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Buffer Space Tradeoffs in Multi-hop Networks
Yanxia Jia, Ioanis Nikolaidis, Pawel Gburzynski
Department of Computing Siene
University of Alberta
Edmonton, Alberta, CANADA T6G 2E8
fyanxia,yannis,pawelgs.ualberta.a
of servie (QoS) requirements of those appliations. These
QoS
requirements are usually speied in terms of bandWe onsider the problem of buer spae alloation in a
width, paket loss, end-to-end delay, and jitter.
multi-hop store-and-forward network and study the tradeAording to ommon wisdom, the most QoS friendly imos between the amount of buer spae alloted to the endplementation
of an end-to-end session involves a networkpoints of a virtual iruit and that assigned to the ore
layer virtual iruit, whereby all pakets of the session folnodes, i.e., routers. Simulation results hint at the possibillow exatly the same path from soure to destination. Inity that the single-path paradigm of implementing networktuitively, the deterministi harater of suh a onnetion
layer virtual iruits is fundamentally awed (rather than
makes it easier to set aside the right amount of resoures at
merely inonvenient from the viewpoint of bandwidth alloevery
intermediate node and predit what is going to hapation and routing exibility). Despite its intuitive appeal
pen when several virtual iruits pass at the same router.
(paket ordering, preditability of end-to-end delays, et.),
Consequently, most work on QoS-driven resoure alloation
single-path forwarding neither results in eÆient utilization
fouses on path seletion algorithms [1, 8, 9, 15℄, assuming
of available buer spae from the point of view of the entire
that one seleted the (single) path will be followed by all
network, nor does it provide the best overall performane in
pakets of the session. This approah essentially equates a
terms of global bandwidth utilization and end-to-end quality
transport-layer session with a network-layer virtual iruit,
of servie. We demonstrate that the best quality of servie
even if (as in the Internet) the network-layer virtual iruit
for virtual iruits (in terms of drop rate) is ahieved when
is not expliit.
1. most of the buer spae in the network is at the destinaWhile moderate attempts at multi{path routing shemes
tions, and 2. a single virtual iruit explores multiple paths,
found
in the literature [5, 14℄ do demonstrate that a better
essentially following the general priniples of deetion routload balaning an be ahieved this way, they still restrit
ing.
the seletion of alternative routes based on a more or less expliit notion of a network layer session. This often tait and
Categories and Subject Descriptors
automati assumption about the inherent superiority of virC.2.1 [Network Arhiteture and Design℄: Paket-swithing tual iruits over datagrams has resulted in a omplete oblivion of forwarding ideas based on deetion [3, 10℄ (whih an
networks
be viewed as an extreme implementation of unkempt spontaneous routing) and has brought us the paradigm of ATM
General Terms
networks, whih, until not so long ago, was viewed by many
Performane
authors as the ultimate solution to all problems of networking.
Even if one was to onsider a pure datagram networkKeywords
layer protool, suh as IP, where virtual iruits are absent,
routing, multiple path routing, deetion
one an still identify a strong insistene on deterministipath forwarding. As keeping trak of TCP sessions in the
network (IP) layer is neither easy nor natural, this insistene
1. INTRODUCTION
pratially removes all exibility from the transport layer.
The problem of resoure alloation in ontemporary netThis is beause, with the splitting of a single session over
works, atering to a variety of interative and bandwidthmultiple paths onsidered harmful, there seems to be no
hungry appliations, is dened within the ontext of quality
alternative to forwarding all IP traÆ between a given host
pair via the same route. This in turn eetively kills all
opportunities for load balaning.
Permission to make digital or hard copies of all or part of this work for
Moreover, a oneptually similar approah to ATM virtual
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
iruits survives to this day in the guise of Multi-Protool
bear this notice and the full citation on the first page. To copy otherwise, to
Label Swithing (MPLS) [6℄ whereby bundles of transport
republish, to post on servers or to redistribute to lists, requires prior specific
layer ows are grouped (for the sake of eÆieny) together
permission and/or a fee.
in logial virtual iruits and are routed together. UnsurCNSR 2003 Conference, May 15-16, 2003, Moncton, New Brunswick,
prisingly,
MPLS further limits the potential for load balanCanada.
Copyright 2003 CNSR Project 1-55131-080-5 ...$5.00.
ABSTRACT
ing that ould exist between transport layer ows. While
the potential for load balaning at the level of MPLS \bundles" still exists, the fat that it an only be aomplished by
rather ostly routing deisions involving route (re-)alulations,
results in MPLS being less than attrative for responsive
load balaning.
In this paper, we onsider a exible routing model based
on deetion, whose degree is aeted by the amount of
buer spae available at the router. Our objetive is to
investigate how the QoS pereived by a transport-layer session depends on the way the buer spae available globally in the network is partitioned among the routers and
the destinations. We onlude that with a global view of
network resoures, multiple alternative paths explored by
dierent pakets of the same transport-layer session need
not be harmful. Just the opposite, they may in fat improve the utilization of those resoures and, at the same
time, improve the ritial QoS harateristis of isohronous
sessions. This is in ontrast to what most people seem to believe. While one an easily agree that the inreased routing
exibility naturally translates into a more balaned utilization of network resoures, realizing that this approah may
also imply better (more preditable) end-to-end delivery is
a less obvious (and somewhat ounterintuitive) step to take.
This seems to onrm the speulations expressed in [2℄ and
suggests that single-path forwarding is an inherently awed
routing strategy.
The rest of the paper is organized as follows: Setion 2 introdues the basi design tradeos related to the plaement
hoie for storage (buer spae) in the interior of the network versus the periphery. Setion 3 provides a simplied
network model for the sake of exploring the tradeos using a
quantitative framework. Setion 4 reviews the relevant simulation results and observations. Finally, onlusions and
avenues for further researh are summarized in Setion 5.
2.
THE TRADEOFF
Consider a router within the network ore that is about
to forward a paket belonging to a transport-layer session.
Regardless of the assumed routing paradigm, the omplete
list of options regarding the fate of this paket onsists of
the following possible outomes:
1. The paket is queued for transmission on the \best"
output port (oering the \most attrative" route to
the destination).
2. The paket is dropped, e.g., beause of the lak of
buer spae at the router.
3. The paket is queued for transmission on an output
port that is onsidered a seondary hoie (by the assumed route preferene sheme).
With the single-path forwarding paradigm, the third possibility is exluded. The optimization eort regarding the
utilization of network resoures is thus direted toward a
preise desription of what is meant by the \best" route
to the destination, as well as determining the right paket
sheduling poliy at the router. The latter an be interpreted as part of the buer management sheme, as it also
presribes the paket dropping rules.
If the third option is admissible, an alternative to dropping a paket (or sending it over the ongested preferred
path) is to forward it via a suboptimal route. The most
serious onsequene of this deision is that the paket may
(legitimately) arrive at the destination out of order. Thus,
to onsistently play bak the reeived pakets as fragments
of the transport-layer session, the reipient must use a reassembly buer [4, 13, 12℄ to re-order and possibly delay
pakets arriving out of shedule.
Consider a session with some spei QoS expetations
arried out between a soure S and destination D. Suppose
that the global forwarding sheme of the network exludes
option 3, i.e., the session path is xed. A router R along
the session's path may drop a paket if it runs out of buer
spae, but all pakets eventually delivered to D are going to
arrive in order. Consequently, D needs no reassembly buer
to play the session bak, although, depending on the session type, it may still need some buer spae to smooth out
the jitter aused by variable buering delays at the routers.
Larger buers at the routers will result in a lower paket
dropping rate pereived by D, although they may inrease
the jitter, whih, at least for some session types, may render
the pakets useless upon arrival. Depending on the sheduling poliy (or poliies) adopted by the routers, late pakets
may also be identied (and dropped) before they reah their
destinations.
If option 3 is admissible, pakets may arrive at D out
of order, and D may have to reassemble them, for whih
task it may need some extra buer spae. But with this
option, R is able to arry out its duties with less buer
spae than in the previous senario. This is beause now
R has an alternative to dropping a paket. Consequently,
it is possible that the redued amount of buer spae at
the router will be ompensated by the inreased amount of
buer spae at the destination.
In [2℄, it is argued that deeting instead of dropping may
be a fundamentally better approah from the global viewpoint of network resoure management. First, managing the
private per-session playbak buer at D is onsiderably simpler (and better dened as a problem) than managing the
shared buer spae at R in the fae of multiple and diverse
sessions passing through the router and (possibly) its multiple sheduling poliies. In ontrast to R, D applies the buer
to a single session at the exat point where its delivered QoS
parameters an be monitored with ultimate delity and authority. Thus, it an easily, onsistently, and meaningfully
adjust the buer size to ompensate for oasional utuations of the pereived QoS measures. Seond, if the session
an put up with pakets arriving out of order (e.g., the pakets an be proessed as independent datagrams), D does not
have to bother with reassembly buers, while R would still
try to \x what ain't broke" and buer the pakets in its
eort to provide for (unneeded) in-order delivery. This is
beause R doesn't know any better: even if it dierentiates
some elements of the servie (the sheduling poliy), this
one element (i.e., the individual route of a datagram) oers
no degree of freedom.
3. THE NETWORK MODEL
Our experiments reported in this paper an be viewed as
the rst step aimed at putting the above speulations on
a formal ground. As the routing approah in our network
model, we use asynhronous deetion, somewhat similar
to that desribed and analyzed in [7℄, but admitting limited buers at the routers. In our model, no paket is ever
dropped at a router. When a paket arrives for forwarding
and there is no buer spae available to queue it for transmission on the preferred output port, the paket is direted
to an alternative output port instead of being dropped. This
way, some pakets that would have to be dropped by a onventional router are now likely to reah their destinations
via alternative paths.
Eah node ranks its repertoire of alternative paths using
the approah desribed in [7℄, and limiting the hoie to 4
paths. In essene, it alulates the four shortest rst-hopdisjoint paths to eah destination, with the shortest path
onsidered most attrative. Obviously, to oer alternatives
from the viewpoint of routing, the dierent paths annot
share their rst hop.
The buer spae available at a router is partitioned among
all the output ports, suh that eah port is assigned the same
xed amount. Every time a paket arrives at the router, it
will be direted to the best output port with available buer
spae. The degree of deetion in this model an be adjusted
by modifying the amount of buer spae at the router. In
partiular, single path routing an be viewed as the limiting
ase of deetion routing with innite buers. Although no
pakets will ever be dropped in this model, the late arrivals
of exessively delayed pakets will render them useless at the
destinations.
One may be somewhat onerned about the inexibility
inurred by the rigid partitioning of buer spae at the
router. This approah simplies the model and seems to
be aeptable in a senario involving regular network ongurations and balaned traÆ patterns. Besides, one an
easily see that the onlusions from our experiments annot
be reversed (and are likely to be amplied) when a more
exible buer alloation sheme is used.
Eah node in our network behaves both as a router and a
host, i.e., a soure and/or a destination of a traÆ session.
The total amount of buer spae in the network is equal to
B + b, where B denotes the amount of spae assigned to
the destinations (to be used for reassembly buers) and b
stands for the amount of storage available at the routers.
Intentionally, B + b remains xed in a given experimental
setup, while the ratio B=b determines the adjustable balane
between the two ategories of storage.
The network aters to an isohronous appliation desribed
by a Pulse Code Modulation (PCM) voie traÆ model,
whereby 53-byte pakets (orresponding to ATM ells) are
sent at the average rate of 64Kbps. Their atual arrival
proess is Poisson. We look at the behavior of a seleted
soure/destination (S/D) pair involved in an isohronous
session, with the remaining nodes uniformly ontributing
Poisson-distributed bakground traÆ.
We onsider perfetly regular 4-onneted torus networks
with sizes varying from 4 4 to 14 14 nodes. All links have
the same bandwidth of 1Mbps and the length of 1000km.
We also investigated the ase where link lengths are dierent and obtained similar results. While suh networks may
seem large, one should notie that geographially smaller
networks an only be more advantageous for deetion (owing to a smaller variane in multi-hop propagation delays),
whih will result in more pronouned onlusions regarding
the observed tradeos. Also, the perfet regularity of the
topology and the uniformity of the bakground traÆ allow us to fous on the essene of the observed phenomena
without having to worry about the multitude of parameters
desribing more realisti ongurations.
Our simulator keeps trak of six performane measures related to the voie session. The loss rate is equal to the ratio
of the number of pakets disarded at the destination to the
total number of pakets transmitted by the soure. Sine a
paket annot be dropped at a router, loss an only our
at the destination|in two possible senarios. First, it may
happen that when the paket arrives, the reassembly buer
is full and there is no way to store the paket until its sheduled playbak time. Seond, the paket may arrive too late,
i.e., after its playbak time, in whih ase the reassembly
buer annot help, even if storage is available.
The network delay of a paket is measured as the interval separating the paket's generation at the soure and its
arrival at the destination. It is omposed of the queuing
delay and the propagation delay, the latter of whih also inludes the (re)transmission delay experiened by the paket.
The playbak lag represents the time elapsing after a paket
arrives at the destination and before it is played bak. It
reets the pure impat of the reassembly buer. The endto-end delay aptures the overall proessing time of a paket
within the network ounting from the moment the paket is
generated at the soure, until its playbak at the destination. It is the sum of the network delay and the playbak
lag.
4. THE RESULTS
The neessarily limited size of this paper allows us to
present only a small fragment of the large olletion of results from our simulation experiments. As long as the network size is nontrivial (bigger than 4 4), all experiments
produe results that are highly onsistent in qualitative terms.
Thus, we illustrate our observations with the 5 5 network,
whih is the smallest onguration in whih the desribed
tradeos are learly visible.
A single soure/destination node pair is seleted for a
voie session, and the remaining nodes are uniformly seleted to generate Poisson bakground traÆ with the average rate of 40Mbps, unless otherwise speied. The simulated time period is 400; 000ms, orresponding to over 60; 000
pakets. Six independent experiments have been run for
eah data point.
Figures 1{ 6 show how the observed performane measures in the network depend on the partitioning of the global
buer spae between the routers and destinations. Every
single urve orresponds to a spei xed total amount of
buer storage (B + b) and is a funtion of its alloation
(B=b).
Starting from Figure 1, we an see that the observed drop
rate tends to derease as the mass enter of the buer spae
is shifted from the routers to the destination, then attens for a while, and nally inreases sharply. What we
see is two ounterating phenomena in ation. The redued
amount of buer storage at the routers results in more pakets being deeted (and misordered), while the inreased
size of the reassembly buers ompensates for the misordering and makes it possible to reonstrut the session without dropping pakets. It appears that below a ertain B=b
threshold this ompensation is more beneial than the inreased level of deetion is harmful. Aording to Figure 1,
a workable low-loss regime falls roughly within the range
1 < log(B=b) < 4, whih translates into 0:4 < B=b < 55.
This means that we have a large seletion of B=b resulting in
torus 5x5, Loss vs. B/b, r = 30M, with fixed Total_Buf_Size
1
Deflection, Total Buf Size = 100
Deflection, Total Buf Size = 200
Deflection, Total Buf Size = 500
B=4,b=96
B=20,b=180
0.8
B=20,b=80
B=4
b=496
B=4
b=196
Loss
0.6
B=95,b=5
B=98,b=2
B=20
b=480
0.4
B=195,b=5
B=198,b=2
0.2
B=495 B=498
b=5
b=2
0
−6
−4
−2
0
log(B/b)
2
4
6
Figure 1: Loss rate.
torus 5x5, E2EDelay vs. B/b, r = 40M, with fixed Total_Buf_Size
3500
3000
Deflection, Total Buf Size = 100
Deflection, Total Buf Size = 200
Deflection, Total Buf Size = 500
E2EDelay (ms)
2500
2000
1500
1000
500
0
−6
−4
−2
0
log(B/b)
2
4
6
Figure 2: End-to-end Delay.
torus 5x5, NetworkDelay vs. B/b, r = 40M, with fixed Total_Buf_Size
550
Deflection, Total Buf Size = 100
Deflection, Total Buf Size = 200
Deflection, Total Buf Size = 500
500
450
400
NetworkDelay (ms)
an aeptably low loss rate, whih widens as the total buer
spae (B + b) beomes larger.
The negative impat of the reassembly buer on the QoS
measures pereived by the voie session onsists in inreasing
the end-to-end delay, as shown in Figure 2. The end-to-end
delay is omposed of the network delay (Figure 3) and the
playbak lag (Figure 4). Aording to these two graphs, the
playbak lag is the dominating fator, and we observe an inreasing end-to-end delay. The playbak lag inreases along
with B beause the destination buer has to be lled up to
a ertain fration of its total apaity before playbak an
ommene. (This fration was set at 80% based on the previous work [12℄.) The dereasing trend of the network delay
is not surprising beause, between its two omponents, the
queuing delay (Figure 5) and the propagation delay (Figure 6), the former is the dominating fator.
In the following, we only fous on the loss rate and the
end-to-end delay beause these two QoS metris are diretly
pereived by the end users. Figures 7 and 8 show that these
two performane measures an be traded to some extent.
Eah urve represents a single B=b ratio, with the total
amount of buer spae ranging from 100 to 1000 pakets.
We nd that, for a wide range of the total amount of buer
spae, some B=b ratios (e.g., 0, 1, 2, and 3 in Figure 7), offer onsistently aeptable loss and delay measures. It's also
interesting to note that a large ratio of B=b results in a better ombined loss and delay performane. In other words, a
large destination buer ombined with a small buer at the
router is more likely to provide both a satisfatory loss rate
and an aeptable end-to-end delay.
The relatively small amount of buer spae at the routers
at whih they appear to perform satisfatorily, and the sharp
350
300
250
200
150
100
50
0
−6
−4
−2
0
log(B/b)
2
Figure 3: Network Delay.
4
6
torus 5x5, Loss vs. Delay, r = 40M, Buffer size: 100 ~ 1000, even link length
0.8
2500
Deflection, Total Buf Size = 100
Deflection, Total Buf Size = 200
Deflection, Total Buf Size = 500
0.6
Loss
3000
2000
PlayLag (ms)
Log(B/b) = −1
Log(B/b) = 0
Log(B/b) = 1
Log(B/b) = 2
Log(B/b) = 3
0.7
torus 5x5, PlayLag vs. B/b, r = 40M, with fixed Total_Buf_Size
0.5
0.4
1500
0.3
1000
0.2
500
0
−6
−4
−2
0
log(B/b)
2
4
6
0
1000
2000
3000
4000
End to End Delay (ms)
5000
6000
Figure 7: Loss rate vs. end-to-end delay, even link
lengths
Figure 4: Playbak Lag.
torus 5x5, Loss vs. Delay, r = 8M, Buffer size: 100 ~ 1000, biased link length
0.9
Log(B/b) = 0
Log(B/b) = 1
Log(B/b) = 2
0.8
0.7
Loss
0.6
torus 5x5, QueuingDelay vs. B/b, r = 40M, with fixed Total_Buf_Size
500
Deflection, Total Buf Size = 100
Deflection, Total Buf Size = 200
Deflection, Total Buf Size = 500
450
0.5
0.4
QueuingDelay (ms)
400
0.3
350
300
0.2
250
0
1000
2000
3000
4000
End to End Delay (ms)
5000
6000
7000
200
150
Figure 8: Loss rate vs. end-to-end delay, biased link
100
lengths
50
0
−6
−4
−2
0
log(B/b)
2
4
6
Figure 5: Queuing Delay.
torus 5x5, PropDelay vs. B/b, r = 40M, with fixed Total_Buf_Size
65
60
Deflection, Total Buf Size = 100
Deflection, Total Buf Size = 200
Deflection, Total Buf Size = 500
55
5. CONCLUSIONS
PropDelay (ms)
50
45
40
35
30
25
20
15
−6
inrease in the drop rate when that small amount is redued
below a ertain minimum, are onsistent with the observations made in [11℄. In that study, it is shown experimentally
that a moderate amount of buer spae available to the
routers tends to drastially improve the maximum throughput of a deetion network, bringing it quikly to a level
omparable to that of a network with innite buers. In
onfrontation with our results, this seems to suggest that
a single-path router with a large amount of buer spae is
doubly misongured: it should be using little buer storage
while following alternative paths.
−4
−2
0
log(B/b)
2
Figure 6: Propagation Delay.
4
6
Our results suggest that deetion as a routing onept
is less harmful than it would seem at rst sight. From the
global point of view of the entire network, the reassembly
buer is not a serious problem (and does not represent a
new resoure requirement) beause its introdution redues
the resoure requirements at the routers. Besides, the destination, being well aware of the speis of its session, should
be able to make better use of the reassembly buer than a
router having to ope with multiple and essentially unknown
streams of traÆ.
One standard argument against deetion networks is that
the alternative routes inur exessive jitter, whih has a
detrimental impat on the performane of isohronous sessions. Note, however, that by buering pakets that an-
not be forwarded immediately, store-and-forward networks
hardly solve this problem. While a deetion network an
lose pakets that fall outside the window provided by the
reassembly buer, a store-and-forward network an drop
pakets beause of the lak of storage at the routers, or
beause those pakets have been delayed too muh to be
useful. There is no fundamental dierene at this level.
The issue of paket reassembly is often misguided (and
brought forward as an erroneous argument against multiplepath routing) beause of the insistene of some legay appliations on viewing their sessions as ordered sequenes of
pakets. If we look arefully at those ommuniation senarios that truly require the preservation of paket ordering, we
see that they t into three ategories:
Sessions that ould be arried out with pakets arriving
in any order (e.g., le transfers); they enfore paket
ordering beause the appliations have been (unneessarily) designed that way. Symptomati of the ralization that suh ordering is unneessary and over{
restritive, is the reent availability of appliations the
split single ftp le transfers into multiple onurrent
transfers of parts of the le, with the hope of reduing
total download times.
Sessions involving relatively short transfers (e.g., a piee
of text to appear on the sreen), whih an be reassembled in a trivially small buer spae. There is no ompeling reason for onsidering either single{path or deetion as a more preferred approah for this subset of
appliations.
Long sustained isohronous streams (e.g., voie, video),
whih typially aept a non-zero paket loss and thus
an be reasonably reonstruted within limited-size reassembly buers. Note that in this ategory, the storeand-forward single-path approah does not guarantee
zero paket loss. We thus argue that, by being inherently loss{free, deetion routing possesses a denite
advantage.
Let us onsider the Internet, and TCP in partiular. Due
to the inreasing transmission rates of links, most hosts today are apable of handling TCP sessions with relatively
large bandwidth delay produts, whih translate into large
advertised TCP reeiver windows.
The reeiver window
plays the role of a large reassembly buer apable of (a)
re-ordering pakets potentially arriving out of order, and
(b) holding pakets beyond \gaps" aused by losses, while
waiting for retransmissions to ll those gaps. However, the
eetiveness of a large reassembly buer to failitate (b) is
at least debatable, mostly beause the dynamis of TCP
onstrit the window after a loss (and TCP's approah to
window adjustments is quite onservative in general). Thus,
ase (b) provides redued performane dividends but is typial in IP-based networks, where traditional single path routing is used. We argue that TCP would gain the full potential
of reeiver reassembly buers if the balane was tilted in favor of ase (a), whih an be aomplished by deeting
pakets when ongestion ours, instead of dropping them.
More experiments are required to verify the above speulations and put them on a more formal ground. Speially, we need a better insight into the observed phenomena
that would let us extrapolate them onto realisti irregular
topologies and non-uniform traÆ patterns. This is a natural diretion for our further study.
6. REFERENCES
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[2℄ C. Baransel, W. Dobosiewiz, and P. Gburzynski.
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