It has been observed that FAST TCP, and the related protocol TCP Vegas, suffer unfairness when many flows arrive at a single bottleneck link, without intervening departures. We show that the effect is even more marked if a new flow arrives when existing flows share bandwidth fairly, and propose a simple method to ameliorate this effect

Andrew, Lachlan L. H.

Cui, Tony

Tan, Liansheng

Zukerman, Moshe

English

Caltech Authors - Main

414 IEEE COMMUNICATIONS LETTERS, VOL. 10, NO. 5, MAY 2006
Improving the Fairness of FAST TCP to New Flows
Tony Cui, Lachlan L. H. Andrew, Moshe Zukerman, and Liansheng Tan
Abstract— It has been observed that FAST TCP, and the
related protocol TCP Vegas, suffer unfairness when many flows
arrive at a single bottleneck link, without intervening departures.
We show that the effect is even more marked if a new flow arrives
when existing flows share bandwidth fairly, and propose a simple
method to ameliorate this effect.
Index Terms— Congestion control, fairness, buffer dimension-
ing.
I. INTRODUCTION
BOTH TCP Vegas [2], [3], [8] and FAST TCP [5]–[7]achieve high throughput by using queueing delay as a
congestion signal. This is effective because queueing delay
provides a finer measure of congestion and scales naturally
with network capacity [7]. This paper investigates the unfair-
ness which can result when a new flow arrives at a bottleneck
link whose bandwidth is fairly distributed among existing
flows. It then proposes a method to avoid this unfairness.
Because both FAST TCP and TCP Vegas use queueing
delay as congestion signal, their window updating algorithms
rely on the propagation delay, which is estimated by a measure
called baseRTT. This measure is defined as the minimum
round-trip time (RTT) observed so far. Because sometimes the
routers’ queues never become empty, the actual propagation
delay may be inaccurately estimated by baseRTT which results
in unfairness [7], [9], and excessive variations of routers’
queues. We demonstrate that the amount by which the rate of
a newly arriving flow exceeds its fair capacity grows rapidly
as the number of existing flows increases. We present the
calculations for FAST; the results for Vegas are qualitatively
similar, although more complex.
The structure of this paper is as follows. Section II describes
the network scenario to be considered. In Section III, we
analyze the fairness of FAST and Section IV presents a
technique to improve the fairness. Numerical validation of the
proposed technique appears in Section V.
II. NOTATION AND PROBLEM STATEMENT
This paper considers the arrival of new flows at a single
bottleneck link of capacity C [packets/s], already carrying N
flows. Denote the backlog at the link time t by b(t) [packets].
Manuscript received October 21, 2005. The associate editor coordinating
the review of this letter and approving it for publication was Prof. Nasir
Ghani. This work was supported by the Australian Research Council, NSF,
Cisco, and the Caltech Lee Center for Advanced Networking as part of the
FAST Project.
T. Cui and M. Zukerman are with the ARC Special Research Centre for
Ultra-Broadband Information Networks (CUBIN), an affiliated programme
of the National ICT Australia Department of Electrical and Electronic En-
gineering, University of Melbourne, Victoria 3010, Australia (e-mail: {t.cui,
mzu}@unimelb.edu.au).
L. Andrew is with the Computer Science Department of CALTECH (e-
mail: lachlan@caltech.edu).
L. Tan is with the Computer Science Department of Central China Normal
University, Wuhan 430079, P.R. China (e-mail: l.tan@mail.ccnu.edu.cn).
Digital Object Identifier 10.1109/LCOMM.2006.05013.
Let di [seconds] be the true round trip propagation delay
of flow i, let dˆi be the estimated propagation delay, and
let Di(t) = di + qi(t) be the round trip time of flow i,
including queueing delay of qi(t). Let wi(t) [packets] and
xi(t) [packets/s] be the window size and rate for flow i, which
are related by
wi(t) = xi(t)Di(t). (1)
Every flow using FAST aims to have a total of α packets
in queues throughout the network. Quantities without explicit
time dependence are either constants or equilibrium values;
for example, b is the equilibrium backlog.
Previous studies [1], [8], [9] have considered a scenario
called “persistent congestion”, as follows. All flows share a
single bottleneck link of capacity C [packets/s] and have equal
α [packets]. Flows arrive consecutively, spaced far enough
apart for the system to reach equilibrium between arrivals,
and keep transmitting greedily and persistently. Let ti be a
time when the system has reached equilibrium after the arrival
of the ith flow, but before the arrival of the i + 1st flow.
When the ith flow arrives, it causes the queue size at the
bottleneck link to increase by B(i) [packets]. If di were known
exactly, then B(i) would be α. However, the estimate dˆi will
be assumed to be the RTT seen when the flow first arrives,
given by dˆi(i) = di + p(i − 1) [seconds], giving B(i) > α.
Here p(i) =
∑i
j=1 B(j)/C [seconds] is the total queueing
delay of flow i.
It is known that unfairness occurs under persistent conges-
tion. However, when flows depart, the reduction in throughput
causes queues to empty, and allows flows to observe their
true propagation delays. After such an event, new arrivals
experience a situation analogous to persistent congestion,
except for the presence of N additional flows, all of which
know their true di. That is the scenario which will be studied
here. All of these flows will have an equal rate, denoted x0(t),
which will vary as new flows arrive.
III. RECENT ARRIVAL
This section investigates the equilibrium rates when a small
number of flows arrive at a single bottleneck link, which is
currently carrying N long flows. It will be assumed that the N
existing flows all know the true round trip propagation delay.
This is reasonable since the queue occupancy drops whenever
a flow departs; any long flow has a good chance of seeing the
queue empty, and hence knowing the true propagation delay.
The N existing flows will be referred to as flows −N ,
-N+1,. . . , −1. Quantities such as the estimated queueing delay
and rate are equal for all of these flows; this symmetry is
indicated by denoting quantities with a subscript “0”. Newly
arriving flows will be numbered from 1.
The update rule for FAST can be written as [7]
wi(t + 1) = γ
(
dˆiwi(t)
Di(t)
+ α
)
+ (1− γ)wi(t) (2)
1089-7798/06$20.00 c© 2006 IEEE
CUI et al.: IMPROVING THE FAIRNESS OF FAST TCP TO NEW FLOWS 415
for some constant γ ∈ (0, 1], giving the equilibrium condition
wi = α
dˆi
Di − dˆi
. (3)
Following [9], let bi [packets] denote the increase in queue
size when the ith flow arrives. In equilibrium, each flow will
maintain α of its own packets in the queue in addition to the
smallest queue size which it has observed. The flows −N to
−1 know their true propagation delays, and will each maintain
b0 = α packets in the queue. Since there are N such sources,
the queue observed by “flow 1” will be Nb0 = Nα.
When flow i enters the link, it estimates the propagation
delay as di + Nb0 +
∑i−1
k=1 bk/C. It observes the queueing
delay qi = bi/C, flow j (1 ≤ j ≤ i) observes the queueing
delay qj = (
∑i
k=j bk)/C, and flows −N to −1 observe the
queueing delay q0 = (Nb0 +
∑i
k=j bk)/C. Since
Nx0(ti) +
i∑
k=1
xk(ti) = C, (4)
and xk = α/qk, it follows that
N
Nb0 +
∑i
k=1 bk
+
i∑
j=1
1∑i
k=j bk
=
1
α
. (5)
This yields an i + 1th order polynomial equation for bi.
Thus
b1
α
=
1 +
√
1 + 4N
2
, (6)
and as N∞,
b2
α
= a2
√
N + o(
√
N), (7)
where a2 ≈ 0.801938 is the solution to 2a2+1 = a2(a2+1)2.
By induction on i,
bi
α
= ai
√
N + o(
√
N), (8)
as N∞, where ai is the solution of the i+1th order polynomial
given by
i∑
j=1
1∑i
k=j ak
=
i∑
j=2
ak, (9)
which is independent of the network parameters and of N .
Note that (7) and (8) are asymptotic for large N ; they are a
fair approximation for finite N when the denominator of the
first term of (5) is dominated by Nb0, which occurs when
i <
√
N .
The equilibrium rate of flow i ≥ 1 between the arrivals of
flows j and j + 1 is
xi(tj) =
αC∑j
k=i bk
. (10)
The rate of flows −N to −1 in the same interval is
x0(tj) =
αC
Nb0 +
∑j
k=i bk
. (11)
Significantly, (8), (10), and (11) imply that the newly arrived
flows, i ≥ 1, get O(C/√N), while the original flows only get
O(C/N), which is the same order as their fair share. This is
in contrast to pure persistent congestion (N = 0) studied in
[1], [8], [9]; in that case the most recently arriving flow only
gets O(logN) times its fair share. However, since the extra
bandwidth is “borrowed” from all N existing flows, no flow is
starved of bandwidth as occurs in pure persistent congestion.
Another difference with persistent congestion is that when
N = 0, the bi need not be monotonic increasing. For example,
b2 < b1 for N > 6.
I think that for i >> N , b(N)i /b
(1)
i 1, but I’m not sure if this
is worth pursuing.
Are ai monotonically decreasing?
IV. REMOVING UNFAIRNESS
FAST can only achieve fairness if each flow has an accurate
estimate of its true propagation delay, d. Unless there is
network support, such as allowing probe packets to bypass the
queue [9], the only way to obtain the true propagation delay
is for the queue to empty occasionally. This section presents
a means to achieve this, without network support and with
vanishing impact on network throughput.
Since a newly arrived flow i ≥ 1 obtains excessive rate, it is
well placed to drain the bottleneck queues, to allow all flows
using those links to estimate d. The proposed approach is for
each newly started flow to pause briefly to allow the queue to
drain, and then resume at full rate. This can be implemented
by introducing a rate scaling factor r, and using the following
phases, once the window size has stabilized:
a) reduction: In the first additional phase lasting one
round trip time, the congestion window size is decreased such
that for every r acknowledgements received, only one new
packet is transmitted. This reduces the rate of this source by
a factor of r, allowing the bottleneck queues to empty.
b) depletion: In this phase, the congestion window size
is kept constant to allow the queues to empty. This phase ends
once baseRTT (dˆi) stabilizes, or after at most two RTTs.
c) refilling: The third phase increases the window size
by r − 1 each time an acknowledgement arrives. This phase
continues until the congestion window size reaches its equilib-
rium given by (3) with Di being the RTT before the reduction
phase and dˆi being the baseRTT after the depletion phase.
d) stabilization: Because the measured RTT in the pre-
vious phases is very low, the FAST update rule would increase
the window size dramatically. To prevent this, this final
additional phase maintains the window size constant for one
RTT to allow an accurate RTT estimate to be made. After this,
FAST resumes normal operation.
The rate reduction parameter, r, must balance several
factors. The larger r is, the faster the queue will drain,
increasing the probability of it emptying entirely within the
RTT. However, the role of the packets sent during depletion
is to sample the RTT, and larger r leads to coarser sampling;
flows with short RTTs may respond to the reduced queueing
before the end of the depletion phase, and so the sampling
must be fast enough to detect the minimum queue occupancy.
Moreover, increasing r increases the size of the bursts sent
in the refilling phase. However, if r < α then the queueing
induced by these bursts should not exceed α, which is the
amount of queueing due to the source in equilibrium. For this
reason, a value of r ≈ α appears reasonable.
The number of acknowledgements arriving during refilling
is approximately w/r, where w is the window size. However,
416 IEEE COMMUNICATIONS LETTERS, VOL. 10, NO. 5, MAY 2006
0
2000
4000
6000
8000
10000
12000
14000
0 10 20 30 40 50 60 70 80
So
ur
ce
 ra
te
 (p
ac
ke
t/s
)
Time (seconds)
FAST source 0
FAST source 1
FAST source 2
Fig. 1. Source rates of three modified FAST sources (α = 200 packet).
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2 4 6 8 10 12 14E
xi
sti
ng
 so
ur
ce
s’
 ra
te
/N
ew
 so
ur
ce
’s
 ra
te
Number of existing sources
Pure FAST algorithm
New algorithm
Existing 200ms, New 200ms
Existing 40ms, New 200ms
Existing 200ms, New 40ms
Theoretical result from Equation 6
Fig. 2. Ratio of existing source rate and new source rate (α = 50 packet).
random packet delays may cause the number to be slightly
higher. Thus, if every acknowledgement generates r packets,
the number of packets transmitted in that RTT may signifi-
cantly exceed w. That is prevented by sending the minimum
of r packets and the number permitted by the window.
This entire operation requires only a few round trip times
per flow, and the throughput is reduced only during the
reduction and depletion phases. Since even short connections
require many round trips for MI to achieve the correct rate,
the reduction in throughput is negligible.
The primary limitation of the proposed approach is that, as
the proposed algorithm reduces the queueing by reducing its
own rate, competing flows respond by increasing their rates. If
other flows did not respond, it would take αN3/2/C +O(N)
[seconds] for a single bottleneck queue to be emptied. The new
source must then have time to observe the empty queue. Since
its rate during this phase is approximately its fair share (C/N )
divided by r = α, it estimates the RTT every αN/C [seconds].
Thus, an empty queue will be observed if α(N3/2+N)/C is
less than the RTT of the existing flows.
V. SIMULATION RESULTS
To test the new algorithm, persistent congestion of three
sources with equal α sharing a single link was simulated using
NS2 [4], [10]. Fig. 1 shows that the modified algorithm of
Section IV results in greater fairness than that reported in [8],
[9] for standard FAST.
For cases when more flows share the link, Fig. 2 plots the
ratio between the rate of the existing sources and that of the
new one as a function of the number of existing sources.
The round trip propagation delays for all existing flows were
equal to d−1, and that of the new flow was d1. Three cases
were considered: (a) d−1 = 200ms, d1 = 200ms, (b) d−1 =
200ms, d1 = 40ms and (c) d−1 = 40ms, d1 = 200ms.
The above calculation for the time to drain the queue, and
observe the the empty queue, gives about 4.16(N3/2 + N)
ms. This is less than d0 = 200ms for N ≤ 11, and less than
d0 = 40ms for N ≤ 3. The values are indeed the thresholds
observed in Fig. 2 below the scheme yields fairness.
Fig. 2 also plots results for pure FAST, and the value
predicted by (6). The results agree except that a much better
fairness is achieved when the propagation delay of the new
source is much larger than that of the existing sources. This
is because the new flow with larger RTT “overshoots” its fair
share, causing the existing flow to back off too much. When
the new flow corrects its rate to its fair share, the link is briefly
underutilised. This may even allow the queue to empty, and the
new source to observe its true propagation delay. The effect
does not occur when the new flow has a small RTT, as the size
of the overshoot is smaller, nor does it occur when the existing
flows have a large RTT, as they then respond sluggishly to the
increased queue size.
VI. CONCLUSION
FAST TCP has difficulty in estimating the queueing delay,
and hence setting its rate, if a link is always congested [8], [9].
A flow newly arriving to a link already carrying N flows which
know the true queueing delay, receives a throughput O(
√
N)
times theirs. We have proposed a novel way to allow the
queueing delay to be measured accurately without assistance
from routers. Simulation results confirm that this improves
fairness significantly.
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