I S GREE N
A. Bimodal Mechanism
Bimodal Congestion Avoidance and Control mechanism [5]
measures the fair-share of the total bandwidth that should
be allocated for each flow, at any point, during the system’s
execution. If the fair-share were known, then the sources could
avoid congestion by adjusting immediately after the fair-share
was discovered, to a new state where the bandwidth allocation
of each flow is exactly its fair-share. However, bandwidth
availability is not only a matter of channel capacity but is
also dependent upon the number of participating flows, and
the transmitting behavior of the sources. So, fair-share can be
measured only in an equilibrium state.
Authors proposed in [5] a bimodal mechanism, which is
based on the idea that upwards and downwards adjustments
need to operate in association with the system state. Action
is determined based on whether the system is in equilibrium
(fair-share is known) or not (fair-share is unknown).
When the fair-share is unknown, the algorithm behaves like
AIMD, until two congestion cycles have passed, which is
sufficient to recalculate the fair-share. The algorithm then sets
the bandwidth allocation for flow f to (1 −)4times the
calculated fair-share, and shifts to known fair-share mode. So,
bimodal congestion control algorithm explicitly calculates the
fair-share and converges in two congestion cycles to the fair-
share. In this mode, the algorithm continues to use additive
increase and multiplicative decrease, but the multiplicative
decrease factor is αinstead of β.
This algorithm is distinguished from the class of TCP-
friendly algorithms. TCP-friendly algorithms favor smoothness
at the cost of fairness. This algorithm calculates fair-share
explicitly, and so fairness is not compromised in this approach.
Furthermore, since this algorithm restricts its flows to use
only their fair-share, it can be used in conjunction with
any other transport protocols (e.g., standard AIMD) without
monopolizing for itself most of the available bandwidth. This
is in contrast with the TCP-friendly protocols, which attempt
to grab all available bandwidth. Of course, this algorithm
will not work well in conjunction with other protocols that
aggressively (and unfairly) grab a disproportionate share of
the bandwidth for their flows.
There are also some open issues related to the bimodal
mechanism:
•The more the gain we have in goodput (i.e., by using a
smaller ) the less the free space left for incoming flows
when contention increases.
•Investigating the optimal value of in conjunction with
the dynamics of specific environments is a subject of
future work.
•The modification of the algorithm for the asynchronous
scenario by integrating the RTT into the fair-share calcu-
lation. For example, bandwidth allocation of a flow can
be increased when the RTT of its packets decreases and
be decreased when the RTT increases.
•The integration of such ideas with a receiver-oriented
feedback approach (like TCP-Real [78]).
B. Network-Assisted Congestion Control
Red Gateways [19] drop packets when congestion is about
to happen. RED randomly drops packets, triggering multi-
plicative decrease in some flows when the length of the
queue exceeds a predetermined threshold. RED can function
without requiring any change to the current transport level
infrastructure.
Ramakrishnan and Floyd in [62] proposed an Explicit
Congestion Notification (ECN) to be added to the IP protocol
in order to trigger TCP congestion control. Unlike RED, ECN
enables routers to probabilistically mark a bit in the IP header,
rather than drop the packet, to inform end-hosts of pending
congestion when the length of the queue exceeds a threshold.
End-hosts multiplicatively reduce their congestion windows
upon receiving packets with ECN bit set, before the router
buffer overflows and packet drops are inevitable. A duality
is served with ECN: TCP performance can be enhanced by
means of avoiding losses of data windows due to limited buffer
space at the bottleneck router, and congestion collapse can be
avoided.
Recent work [52] presents a critical discussion of the per-
formance expectations with RED. An interesting observation
about RED and ECN is that they could, somehow, confine
future evolution. Imagine a more sophisticated TCP which
4where is a small tuneable parameter

30 JOURNAL OF INTERNET ENGINEERING, VOL. 1, NO. 1, JANUARY 2007
distinguishes between congestion and wireless losses. Since
RED drops packets in proportion to sending rates, it is unclear
how fair RED would be to the sophisticated TCP which just
happens not to unnecessarily back off in case of transient
wireless losses [36].
In [18] Floyd and Fall introduced mechanisms based on the
identification of high-bandwidth flows from the drop-history of
RED. The RED-PD algorithm (RED with Preferential Drop-
ping) [47] uses per-flow preferential dropping mechanisms.
Two other approaches that use per-flow preferential dropping
with FIFO scheduling are Core-Stateless Fair queuing (CSFQ)
[68] and Flow Random Early Detection (FRED) [43]. CSFQ
marks packets with an estimate of their current sending rate.
The router uses this information in conjunction with the flow’s
fair-share estimation in order to decide whether a packets
needs to be dropped. FRED does maintain a state although
only for the flows which have packets in the queue. The flows
with many buffered packets are having an increased dropping
probability.
The CHOKe mechanism [59] matches every incoming
packet against a random packet in the queue. If they belong
to the same flow, both packets are dropped. Otherwise, the
incoming packet is admitted with a certain probability. How-
ever, a high-bandwidth flow may have only a few packets in
the queue. Authors in [1] show that a minor modification to
the CHOKe active queue management policy ensures efficient
operation as well as reasonable fairness at Nash equilibrium.
Authors of [58] continued the CSFQ and CHOKe [59]
approaches. Their proposed mechanism keeps a sample of
arriving traffic. A flow with several packets in the sample, has
an increased dropping probability. The Stochastic Fair Blue
(SFB) [12] uses multiple levels of hashing in order to identify
high-bandwidth flows. As the authors state, their mechanism
works well only with a few high-bandwidth flows. Anjum
and Tassiulas proposed in [3] a mechanism that drops packets
based on the buffer occupancy of the flow while ERUF [63]
uses source quench to have undeliverable packets dropped at
the edge routers. On the other hand, SRED [55] caches the
recent flows in order to determine the high-bandwidth flows.
A network-assisted proposal relevant to Bimodal Conges-
tion Avoidance and Control mechanism [5] is Multimodal
Control Protocol (MCP) [60]. MCP design relies on three
key principles: multiple modes of operation, sufficiently high
fairness after a relatively short sequence of transmission ad-
justments, and constant-rate transmission in the steady state.
One of MCP contributions is its mechanism for limited explicit
communication between hosts and routers. The mechanism
enables the sender of a flow to urge all flows sharing its bot-
tleneck links to operate in a fairing mode for seven increase-
decrease cycles of AIMD(80 kbps; 0.5) control.
C. VCP, XCP and JETMAX
The variable-structure congestion control protocol (VCP)
requires explicit feedback from the network about the state of
congestion (see [74] for a detailed description). It relies on the
two ECN bits that are available in current implementations of
the IP header. Each router in the network calculates a load
factor that is used to classify the level of congestion into
three regions: low-load, high-load, and overload. Routers are
responsible to encode the current state into the ECN bits. Upon
receiving the congestion information that corresponds to one of
the three regions, the sender performs multiplicative increase
(low load), additive increase (high load), and multiplicative
decrease (overload), respectively.
The explicit congestion control protocol (XCP) can be
seen as a generalization of the ECN proposal [34]. Instead
of one or two bits congestion notification, an XCP capable
router communicates the explicit bandwidth share back to
the senders. This is done via two control functionalities:
fairness and efficiency controls. Efficiency control aims at
maximizing link utilization while fairness control aims at
enforcing fair bandwidth sharing between competing flows.
The main drawback of XCP, however, is its unstable behavior
in a multilink environment, where senders receive feedback on
different time scales, that is, the feedback is heterogeneously
delayed. In this case, the bottleneck may oscillatory switch
between routers and the senders are not able to timely detect
the most congested resource.
To address this issue, JetMax has been proposed in [80].
This protocol relies on single-router feedback (as opposite
to additive feedback approaches) and achieves max-min fair
rate allocation in its steady state. The feedback is provided in
form of changes to the packet loss. Each sender is assigned a
bottleneck router which is the router with the highest packet
loss value pon the path. pis periodically computed by each
router lapplying the equation:
pl(n) = yl(n)−γlCl
yl(n)(27)
where yl(n)is the total load observed by router lat the time
instance n,γl∈(0,1] is the desired link utilization and Cl
the link capacity.
Within each router, the passing flows are divided into
two categories (the bottlenecked and any additional flow).
The authors call the first category of flows responsive and
the second category unresponsive. Each router lperiodically
computes the fair rate of the responsive flows gl(n)applying
the equation:
gl(n) = γlCl−ul(n)
Nl(n)(28)
where ul(n)is the aggregate rate of the unresponsive flows and
Nl(n)is the estimated number of responsive flows and inserts
this value into the header of the data packets of the responsive
flows. Each sender rupdates its sending rate according to the
equation:
xr(n) = xr(n−Dr)−τ[xr(n−Dr)−gl(n−D←
r)] (29)
where Dr=D→
r+D←
ris the RTT D→
rthe forward delay
between the sender and the bottleneck router and D←
rthe
backward delay between the bottleneck router and the sender.
τ∈(0,1] is the gain parameter.
As stated in [80] the features of JetMax are:
1) Monotonic convergence to stationarity.
2) Capacity-independent convergence time (same number
of RTT steps).
3) Zero packet loss both in the transient and steady-state.
4) Tuneable link utilization.
5) RTT-independent max-min fairness.
6) Global multi-link stability under consistent bottleneck
assignment for all types of delay.
Furthermore, JetMax is supposed to overcome the problem of
bottleneck oscillations, which leads to instability of XCP in
networks with heterogeneous delays. This is achieved through
monotonic and continuous behaviour of the feedback function

MAMATAS et al.: APPROACHES TO CONGESTION CONTROL IN PACKET NETWORKS 31
pfor bottleneck switches, which leads to consistent choice of
the bottleneck router.
VII. DISCUSSION
The question of efficiency is associated with the utilized
bandwidth; at a first glance, the system dynamics suggest that
the higher the oscillation the less the efficiency. It appears5
that the higher the oscillation, the faster we approach fairness.
In [14], [77], [7], [32], authors attempt to take advantage
of this property. More precisely, it has been observed that
streaming applications could benefit from modest oscillations
since these reflect the smoothness of adjusting the transmission
rate backwards. Such protocols are characterized as TCP-
Friendly because they consume the same amount of bandwidth
as TCP(1, 0.5) does [56]. Theoretically, and in the context
of Figure 2, these algorithms try to push the Efficiency
Line closer to the Bandwidth Limit Line at the expense of
convergence speed to fairness. For example, the GAIMD [77]
algorithm with β=7
8, converges to fairness in O(Blog1.14B)
steps, where B is the link bandwidth; the SIMD [32] with
β=15
16 converges in O(Blog1.06B)steps, the SQRT [7]
algorithm with β= 1 −q1
B, converges in O(B2); so does
the IIAD [7]. The performance of AIMD algorithm (with
parameters α= 1 and β=1
2) and in general of TCP is
studied in [51], [18]. The efficiency of the AIMD algorithm
is described in [51] by the formula:
Ef ficiency =3
4BMSS
RT T (30)
where B is the link bandwidth, MSS is the TCP packet
size and RTT is Round Trip Time. The analysis suggests
a 75% efficiency of the protocol when the system is in
equilibrium. Several congestion control algorithms along with
a cost analysis of their capacity to discover the available
bandwidth have been presented in [33].
Although the system efficiency is well defined and ade-
quately measured, the algorithm’s potential to achieve fairness
need further attention. From our perspective, fairness involves
apunctual, a vertical and a horizontal aspect. The punctual
represents the question whether the algorithm converges or
not. The horizontal involves the issue whether the speed to
convergence is optimal and is frequently called responsiveness.
The vertical involves the question whether the level of window
oscillations is high during the convergence procedure. This
is commonly called smoothness. Note that this aspect can
overlap with system efficiency during convergence; however,
an example of two flows that over and under-utilize their fair-
share, respectively, but do not leave bandwidth unexploited
suffices to demonstrate the distinctive difference: our system
in this case is efficient but not fair.
Furthermore, there was recently a significant effort to dis-
tinguish congestion-related errors from wireless errors. That
effort invested mainly in distinguishing the locus of the error
[6], [67], [21], rather than focusing on the dynamics from the
combination of both errors. For example, persistent congestion
which may be experienced in some router in a wired network
may change to a more transient one when wireless errors are
introduced at the last mile, where some wireless receivers
reside. Furthermore, higher contention can be tolerated under
the same circumstances of congestion. In a similar context, in
a high-speed network congestion may cause more losses due
5Both statements have been made initially in [11]
to the fact that congestion windows may grow to very high
values; however, it will last less and potentially, it will appear
much less frequently [2], [17], [31], [34], [65]. The dynamics
of combined wired and wireless errors appears to be far
more important issue than the ability to geographically locate
the error and apply the well-known techniques. Transient
congestion combined with higher contention may not call
for conservative recovery as this is implemented through the
extension of the timeout and the shrinkage of the congestion
window.
What mechanisms are appropriate to detect the presence of
combined congestion and transient random wireless errors?
A fairly recent probing scheme appears to measure network
performance but also combines the ability to deal with wireless
errors: it freezes the timeout and holds still the congestion
window without transmitting any data when wireless errors
do not allow the probing mechanism to be completed [70].
Other mechanisms measure contention and decouple wireless
errors from others. With what precision can we estimate really
network conditions? How can we take into account the risk of
wrong estimation in order to avoid false recovery strategies.
Or, in another context, what are the situations which may
tolerate some risk? And, beyond detection, what strategies
correspond to each distinctive new class of errors that are
detected? How can we evaluate them? For example, authors
in [69] have shown that congestion control determines the
aggressive/conservative protocol behavior, which in turn af-
fects energy consumption. This issue calls certainly for further
investigation.
The TCP-related work discussed above raises another im-
portant question: where is the right place to add the required
functionality? This question does not have a clear answer;
error control is not exclusively a management property of the
router or the base-station, nor is it exclusively assigned to the
transport layer. A widely accepted approach, presented by the
end-to-end argument [18], states that we can only implement
a function at a lower layer, if that layer can perform the
complete function. Since the lower level cannot have enough
information about the application’s requirements, protocol
parameters, and device constraints, it cannot implement the
whole function of error control; it can only be used to optimize
the function of the higher layer.
One can go beyond architectural optimization criteria and
worry about potential false strategies due to the locality of
router decisions. For example, when a router experiences
congestion or progresses towards congestion, it takes action.
The action is taken in association with an inherent assumption:
that the portion of the network that follows will not change
the major traffic characteristics of the flows - something not
necessarily true when a wireless network is deployed at the
receivers’ end. Certainly TCP throughput allows for assuming
a monotonic behavior. However, when our assumption is
violated, there is no indication that our strategy is still correct.
Departing from the same point, we justified earlier the logic
behind measurement-based protocols. There is a significant
difference however; the receivers have indeed the capability to
measure flow traffic throughout the whole network path, hence
they do not fall into wrong assessments due to limited view
of the network. Perhaps one can trust end-to-end protocols on
that aspect, more than network mechanisms.
By the same token, when many flows compete for a limited
bandwidth, a window back-off strategy will not yield any
significant gain. For example, a large number of flows over a

32 JOURNAL OF INTERNET ENGINEERING, VOL. 1, NO. 1, JANUARY 2007
10Mbps network would probably operate with single-packet
windows that do not permit further shrinkage. Obviously,
under such contention of packets, efficiency of the algorithm
does not really become an issue. Only a proper timeout
adjustment can permit all flows to use the network fairly.
Authors in [61] investigate the properties of timeout when it
becomes the schedule for the link.
Evaluation of congestion control is an important issue in its
own right. Moreover, it lacks appropriate evaluation method-
ologies. It is very common that congestion control mechanisms
are evaluated only in terms of channel exploitation. Our
set of metrics combined (defined in Section II) capture a
more accurate view of the protocol behavior. Furthermore,
application-oriented performance metrics (e.g., jitter) can show
whether protocol performance gains are reflected on user’s
satisfaction.
VIII. CONCLUSIONS
To summarize, we classified different approaches based on
the potential knowledge of network dynamics during commu-
nication. Some approaches assume zero knowledge of such
dynamics until the cliff point; these are classified as blind in
the literature. That is, the network hides all its secrets in a
’black’ box. Some measurements and bandwidth estimation
techniques may reveal some network characteristics; however,
they lack at least precision occasionally and are therefore du-
bious; the box is consider grey. In contrast, when the network
reports explicit information about its state, information is not
hidden and, in addition, is accurate indeed; that is, the box
is green. In another context, the color may represent whether
a corresponding action can be taken with certainty, based on
estimated dynamics. Classification is also possible using other
criteria. For example, protocols may be classified based on the
transmission scheme they are using (e.g., rate-based window-
based) or based on their proactive or reactive strategy (e.g.,
congestion avoidance versus control). We have also described
modeling approaches to congestion control, pricing models
and discussed issues that remain to be solved.
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Lefteris Mamatas received a diploma in Electrical
and Computer Engineering from Demokritos Univer-
sity of Thrace, Greece in 2003, where he is currently
a Ph.D. candidate. Lefteris worked as a research
intern at DoCoMo Eurolabs (May-October 2005 and
July-September 2006). His research interests lie in
the area of transport protocols and their behavior
over heterogeneous networks. He published 10 con-
ference and 3 journal papers.
Tobias Harks received the diploma degree in math-
ematics from University of Muenster, Germany, in
2003. He is currently working towards the Ph.D.
degree at the Technical University Berlin and Zuse
Institute Berlin. His research interests include Com-
binatorial Optimization, Algorithmic Game Theory,
Online Optimization, and Network Management.
Vassilis Tsaoussidis received a B.Sc in Applied
Mathematics from Aristotle University, Greece; a
Diploma in Statistics and Computer Science from
the Hellenic Institute of Statistics; and a Ph.D
in Computer Networks from Humboldt University,
Berlin, Germany (1995). Vassilis held faculty posi-
tions in Rutgers University, New Brunswick, SUNY
Stony Brook and Northeastern University, Boston.
In May 2003, Vassilis joined the Department of
Electrical and Computer Engineering of Demokritos
University, Greece. His research interests lie in the
area of transport/network protocols, i.e., their design aspects and performance
evaluation. Vassilis is an editor-in-chief in the Journal of Internet Engineering.
He is an editor for IEEE Transactions in Mobile Computing, the Journal of
Computer Networks (Elsevier), the journal of Wireless Communications and
Mobile Computing and the journal of Mobile Multimedia. He participates
in several Technical Program Committees in his area of expertise, such as
INFOCOM, NETWORKING, GLOBECOM and several others.