Evaluating the number of active flows in a scheduler realizing fair statistical bandwidth sharing
Abstract
Despite its well-known advantages, per-flow fair queueing has not been deployed in the Internet mainly because of the common belief that such scheduling is not scalable. The objective of the present paper is to demonstrate using trace simulations and analytical evaluations that this belief is misguided. We show that although the number of flows in progress increases with link speed, the number that needs scheduling at any moment is largely independent of this rate. The number of such active flows is a random process typically measured in hundreds even though there may be tens of thousands of flows in progress. The simulations are performed using traces from commercial and research networks with quite different traffic characteristics. Analysis is based on models for balanced fair statistical bandwidth sharing and applies properties of queue busy periods to explain the observed behaviour.
Evaluating the Number of Active Flows in a Scheduler
Realizing Fair Statistical Bandwidth Sharing
A. Kortebi L. Muscariello
∗
S. Oueslati J. Roberts
France T´el´ecom R&D
†
Politecnico di Torino
‡
France T´el´ecom R&D France T´el´ecom R&D
ABSTRACT
Despite its well-known advantages, per-flow fair queueing
has not been deployed in the Internet mainly because of the
common belief that such scheduling is not scalable. The
objective of the present paper is to demonstrate using trace
simulations and analytical evaluations that this belief is mis-
guided. We show that although the number of flows in
progress increases with link speed, the number that needs
scheduling at any moment is largely independent of this rate.
The number of such active flows is a random process typi-
cally measured in hundreds even though there may be tens
of thousands of flows in progress. The simulations are per-
formed using traces from commercial and research networks
with quite different traffic characteristics. Analysis is based
on models for balanced fair statistical bandwidth sharing
and applies properties of queue busy periods to explain the
observed behaviour.
Categories and Subject Descriptors
C.2.1 [Computer-Communication Networks]: Network
Architecture and Design—Packet-switching networks
General Terms
Performance
∗
Work done while visiting France T´el´ecom R&D.
†
A. Kortebi, S. Oueslati, J. Roberts, France T´el´ecom R&D,
CORE/CPN, 38 rue du G´en´eral Leclerc, 92794 Issy-Les-
Moulineaux, France
{abdesselem.kortebi, sara.oueslati,
james.roberts}@francetelecom.com
‡
L.Muscariello, Politecnico di Torino, Dipartimento di Elet-
tronica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
luca.muscariello@polito.it
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SIGMETRICS’05, June 6–10, 2005, Banff, Alberta, Canada.
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Keywords
Fair queueing, statistical bandwidth sharing, trace simula-
tions, analytical traffic model
1. INTRODUCTION
The number of flows traversing a network link is a ran-
dom process that varies as a large population of potential
users independently initiate and complete their applications.
Most flows are established to transfer some kind of digital
document and can adjust their rate to make the best use
of available bandwidth. The way these elastic flows share
bandwidth is currently determined by end-to-end transport
protocols like TCP that hopefully implement standardized
congestion control algorithms. In this paper we consider
an alternative approach where network mechanisms are em-
ployed to govern bandwidth sharing, without having to rely
on end user cooperation.
The assumed sharing objective is max-min fairness be-
tween user flows [1]. This can be realized by performing
per-flow fair queueing on all network links [2]. Users must
still perform end-to-end congestion control but only to en-
sure they fully use the allocated rate.
The proposal to implement fair queueing is clearly not new
and it has already been demonstrated that this is possible
on high rate links [3]. Nevertheless, it is widely considered
that generalized implementation is not scalable: complex-
ity increases with the number of flows in progress and this
number increases with link rate; required operating speed
therefore increases too fast. The objective of the present
paper is to demonstrate that this belief is false and that fair
queueing is both scalable and feasible.
The desirability of max-min fairness as a bandwidth shar-
ing objective has been called into question [4]. In particular,
if users gain different utilities from a given bandwidth alloca-
tion, there are sound economic reasons to realize shares that
reflect these differences. This argument is less compelling,
however, when one takes account of the fact that the popu-
lation of flows in progress varies. It turns out that, under a
realistic stochastic traffic model, the differences in the per-
formance of policies like max-min fairness and weighted pro-
portional fairness are hardly significant and not necessarily
to the advantage of those providing greater discrimination
[5].
We study the scalability of fair queueing by means of trace
driven simulations and analytical modelling. The traces are
recorded on networks with quite different traffic character-
istics. In all cases, the simulations demonstrate that the
number of flows that the scheduler needs to be aware of
at any instant is measured in hundreds, even when there
are tens of thousands of flows in progress. The analytical
model, based on a quasi-stationary separation of flow level
and packet level processes, accurately predicts the simula-
tion results. The model shows how different traffic char-
acteristics impact performance, highlighting the significant
role of the flows’ exogenous rate limits.
Fair queueing scheduling has been widely studied since the
early proposal of Nagle [6]. The main focus of research has
been on the development of algorithms with reduced com-
plexity, precise fairness and provable performance bounds.
For present purposes, a rough degree of fairness is adequate
and we are not interested in delay bounds since there are no
constraints on incoming traffic. Our objective is to evaluate
the complexity of fair queueing in dynamic, random traf-
fic. To this end we consider the specific case of Start-time
Fair Queueing [7]. However, a parallel analysis could be
performed to show the equivalence of alternative schedulers,
like Deficit Round Robin, for example [8].
In view of the imagined complexity of schedulers, a num-
ber of active queue management algorithms have been pro-
posed that realize approximate fair sharing [9, 10, 11]. Our
analysis would also apply roughly to an evaluation of the
number of flows that need to be handled by these schemes.
The characteristics of individual IP flows have been cata-
logued according to a variety of criteria including size, rate,
duration and burstiness [12, 13, 14]. The most significant
characteristic for present purposes is the exogenous flow
rate: the rate the flow would have if the considered link
were of infinite capacity. The measurement study by Zhang
et al. [14] shows that the rate varies widely from flow to
flow. Our own analysis shows that the distribution of rates
can vary significantly depending on the considered network.
We have previously claimed that fair queueing is scalable
in [15, 16] and provided preliminary evidence to back up
this claim. The present work goes much further in both
experimental validation using trace driven simulation and
in developing a comprehensive analytical model.
We first discuss relevant characteristics of IP traffic at
flow level and introduce the three network traces used in
the simulations. In Section 3, we describe the considered
fair queueing algorithm and present simulation results illus-
trating its performance under the traffic of the three traces.
The analytical model is developed in Section 4 and evalu-
ated using data representative of the traces. The impact on
performance of particular traffic characteristics at flow and
packet level is discussed in Section 5. We also highlight a
number of issues raised by the previous analysis. Section 6
concludes the paper and identifies a number of outstanding
issues.
2. FLOW LEVEL CHARACTERISTICS OF
IP TRAFFIC
We elaborate on the representation of traffic as a stochas-
tic process at flow and session levels and introduce the traffic
traces used in our evaluation.
2.1 Traffic as a stochastic process
IP traffic on a network link can be considered as a su-
perposition of independent sessions, each session relating
to some piece of user activity and being manifested by the
transmission of a collection of flows. Assuming sessions are
mutually independent and are generated by a large popu-
lation of users leads naturally to a Poisson session arrival
process. This characteristic has been confirmed empirically
and recognized as one of the rare invariants of IP traffic [17].
Sessions and flows are defined locally at a considered net-
work element. Flows can generally be identified by common
values in packet header fields (e.g., the 5-tuple of IP ad-
dresses, port numbers and transport protocol) and the fact
that the interval between such packets is less than some
time out value (20s, say). It is not usually possible to iden-
tify sessions just from data in packets and this notion cannot
therefore be used for resource allocation.
A useful traffic model is to suppose flows in a session are
emitted one after the other, separated by “think times”. The
number of flows in a session, the sizes of successive flows and
think times and their correlation can vary widely depending
on the underlying applications (mail, Web, P2P,...). We
refer to a Poisson process of sessions of alternating flows
and think times with otherwise general characteristics as the
Poisson session model. It forms the basis of the analytical
model introduced later.
An obvious discrepancy with reality arises if we must iden-
tify flows using the 5-tuple of header fields. For instance, the
transfer of a Web document would be considered as a single
flow in the session model but is frequently realized using sev-
eral distinct TCP connections in parallel. This discrepancy
does not have a significant impact on the present evalua-
tion of the complexity of per-flow fair queueing, however, as
discussed later in Section 5.
A more significant flow characteristic is the exogenous
peak rate at which a flow can be emitted. This is the high-
est rate the flow would attain if the link were of unlimited
capacity. This limit may be due to the user access line ca-
pacity, the maximum TCP receive window or the current
available bandwidth on other links of the path, for instance.
The complexity of fair queueing depends somewhat on
packet length. IP packets are well known to have a size dis-
tribution concentrated around a few particular values such
as 40, 570 and 1500 bytes [18]. This length distribution is
generally correlated with flow characteristics such as the size
or peak rate.
2.2 Statistics of trace data
Traffic characteristics used in the present study are de-
rived from trace data for three network links:
ADSL : an OC3 link concentrating the traffic outgoing to
several thousand ADSL users; the trace represents 5 min-
utes of data recorded on August 25 2003;
Ab-I : an OC48 link on the Abilene research network be-
tween Indianapolis and Kansas City; the trace represents 5
minutes of data recorded on August 14 2002 (10:30 to 10:35
am);
Ab-III : an OC192 link on Abilene III between Indianapolis
and Chicago; the trace represents 2 minutes of trace data
recorded on June 1 2004 (7:31 to 7:33 pm).
The Abilene traces are publicly available on the NLANR
website
1
. The ADSL data is from a commercial network.
Summary statistics for these three traces are shown in
1
See http://pma.nlanr.net/Traces/Traces/long/ipls/1/ and
http://pma.nlanr.net/Special/ipls3.html.
Table 1: Packet trace statistics summary
ADSL Ab-I Ab-III
bandwidth 155Mbps 2.5Gbps 10Gbps
total packets 2.6M 19M 156M
total flows 850K 2.3M 683K
utilization 28% 13% 19%
flows in progress 24000 37000 62000
Table 1. The table refers to 5-tuple flows defined with ref-
erence to a 20s time out. These statistics demonstrate sig-
nificant differences between the traces. In particular, flows
are much bigger on average on Ab-III than on the other two
links. This is due to a small number of large flows with
a very high rate. The utilization of all three links is very
low. The absence of congestion means measured flow rates
can reasonably be assimilated to the exogenous rates dis-
cussed in Section 2.1. The last line of the table gives the
average number of flows in progress over the trace lifetime.
This number is derived on considering flows to be still “in
progress” during the 20s time out. Some 95% of bytes in all
traces are in TCP connections.
Figure 1 presents the empirical complementary distribu-
tion of average flow rates calculated, as in [14], for all flows
lasting longer than 100ms. Flow rates in the ADSL trace are
limited by the offered line rates (all less than 1Mbps). Rates
in the Abilene traces can be much higher though most flows
still have an average rate less than 1Mbps. The Ab-III trace
is somewhat atypical in that it includes some flows with the
exceptionally high average rate of around 300Mbps. These
turn out to be TCP flows using 9000 byte jumbo packets.
1e+03 1e+05 1e+07 1e+09
1e−04 1e−03 1e−02 1e−01 1e+00
Flow Rate [bps]
Empirical ccdf
Ab−III Link
Ab−I Link
ADSL Link
Figure 1: Empirical complementary distribution of
average flow rates.
As an alternative measure of the exogenous rate we have
measured the peak rate attained in successive 10ms intervals
over the flow lifetime (the length of the interval is not critical
since similar statistics were obtained using 100 ms). Results
presented in Figure 2 accentuate the differences between the
three traces revealing notably that flows in Ab-III can attain
more than 1Gbps while rates of ADSL flows are all less than
1e+03 1e+05 1e+07 1e+09
1e−04 1e−03 1e−02 1e−01 1e+00
Flow Rate [bps]
Empirical ccdf
Ab−III Link
Ab−I Link
ADSL Link
Figure 2: Empirical complementary distribution of
flow peak rates.
1Mbps.
Packet lengths are correlated with rate for the Abilene
traces. On Ab-I, all packets are less than 1500 bytes. Most
packets in flows whose peak rate is greater than 10Mbps are
of this length. Lower rate flows, that include flows of TCP
ACKs, have a much higher proportion of 40 byte packets.
Some 67% of bytes in the Ab-III trace are in flows of peak
rate greater than 500Mbps. Almost all packets in these flows
are of 9000 bytes. Lower rate flows in this trace have more
typical packet sizes ranging from 40 to 1500 bytes. The
distribution of packet sizes in the ADSL trace is clustered
around 40, 570 and 1500 bytes and is broadly independent
of flow rate.
3. COMPLEXITY OF PER-FLOW FAIR
QUEUEING
We choose to exemplify the class of fair queueing sched-
ulers by the self-clocked Start-time Fair Queueing (SFQ)
algorithm of Goyal et al. [7]. We discuss how complexity of
SFQ in a dynamic traffic setting depends on the number of
so-called active flows. We then evaluate the distribution of
this number using trace driven simulations.
3.1 Start-time Fair Queueing
Pseudocode for SFQ adapted to the present context of a
dynamically varying flow population is given in Figure 3.
Fairness properties of the algorithm are discussed in [7]. It
is shown, for example, that the amount of data transmitted
by any continuously backlogged flow is always within one
maximum sized packet the ideal fair share.
The complexity of the algorithm is usually evaluated in
terms of the number of operations necessary per packet un-
der the assumption that the flow population is fixed. This
complexity is determined by the sort operation implicit in
line 9 of the pseudocode and thus typically increases with the
logarithm of the number of flows. In the present dynamic
version, the sort must be performed on flows that have a
1. on arrival of l-byte packet p of flow f:
2. if f ∈ ActiveList do
3. TimeStamp.p = FinishTag.f
4. FinishTag.f += l
5. else
6. add f to ActiveList
7. TimeStamp.p = VirtualTime
8. FinishTag.f = VirtualTime + l
9. transmit packets in increasing TimeStamp order
10. at the start of transmission of packet p:
11. VirtualTime = TimeStamp.p
12. for all flows f ∈ ActiveList
13. if (FinishTag.f ≤ VirtualTime) remove f
14. if no packets in scheduler VirtualTime = 0
Figure 3: Pseudocode of SFQ with a dynamic list of
active flows.
packet with a time stamp greater than the current value of
VirtualTime. This is the number of bottlenecked flows since
this condition only occurs when the flow incoming rate ex-
ceeds the current fair rate.
The number of bottlenecked flows is usually much smaller
than the number of active flows. Active flows are flows with
an entry in ActiveList. This includes any bottlenecked flow
but also any flow that has recently emitted a packet, as
manifested by the fact that its FinishTag is still greater than
VirtualTime.
Pseudocode operations 2 and 12-13 depend on the num-
ber of active flows. Operations 12-13 are trivial if the list is
sorted in FinishTag order, implying log complexity for a sort
operation whenever a finish tag is updated. The test in oper-
ation 2 can have O(1) complexity if the size of ActiveList is
small enough to be realized using content addressable mem-
ory. The overall complexity of the algorithm thus depends
mainly on the number of active flows and secondarily on the
number of these that are bottlenecked.
Note that, in any realization, the size of ActiveList is finite
and it is necessary to limit the probability of overflow. It
is thus important to understand how the distribution of the
number of active flows depends on the intensity and char-
acteristics of offered traffic. It is also necessary to specify
what happens when the list is full. We assume packets of
new flows that cannot be recorded are scheduled with time
stamp equal to VirtualTime. List saturation thus has no
impact on scheduling non-bottlenecked flows. Bottlenecked
flows will not be slowed to the current fair rate until a sub-
sequent packet arrival when the list is no longer saturated.
3.2 Trace driven simulations
The link utilization for the three traces presented in Sec-
tion 2 is too low to produce any interesting scheduling be-
haviour. For example, the maximum size of ActiveList ob-
served on the OC192 link was 11 flows. To evaluate the
performance of SFQ we therefore apply the trace data to
a simulated scheduler operating at a rate considerably less
than the rate of the link on which the trace was measured.
The different simulated link capacities are given in Table 2.
Table 2: Simulated link capacities in bps, all traces
Load ADSL Ab-I Ab-III
0.6 72M 541M 3.16G
0.9 48M 361M 2.11G
For each trace in Table 1, link capacities were calculated to
produce a load of 0.6 and 0.9, where the load is defined as
flow arrival rate × mean flow size, divided by the link ca-
pacity. This produces realistic results under the assumption
that the transport protocol controlling each flow is capable
of using the current fair rate, whenever this is less than the
exogenous peak rate. In the simulation, this condition is
satisfied since sufficient buffering is provided to avoid any
packet loss. Figure 4 shows the complementary distribu-
tions of the observed ActiveList size. The most significant
observation is that the number of active flows in all three
cases, even at 90% utilization, is very much smaller than the
average number of flows in progress (see Table 1). Secondly,
the number does not increase with link rate. Indeed, the
worst case is that of the ADSL link. This is due to the fact
that most flows are not bottlenecked on this link because of
the limited peak rate. The distinction between the impact
of bottlenecked and non-bottlenecked flows is clarified in the
development of the analytical model in the next section.
These results are significant in that they suggest fair queue-
ing is scalable and feasible. It is scalable since complexity
does not increase with link speed; it is feasible since the
required ActiveList size is relatively small.
4. ANALYTICAL MODEL
In this section we develop an analytical model to explain
why fair queueing is scalable and to understand the impact
of the various traffic characteristics. An earlier model out-
lined in [16] successfully reproduced simulation results for
another trace but relied for this on a traffic classification
derived from the simulation. The present model relies only
on intrinsic traffic characteristics.
4.1 Traffic model
We assume traffic is generated according to the Poisson
session model introduced in Section 2.1. We further suppose
flows have a constant peak rate drawn from a set {c
1
, c
2
, . . . ,
c
M
} with c
1
> c
2
> · · · > c
M
. Flows with peak rate c
i
constitute class i. The number of class i flows in progress at
time t is denoted X
i
(t).
The analysis is based on a quasi-stationary timescale sep-
aration. We first suppose the X
i
are fixed and evaluate
the distribution of the number of active flows for each state
x = (x
1
, . . . , x
M
). We then introduce assumptions allowing
us to estimate the stationary distribution of X in order to
derive the required unconditional distribution.
4.2 Bottlenecked and active flows
For notational convenience, define c
0
= C and c
M+1
= 0.
If
P
M
i=1
x
i
c
i
> C, fair queueing realizes max-min fair sharing
with fair rate θ given by
θ =
C −
P
i>J
x
i
c
i
P
i≤J
x
i
(1)
0 100 200 300 400 500 600
1e−05 1e−03 1e−01
m
P{Active List Size > m}
OC3 Link load=0.6
OC3 Link load=0.9
(a) ADSL
0 100 200 300 400 500 600
1e−05 1e−03 1e−01
m
P{Active List Size > m}
OC48 Link load=0.6
OC48 Link load=0.9
(b) Ab-I
0 100 200 300 400 500 600
1e−05 1e−03 1e−01
m
P{Active List Size > m}
OC192 Link load=0.6
OC192 Link load=0.9
(c) Ab-III
Figure 4: Complementary distribution of ActiveList
size from trace driven simulations at utilizations of
60% and 90%
where J = J(x) is the unique integer, 1 ≤ J ≤ M, such that
c
J
≥ θ > c
J+1
.
Flows of peak rate greater than or equal to c
J
are bottle-
necked and realize the fair rate θ while the others preserve
their peak rate through the scheduler. If
P
M
i=1
x
i
c
i
≤ C, all
flows preserve their peak rate. Let J(x) = 0 in this case.
Note that J defines a partition of the state space.
Consider now the operation of the SFQ algorithm. All
bottlenecked flows are included in ActiveList. In addition,
any non-bottlenecked flow having emitted a packet in the
recent past, such that its finish tag is less than VirtualTime,
is also included. To evaluate the stationary distribution of
the total number we must make some assumptions about
packet lengths and the arrival process of packets from non-
bottlenecked flows.
The most convenient assumption is to suppose all pack-
ets of bottlenecked flows have maximum size mtu. This
is reasonable given the packet size statistics of high peak
rate flows reported above and is arguably a worst case as-
sumption for the distribution of ActiveList size
2
. Given this
assumption, and taking mtu as the unit of virtual time, it
is easy to see that VirtualTime takes only integer values.
The periods when at least one flow is bottlenecked and
VirtualTime is constant constitute “busy cycles”. Any packet
from a non-bottlenecked flow arriving in a busy cycle ac-
quires the time stamp VirtualTime and further perpetuates
the cycle for the duration of its own transmission. This flow
remains in ActiveList until the end of the cycle. It is then
removed since its finish tag cannot be greater than Virtual-
Time + 1 (it has size l ≤ 1 in mtu units). Figure 5 illustrates
the notion of busy cycle.
busy cycle
10
3
active flows
non−bottlenecked flows
Packets (7) from Bottlenecked
flows (3)
VirtualTime = k (k+1) (k−1)
Figure 5: Illustration of the notion of busy cycle.
Busy cycles also occur when there are no bottlenecked
flows in progress. In this case a busy cycle is initiated by a
packet arriving to an empty system. VirtualTime remains
equal to zero in such cycles.
The size of ActiveList is largest just before the end of
a busy cycle. To evaluate the stationary distribution of
this number MaxList, we assume each non-bottlenecked flow
emits at most one packet in a cycle
3
.
To model the arrival process we assume each flow inde-
2
This is because VirtualTime changes more rarely so that
small non-backlogged packets remain longer in the list.
3
A flow cannot emit more than mtu bytes since this would
contradict its non-bottlenecked status.
pendently emits its packet between time t and t + dt af-
ter the start of the busy cycle with probability αdt + o(dt).
This finite source Poisson process facilitates analysis while
accurately accounting for the number of contributing flows
P
i>J
x
i
.
4.3 Conditional distribution of ActiveList size
From the above description it may be recognized that an
estimate for the number of non-bottlenecked flows contribut-
ing to MaxList can be derived from an evaluation of the busy
period of a queue with exceptional first service. The latter
corresponds to the transmission of one mtu sized packet
from each of the
P
i≤J
x
i
bottlenecked flows
4
.
The arrival process results from N =
P
i>J
x
i
flows inde-
pendently emitting at most one packet according to the pro-
cess described at the end of the last section. The service time
distribution derives from that of the packet length F (s).
We assume packet lengths are i.i.d. for all non-bottlenecked
flows
5
. Let packet length be measured in units of mtu and
denote the mean by σ.
The assumed per-flow arrival rate α is the average rate
for all non-bottlenecked flows: α = R/(Nσ) where R =
P
i>J
x
i
c
i
is their overall bit rate. The probability k packets
arrive in an interval of length u from the start of the busy
cycle is then:
Λ
N
(k, u) =
N
k
!
(1 − e
−αu
)
k
e
−(N−k)αu
(2)
The conditional distribution of MaxList is given by the
following proposition.
Proposition 1. Let g(m; b, n, r) be the conditional dis-
tribution of MaxList given b bottlenecked flows and n non-
bottlenecked flows contributing overall rate r. Assuming pack-
ets arrive according to process with distribution Λ and have
independent length drawn from distribution F , we have:
g(m; b, n, r) =
8
<
:
1
m
R
Λ
n
(m − 1, u)dF
[m]
(u), b = 0, m ≥ 1,
Λ
n
(0, b), b > 0, m = b,
b
R
Λ
n
(m − b − 1, u)/udF
[m−b]
(u − b), b > 0, m > b,
(3)
where F
[m]
is the m-fold convolution of F .
Proof. We adapt classical results for the M/G/1 queue
by substituting Λ
n
for the corresponding Poisson distribu-
tion. This is possible because the considered arrival process
has the same indiscernible properties as the Poisson process
allowing us to apply the combinatorial lemma of Tak`acs [19,
page 231] and its generalization by Niu and Cooper [20].
The first case, when no flows are bottlenecked, derives from
the classical result for the number of customers served in an
M/G/1 busy period [19, page 63]. The second case just ex-
presses the probability that no non-bottlenecked flow emits
a packet in the busy cycle. The third case is derived from
results in [20] for the number of customers served in a busy
period starting with an exceptional first service correspond-
ing to b packets from the bottlenecked flows.
4
The order of service of packets with the same time stamp
has no impact on MaxList; it is convenient to suppose the
bottlenecked packets are emitted first.
5
We therefore ignore the fact that this distribution depends
on the number of flows in each class and its specific distri-
bution.
From the distribution of MaxList we can derive the dis-
tribution of the active list size at the moment when a flow
should be added. Let this random variable be AddToList.
Under the quasi-stationary assumption, the flow population
x is fixed and only non-bottlenecked flows are ever added
to the list. The following proposition gives the conditional
distribution of AddToList.
Proposition 2. Let h(m; b, n, r) be the conditional dis-
tribution of AddToList given that there are b bottlenecked
flows and n non-bottlenecked flows contributing overall rate
r. We have, for m ≥ b ≥ 0, n > 0:
h(m; b, n, r) =
P
k>m
g(k; b, n, r)
P
l>b
(l − b)g(l; b, n, r)
(4)
Proof. The distribution g(k; b, n, r) gives the relative fre-
quency of busy cycles starting with ActiveList size b and
terminating with size k due to k − b packet arrivals. The
probability that that an arbitrary arrival occurs in such a
busy cycle is thus (k − b)g(k; b, n, r)/
P
l>b
(l − b)g(l; b, n, r).
The probability that arrival encounters m flows in ActiveList
is then 1/(k − b) for b ≤ m < k. The expression for h is
derived on multiplying the two probabilities and summing
over all possible values of k.
4.4 Flows in progress
Consider now the stationary distribution of X(t) assum-
ing a fluid model where flow rates adjust instantly as flows
start and end. The fair queueing scheduler realizes max-
min fair sharing with fair rate θ as defined in equation (1).
Unfortunately, analysing max-min sharing is intractable un-
der any realistic traffic assumptions. We therefore consider
the alternative sharing objective of balanced fairness. This
leads to a relatively simple expression for the distribution of
X [21]. The assumption, that we partially justify later, is
that the distribution of X is approximately the same under
max-min and balanced fairness.
4.4.1 Balanced fair allocation
Under balanced fairness it is possible to evaluate exactly
the stationary distribution of X. Moreover, this distribution
is insensitive to all characteristics of the Poisson session traf-
fic model defined in Section 2 other than the respective class
demands a
i
(= class i flow arrival rate × average class i flow
size). The load is equal to a/C where a =
P
M
i
a
i
.
Following Bonald and Virtamo [22] we adopt the short-
hand c
x
=
Q
M
i=1
c
x
i
i
, a
x
=
Q
M
i=1
a
x
i
i
and x! =
Q
M
i=1
x
i
! and
denote by e
i
the M vector with 1 in position i and 0 else-
where. The stationary distribution π
BF
is then given by:
π
BF
(x) = Φ(x)a
x
/G (5)
where G is a normalizing constant ([22] provides a recur-
sive formula to evaluate G) and the balance function Φ is
determined recursively as follows:
Φ(x) =
1/(x!c
x
) if xc
T
≤ C,
P
M
i=1
Φ(x − e
i
)/C if xc
T
> C.
(6)
4.4.2 Recurrence relations
Let B
j
=
P
i≤j
X
i
, N
j
=
P
i>j
X
i
and R
j
=
P
i>j
X
i
c
i
for 0 ≤ j ≤ M. We need to evaluate, from π
BF
(x), the
joint stationary distribution of B
J
, N
J
and R
J
where J is
the index defined in Section 4.2. Note that as J defines a
partition of states x, it also partitions allowable values of
(B
J
, N
J
, R
J
) (we have, for example, θ = (C − R)/B and
c
J
≤ θ < c
J+1
).
Let Q
BN R
J
(b, n, r) denote the joint distribution of B
J
, N
J
and R
J
. To evaluate this distribution directly is impractical
in view of the huge size of the corresponding array. We
therefore evaluate the following approximation:
Q
BN R
J
(b, n, r) = P{B
J
= b|N
J
= n, R
J
= r}Q
NR
J
(n, r)
≈ Q
BR
J
(b, r)Q
NR
J
(n, r)/Q
R
J
(r), (7)
with the obvious interpretation for the distributions on the
right hand side. This is reasonable since N
J
and R
J
are
closely correlated. To evaluate the two-term distributions
we apply the recurrence relations stated in the following
propositions (proofs are in the annex).
Proposition 3. The joint distribution of B
J
and R
J
, for
0 ≤ J ≤ M , is given by Q
BR
J
(b, r) = q
J
(b, r), where the
q
j
(b, r), for 0 ≤ j ≤ M , satisfy the following recurrence
relations:
q
j
(b, r) =
X
i≤j
a
i
C
[q
j
(b − 1, r) +
C−r
X
s=C−r−c
i
+1
p
j
(b − 1, s, r)]
+
X
i>j
a
i
C
[q
j
(b, r − c
i
) +
C−r+c
i
X
s=C−r+1
p
j
(b, s, r − c
i
)]
(8)
and
p
j
(b, s, r) =
X
i≤j
a
i
(s + r) ∧ C
p
j
(b − 1, s − c
i
, r)
+
X
i>j
a
i
(s + r) ∧ C
p
j
(b, s, r − c
i
). (9)
Values of q
j
and p
j
are zero if any argument is negative
and q
j
(0, 0) = p
j
(0, 0, 0) = π
BF
(0) is determined by the
normalization condition.
Proposition 4. The joint distributions of N
J
and R
J
,
for 1 ≤ J ≤ M , is given by Q
NR
J
(n, r) = q
J
(n, r), where
the q
j
(n, r), for 1 ≤ j ≤ M, satisfy the following recurrence
relations:
(1 −
X
i≤j
a
i
C
)q
j
(n, r) =
X
i≤j
a
i
C
C−r
X
s=C−r−c
i
+1
p
j
(s, n, r)
+
X
i>j
a
i
C
[q
j
(n − 1, r − c
i
) +
C−r+c
i
X
s=C−r+1
p
j
(s, n − 1, r − c
i
)]
(10)
and
p
j
(s, n, r) =
X
i≤j
a
i
(s + r) ∧ C
p
j
(s − c
i
, n, r)
+
X
i>j
a
i
(s + r) ∧ C
p
j
(s, n − 1, r − c
i
) (11)
Values of q
j
and p
j
are zero if any argument is negative
and p
j
(0, 0, 0) = π
BF
(0) is determined by the normalization
condition.
4.4.3 Comparison between max-min and balanced
fair sharing
Previous work has shown that max-min and balanced fair-
ness result in similar flow level performance [21]. This has
been confirmed in the present case by evaluating the be-
haviour of max-min fair sharing by fluid simulation and com-
paring the marginal distributions of B and R (over all J)
with that derived for balanced fairness.
We assume a Poisson arrival process of flows having a
Weibull size distribution with shape parameter equal to 0.3
(yielding a long tailed distribution) in the first simulation
scenario, and an exponential size distribution with the same
mean size equal to 1Mbit in the second one. Arrival rates
were chosen to produce the demand proportion associated
with each class. Flow peak rates in Mbps are c = {1500,
1000, 800, 500, 100, 50, 10, 1} with respective demands in
proportion to a = {21, 22, 17, 7, 6, 17, 6, 4}. These data
are representative of the Abilene III OC192 trace.
0 20 40 60 80 100
1e−05 1e−03 1e−01
b
P{B=b}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Balanced Fairness
Max−Min Fairness (exponential flow size)
Max−Min Fairness (weibull flow size)
Figure 6: Comparison between balanced and max-
min allocations, load = 0.9, AbileneIII trace.
0 20 40 60 80 100
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07
r/C[%]
P{R=r}
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
+
+
Balanced Fairness
Max−Min Fairness (exponential flow size)
Max−Min Fairness (weibull flow size)
Figure 7: Comparison between balanced and max-
min allocations, load = 0.9, AbileneIII trace.
Table 3: Flow classes and traffic proportions
ADSL Ab-I Ab-III
Class c a
i
/a c a
i
/a c a
i
/a
[bps] [%] [bps] [%] [bps] [%]
C
1
1M 52 100M 24 1.5G 21
C
2
512K 26 20M 10 1G 22
C
3
128K 12 15M 9 800M 17
C
4
50K 10 12M 14 500M 7
C
5
- - 10M 14 100M 6
C
6
- - 5M 11 50M 17
C
7
- - 1M 4 10M 6
C
8
- - 500K 12 1M 4
Figures 6 and 7 compare the marginal distributions of
B and R, respectively, for link load 0.9. The rough agree-
ment is typical of results for data corresponding to the other
traces. Note the somewhat erratic fluctuations in these dis-
tributions due to the discrete mixture of peak rates. In this
fluid model, all flows belonging to the same class become
bottlenecked or non bottlenecked simultaneously which ex-
plains the observed jumps in the distribution of B. Errors
introduced by the approximation do not appear to be too
significant. At load 0.6, there is little controlled sharing
(i.e., J = 0 with high probability) and max-min and bal-
anced fairness are practically the same.
4.5 Unconditional ActiveList size distribution
We can now estimate the distribution of ActiveList size
by combining the results of Sections 4.3 and 4.4, i.e.
P{ActiveList size = m} =
8
<
:
P
(b,n,r):J <M
h(m; b, n, r)Q
BN R
J
(b, n, r) J < M
Q
BN R
M
(m, 0, 0) J = M
We perform the calculations with data representative of
the three traces described in Section 2.2 The peak rate classes
(in bps) and respective traffic proportions (in %) are given
in Table 3.
These values are derived by choosing a set of peak rates
roughly covering the domain of the distributions in Figure
2 and attributing to each class the traffic from flows whose
peak rate is closest. We set C and adjust the absolute values
of the demand vectors a to attain link loads of 0.6 and 0.9, as
in the simulations described in Section 3.2 and summarized
in Table 2.
For the packet size of non-bottlenecked flows we have used
a distribution with just two values as it is difficult to nu-
merically evaluate the convolution in Proposition 1 for more
terms. We chose packet sizes of 40 and 1500 bytes with rel-
ative proportions derived roughly from the trace statistics
(50% for each packet size for the ADSL and Abilene traces,
30% and 70% respectively for the Abilene III trace). The
value of MTU was 1500 bytes for the first two traces and
9000 bytes for the third.
Results are presented in Figure 8. As can be seen, the
analytical model predicts the simulated ActiveList size dis-
tribution quite accurately. These results are discussed in the
next section.
0 100 200 300 400 500 600
1e−05 1e−03 1e−01
m
P{Active List Size > m}
model
ns simulation
(a) ADSL
0 100 200 300 400 500 600
1e−05 1e−03 1e−01
m
P{Active List Size > m}
model
ns simulation
(b) Ab-I
0 100 200 300 400 500 600
1e−05 1e−03 1e−01
m
P{Active List Size > m}
model
ns simulation
(c) Ab-III
Figure 8: Complementary distribution of ActiveList
size from analytical model at utilizations of 60% and
90%
5. DISCUSSION
In this section we discuss the relative importance of traffic
characteristics at flow and packet timescales and highlight a
number of important issues.
5.1 Impact of traffic characteristics
First recall the lack of impact on the population of flows
in progress X of the detailed session structure under the
assumed Poisson session traffic model. This insensitivity is
strictly valid only for balanced fairness but we believe it to
be true also for all practical purposes for max-min fairness.
The only significant characteristics are the overall load and
the distribution of this load over the range of exogenous flow
peak rates.
The assumption in the model that the peak rate is one of
a finite set of values and is the same throughout the flow
lifetime is clearly a simplification. It nevertheless appears
to predict performance reasonably accurately. The main
impact of the rate distribution is to determine for any load
which proportion of traffic is in bottlenecked flows and which
is not. These two types of traffic are shown to have qualita-
tively different impacts on ActiveList size.
Bottlenecked flows are few in number up to high loads of
around 90%. The majority of active flows correspond to iso-
lated packets emitted by relatively low rate non-bottlenecked
flows. This explains why the ADSL trace gives rise to the
largest list: its peak rate limited flows are rarely bottle-
necked even at 90% load. The very high rate flows in Ab-III,
on the other hand, have a beneficial impact on the statistics
of ActiveList size.
The packet length of non-bottlenecked flows has a signifi-
cant impact. The smaller the packets, the greater the packet
arrival rate and, in consequence, the greater the number of
flows contributing to a busy cycle and momentarily entering
ActiveList.
5.2 Benefits of fair queueing
Imposed fairness relieves the network from relying on user
cooperation to ensure satisfactory performance. It does re-
main possible, however, for users to establish multiple paral-
lel flows and thus acquire a greater rate than the fair share.
The present models show that such advantage would only
accrue to the small proportion of users whose flows are bot-
tlenecked. Such users already realize high throughput. If
they nevertheless “cheat” by setting up parallel flows, this
should be fairly easy to detect and counter given their small
number.
The Poisson session model (with alternating flows and
think times) remains appropriate for users whose combined
peak rate is less than the fair rate, whatever the number of
5-tuple flows they actually use in parallel. This is because
packets of the combination still arrive in isolation (i.e., ≤ 1
in any busy cycle) and add 1 to the current ActiveList size
independently of the particular 5-tuple flow to which they
belong.
When fairness is assured by the network, new transport
protocols can be tested and introduced without having to
ensure they are not overly aggressive to legacy TCP variants.
This is an appreciable advantage, notably for the design of
protocols adapted to high speed transmission (see Section
5.5 below). It is also possible to introduce known techniques
for improving the behaviour of TCP slow-start.
A particularly interesting benefit of fair queueing is the
protection afforded to relatively low rate real time flows. As
long as the rate of audio and video flows is less than the
current fair rate (and our models demonstrate that this is
typically quite high), their packets achieve low latency in
traversing the FQ scheduler. This effectively realizes service
differentiation without the cumbersome requirement to ex-
plicitly mark packets as real time or delay tolerant. Packet
latency can be further reduced for flows whose peak rate
is less than the current fair rate by giving priority to their
packets (i.e., packets that acquire time stamp VirtualTime
in line 7 of the SFQ code go to the head of the schedule), as
proposed in [15].
5.3 Alternative realizations
We have used the SFQ algorithm to exemplify the perfor-
mance of fair queueing but it is clearly possible to use differ-
ent algorithms. Similar results would apply for other self-
clocking schedulers and to round robin variants like DRR
[8].
Some authors have proposed to use active queue man-
agement schemes to avoid the pretended scalability issues of
scheduling [9, 10, 11]. The present discussion would also ap-
ply (with somewhat less precision) to determining the per-
formance of these algorithms in a realistic dynamic traffic
setting. These algorithm aim to operate only on the bot-
tlenecked flows but would presumably need to account mo-
mentarily for active flows in order to be able to detect new
bottlenecked ones.
Core stateless fair queueing [23] distributes the complexity
of scheduling to the network edge where the current rate of
each flow is estimated. Note that all in progress flows must
be tracked and measured with this approach.
Of course, the congestion control of TCP currently real-
izes approximate fair sharing with simple FIFO queues (al-
beit with well known biases and inefficiencies). The present
models are again useful in understanding how the number of
flows actually contending for resources on a given link (the
bottlenecked flows) is typically very small.
5.4 Avoiding overload
In this paper we have shown that fair queueing is scalable
and feasible at normal to heavy loads. When demand ex-
ceeds around 90% of link capacity, however, the number of in
progress and active flows increases rapidly. In such overload
the scheduler (like the above mentioned AQM mechanisms)
tends to revert to a FIFO queue. Per-flow throughput gets
smaller and smaller as an increasing number of flows com-
pete for the available bandwidth.
It is clearly desirable to avoid such overload, whatever
queue management scheme is employed. A possible solu-
tion avoiding the current requirement for excessive over-
provisioning would be to use per-flow admission control as
advocated in [15]. The measure of the current fair rate re-
alized by the scheduler is a convenient criterion for deciding
when new flows should be blocked.
5.5 Buffer sizing
It has recently been observed that the rule of thumb whereby
router buffers should be able to store some 200 ms of data
at line rate is excessive and unsustainable as link bandwidth
increases [24]. The present discussion on the numbers of in
progress, active and bottlenecked flows throws more light on
typical buffer requirements.
It is shown in [24] that buffer requirements decrease sub-
stantially as the number of flows in progress increases, under
the assumption that these flows are all bottlenecked. This
trend is confirmed using different models in [25], again as-
suming traffic is composed mainly of “locally bottlenecked
persistent flows”. In fact, our results demonstrate that the
number of locally bottlenecked flows is typically relatively
small, the vast majority of flows having a peak rate con-
siderably less than the current fair rate. If more than a
hundred flows are actually bottlenecked, this is usually a
sign of severe overload that buffering alone cannot control,
as discussed in the previous section.
If only a handful of flows are bottlenecked (there is a non-
negligible probability that the number is only one or two),
they necessarily have a high rate and the models in [24] show
that a large buffer is indeed necessary to sustain 100% uti-
lization using TCP. We might therefore argue that the above
rule of thumb should be applied, at least to the sizeable line
rate fraction used by the bottlenecked flows. However, this
is not what we would advocate.
Most of the time, on most links, no flow is bottlenecked
and a small buffer (for around 100 packets) is adequate to
ensure low loss. Rather than applying the rule of thumb to
cater for the small number of exceptional flows that can sat-
urate the residual link capacity, it seems more appropriate
to require that these flows employ one of the recently pro-
posed high speed TCP variants (e.g., [26, 27, 28]). A feature
of these protocols is that they require much less buffering to
attain 100% link utilisation.
6. CONCLUSION
We have shown that the advantages of network assured
max-min fair sharing can be realized because per-flow fair
queueing is scalable - since the number of flows that need
to be scheduled is independent of link speed - and feasible -
since this number is relatively small. Performance has been
evaluated using trace driven simulations and explained by
means of an analytical model.
The model demonstrates that, after the average link load,
the most significant traffic characteristics are the exogenous
peak rates the flows can attain in the absence of link con-
gestion. These determine the proportion of flows that are
bottlenecked and those that are not. The model shows
how these flows combine to determine the complexity of the
scheduler and explains why this remains low up to utiliza-
tions of around 90%.
The number of bottlenecked flows is typically measured
in tens. Many more flows are in progress but they are non-
bottlenecked and only contribute episodically to the list of
active flows to be accounted for by the scheduled. The over-
all number of flows that need to be scheduled is limited to
a few hundreds, independently of the proportions of traffic
in bottlenecked and non-bottlenecked flows.
In addition to protecting the quality of service of indi-
vidual flows against possible user misbehaviour, the use of
fair queueing would bring two significant advantages. First,
it would be possible to test and introduce new, more ef-
ficient transport protocols without requiring that they be
TCP-friendly. This is useful notably for very high speed
transfers for which the congestion avoidance algorithm of
TCP is known to waste bandwidth. Second, fair queueing
ensures low packet latency for flows whose rate is less than
the current fair rate, the non-bottlenecked flows. This al-
lows audio and video flows to coexist with high speed data
transfers without the need to explicitly identify the former.
The present work suggests several directions for further
research. The more approximate fairness realized by AQM
mechanisms may be sufficient for elastic data traffic but it
remains to evaluate the performance they provide for below
fair rate audio and video flows. How could a transport pro-
tocol best exploit the assurance of max-min fairness in order
to improve the current slow-start and congestion avoidance
algorithms? Fair queueing is feasible as envisaged only up to
a load of around 90%: it is necessary therefore to implement
some means to prevent overload. This may take the form
of dynamic load balancing or adaptive routing. A necessary
component appears to be some form of flow-level admission
control, as envisaged in [15].
This paper presents credible technical arguments, based
on analysis, simulations and recent Internet measurements,
in favour of the feasibility and desirability of fair queueing.
We hope these arguments will encourage router architects
to reconsider the opportunity of implementing fair queueing
in the design of next generation routers allowing the devel-
opment of a more efficient and reliable Internet.
Annex
Proof of Proposition 3
Define variables S
j
=
P
i≤j
x
i
c
i
and sets S
j
(b, s, r) = {x :
B
j
= b, S
j
= s, R
j
= r}. Consider the probabilities p
j
(b, s, r) =
P{B
j
= b, S
j
= s, R
j
= r} for j > 0:
p
j
(b, s, r) =
X
x∈S
j
(b,s,r)
π(x)
=
X
x∈S
j
(b,s,r)
M
X
i=1
a
i
(s + r) ∧ C
π(x − e
i
)
=
X
i≤j
a
i
(s + r) ∧ C
X
x∈S
j
(b−1,s−c
i
,r)
π(x) +
+
X
i>j
a
i
(s + r) ∧ C
X
x∈S
j
(b,s,r−c
i
)
π(x),
and this is (9). The second step uses properties (5) and
(6), (see [22]). If b = 0 then q(0, r), for r = 0, . . . , C, is
directly given by the Kaufman-Roberts recursion (see below
and [22]). Observe that when b > 0, S
J
+ R
J
> C. Thus we
can define q
j
(b, r) =
P
s>C−r
p
j
(b, s, r) for j > 0 so that
q
j
(b, r) =
X
s>C−r
p
j
(b, s, r) =
=
X
i≤j
a
i
C
X
s>C−r
p
j
(b − 1, s − c
i
, r)
+
X
i>j
a
i
C
X
s>C−r
p
j
(b, s, r − c
i
),
=
X
i≤j
a
i
C
X
s>C−r−c
i
p
j
(b − 1, s, r)
+
X
i>j
a
i
C
X
s>C−r
p
j
(b, s, r − c
i
),
The last two sums can be split as in (8). Q
BR
J
(b, r) is given
limiting q
j
(b, r) in the state space partition induced by J.
Proof of Proposition 4
Define variables S
j
=
P
i≤j
x
i
c
i
and sets S
j
(s, n, r) = {x :
S
j
= s, N
j
= n, R
j
= r}. Consider the probabilities p
j
(s, n, r) =
P{S
j
= s, N
j
= n, R
j
= r} for j > 0:
p
j
(s, n, r) =
X
x∈S
j
(s,n,r)
π(x)
=
X
x∈S
j
(s,n,r)
M
X
i=1
a
i
(s + r) ∧ C
π(x − e
i
)
=
X
i≤j
a
i
(s + r) ∧ C
X
x∈S
j
(s−c
i
,n,r)
π(x) +
+
X
i>j
a
i
(s + r) ∧ C
X
x∈S
j
(s,n−1,r−c
i
)
π(x),
and this is (11). The second step uses properties (5) and
(6) (see [22]) as in the previous proof. Now let q
j
(n, r) =
P
s>C−r
p
j
(s, n, r) so that
q
j
(n, r) =
X
s>C−r
p
j
(s, n, r) =
=
X
i≤j
a
i
C
X
s>C−r
p
j
(s − c
i
, n, r)
+
X
i>j
a
i
C
X
s>C−r
p
j
(s, n − 1, r − c
i
),
=
X
i≤j
a
i
C
X
s>C−r−c
i
p
j
(s, n, r)
+
X
i>j
a
i
C
X
s>C−r
p
j
(s, n − 1, r − c
i
),
The last two sums can be split as in (10) where the first
term does not depend on i. If J = 0 we obtain again the
Kaufman-Roberts recursion. Q
NR
J
(n, r) is given considering
q
j
(n, r) in the state space partition induced by J.
Kaufman-Roberts Recursion
P{X
1
c
1
+ · · · + X
M
c
M
= n} = q(n) for n ≤ C satisfies the
following recursion:
q(n) =
M
X
i=1
a
i
n
q(n − c
i
)
with q(n) = 0 if n < 0.
Proof. The joint distribution defined in (5),(6) in the
case xc
T
≤ C satisfies the relation x
i
c
i
π(x) = a
i
π(x − e
i
).
Thus, summing over i, nπ(x) =
P
M
i=1
a
i
π(x − e
i
). Finally,
summing over all x such that xc
T
= n we conclude the
proof.
7. REFERENCES
[1] D. Bertsekas and R. Gallager, Data Networks,
Prentice Hall, Englwood Cliffs, N.J., 1992.
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- "If equal bandwidth sharing is provided by the inner nodes then it becomes possible to decouple fairness control from the transport layer protocol , as fairness can be treated in an orthogonal way. The feasibility of this approach is supported by the scalability of per-flow fair queuing [34,35] . "
[Show abstract] [Hide abstract] ABSTRACT: In this paper, we propose a networking paradigm built upon a fountain code based data transfer mechanism. We advocate that, instead of controlling the congestion as it is applied in recent Internet by the Transmission Control Protocol (TCP), we can utilize congestion and neglect control algorithms with all of their drawbacks. We present our envisioned network architecture relying on a novel transport protocol called Digital Fountain based Communication Protocol (DFCP) and highlight some potential application areas. We have implemented DFCP in the Linux kernel and we provide its validation results gained from three different testing platforms including our laboratory testbed, the Emulab network emulation environment and the ns-2 network simulator. Moreover, we present and discuss a comprehensive performance evaluation of DFCP in comparison with widely used TCP versions.- "It is well-known that fairness queueing algorithms can improve flow fairness characteristics [35], and indeed it is a design goal for such algorithms (hence the term fairness queueing). However, fairness characteristics of pure AQM algorithms are not well understood. "
[Show abstract] [Hide abstract] ABSTRACT: Several new active queue management (AQM) and hybrid AQM/fairness queueing algorithms have been proposed recently. They seek to ensure low queueing delay and high network goodput without requiring parameter tuning of the algorithms themselves. However, extensive experimental evaluations of these algorithms are still lacking. This paper evaluates a selection of bottleneck queue management schemes in a test-bed representative of residential Internet connections of both symmetrical and asymmetrical bandwidths as well as WiFi. Latency under load and the performance of VoIP and web traffic patterns are evaluated under steady state conditions. Furthermore, the impact of the algorithms on fairness between TCP flows with different RTTs, and also the transient behaviour of the algorithms at flow startup is examined. The results show that while the AQM algorithms can significantly improve steady state performance, they exacerbate TCP flow unfairness. In addition, the AQMs severely struggle to quickly control queueing latency at flow startup, which can lead to large latency spikes that hurt perceived performance. The fairness queueing algorithms almost completely alleviate the algorithm performance problems, providing the best balance of low latency and high throughput in the tested scenarios. However, on WiFi the performance of all the tested algorithms is hampered by large amounts of queueing in lower layers of the network stack inducing significant latency outside of the algorithms’ control.- " Monitoring all conversations is far too expensive but we are concentrating on the active conversations only, those for which packets are queued in the buffer, to reduce the number of states stored in the router. It has been shown in the past (cf. [15]) that such per flow control is scalable because of the relatively small number of active flows. A conversation is considered to be active if a transmission queue of the router owns at least one packet of this conversation."
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