Router buffer re-sizing for short-lived TCP flows
Takeshi Tomioka

Go Hasegawa, Masayuki Murata

Graduate School of Law
Osaka University
1-6 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan
Email: q06065h@lawschool.osaka-u.ac.jp

Graduate School of Information Science and Technology
Osaka University
1-32 Yamadaoka, Suita, Osaka, 565-0871, Japan
Email: {hasegawa, murata}@ist.osaka-u.ac.jp

Abstract— Traditionally, the size of router buffers is determined by the bandwidth-delay product discipline (normal discipline), which is the product of the link bandwidth and averageround-trip time (RTT) of flows passing through the router. However, recent research results have revealed that when the numberof flows is sufficiently large, the buffer size can be decreased tothe bandwidth-delay product divided by the square-root of thenumber of flows (sqrtN discipline), without introducing underutilization of the link bandwidth. This assertion has been verified
mainly for long-lived flows; in contrast, there has not been athorough verification of short-lived flows, which are the majority
of Internet flows. Furthermore, the effects of network parameters,such as the link bandwidth and propagation delay, have notbeen investigated. In this paper, we compare the performanceof the above two disciplines, normal and sqrtN, for sizing therouter buffer. We focus on the performance of both long-lived andshort-lived TCP connections traversing the router under various
network environments. Through extensive simulations, we showthat the sqrtN discipline would degrade the TCP performance interms of the packet loss ratio and file transmission delay, and it
may be useful only when the transferring file size is about 50-100
Kbytes or when the propagation delay between the sender andthe receiver hosts is significantly small.
Index Terms— router, buffer size, TCP, bottleneck link, accesslink, bandwidth, bandwidth delay productI. I NTRODUCTION
Today, many applications rely on Transmission Control
Protocol (TCP) [1] to avoid and resolve congestion in theInternet. Although other applications utilize User Datagram
Protocol (UDP) [2] to control the network congestion on
their own, the proportion of UDP traffic is very small compared with TCP traffic on the current Internet [3]. Therefore,
evaluating the performance of TCP traffic on a network isvery important. TCP performance is largely affected by theround-trip time (RTT) and packet loss ratio of the network
path [4, 5]. The output link buffer of almost all of Internet
routers deploys the First-In First-Out (FIFO) discipline, andthe size of this buffer affects the RTT and packet loss ratioof TCP connections passing through the router. Packets canaccumulate at this buffer and cause a queuing delay and delayvariance. It also causes packet losses when packets arrive ata fully-utilized buffer. Therefore, the packet loss ratio can be
reduced by utilizing a larger-sized buffer, but this can causea larger queuing delay since a larger number of packets areaccumulated at the buffer.
The size of router buffers is traditionally determined based
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on a rule-of-thumb attributed to [6]. As stated in this paper, thesize of a router’s buffer should be more than B = C × RT T :that is, the product of the link bandwidth and the average
RTT of flows that pass through the router. This is well known
as the bandwidth-delay product discipline (we call this thenormal discipline in this paper), and many routers are equippedwith a buffer whose size is determined by this discipline. Thisdiscipline is also described in a recent RFC [7].
However, according to [8], it is difficult to construct arouter buffer based on this discipline due to the hardware
limitation. Today’s backbone networks generally carry morethan 10,000 concurrent flows and their link bandwidth is
2.5 Gbps or 10 Gbps [9]. If the average RTT equals 250 msec,
a 10 Gb/s router needs 250 msec ×10 Gbps = 2.5 Gbits
for its buffer. The size of the largest commercial static RAM(SRAM) chip is currently 72 Mbits, which means many SRAM
chips are needed to provide a 2.5 Gbps buffer. This size also
results in large overhead in terms of board size, electrical
power consumption, and monetary cost. On the other hand,a dynamic RAM (DRAM) chip is available up to 1 Gbps
and it has significant advantages in monetary cost and board
size. However, DRAM has a random access time of about
tens of ns, which is from 5 times to 10 times slower thanthat of SRAM. Therefore, the problem will become worse
as line-rates increase in the future. In addition, the electrical
power consumption of DRAM is larger than that of SRAM. In
summary, it is extremely difficult to build a router buffer for
current and future high-speed networks based on the normal
discipline.
One possible solution for this problem is stated in [8]. It
is shown that the router buffer size can be reduced to the
bandwidth-delay product divided by the square root of the√ T , when there arenumber of flows, N , that is, Bs = C×RT
N
many flows (500 or more) passing through the link. We callthis guideline the sqrtN discipline. The authors in [8] assertthat this small buffer size is enough to keep the link utilization
as well as that in the normal discipline. In [10], the authors
state that we need only tens of packets for the router buffer
size when the input link bandwidth is far smaller than the
output link bandwidth (for example, 10 Mbps input and 1 Gbps
output), and/or when using pacing TCP [11] (TCP which
prevents the data packet from being sent in bursts).
However, these studies pay attention only to the utilizationof the bottleneck link bandwidth as a performance metric

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in the simulations and implementation experiments, and theperformance of TCP flows passing through the router is almost
ignored. In addition, the network environments in these experiments are quite limited and the effects of various network
parameters, such as link bandwidth and propagation delay,
have not been investigated. Furthermore, we believe that theconditions stated in [10] cannot be satisfied in future networks:
the link bandwidth of the access network is increasing rapidly
in recent years, and pacing TCP is not currently widespreadand is not easily implemented, especially when the access link
bandwidth increases. One possible way to spacing TCP packets is to use traffic shaping mechanism at the network edge.
However, most of traffic shaping mechanisms would arrowsmall burst of packets, so the short packet-burst generated by
the slow start phase of a TCP connection can not be spaced
effectively.
Therefore, in this paper, we evaluate the effect of the buffer
size on the following, in addition to link utilization: the packet
loss ratio and queuing delay at the router, and the performanceof TCP flows passing through the router. Especially, we focus
on the performance of short-lived TCP connections when asmall-sized buffer is used at the bottleneck link, since theperformance of a short-lived TCP data transfer is affected
not only by various factors of the bottleneck link utilization,
but also by factors including the RTT, packet loss ratio andavailable bandwidth. We also investigate the effect of othernetwork parameters such as the propagation delay and physicalcapacity of the bottleneck link, and derive the parameter range
where the sqrtN discipline is effective or ineffective.
As we know, [12] is the only paper which discusses theeffect of the router buffer size on the performance of shortlived TCP connections. It revealed that the packet loss ratio
becomes larger when we use the smaller-sized buffer recommended in [8], and it sometimes hinders the performance of
TCP data transfer. However, the investigation in [12] wasdone with a fixed network environment, and the authors
only considered congested networks with almost 100% link
bandwidth utilization. In this paper, on the other hand, weinvestigate the effects of the network parameters and consider
under-utilized networks where the link utilization is far below
100%. We also consider the realistic distribution of the filesizes which TCP connections transmit, unlike the fixed value
for transferred file sizes used in [12].
The rest of the paper is organized as follows. Section 2
reviews the two disciplines for determining router buffer size:that is, the normal discipline and the sqrtN discipline. Section 3
describes the network model, parameter setting, and evaluation
metric for the simulations. In Section 4, we show extensive
simulation results and discuss router buffer sizing. Section 5
concludes the present paper and gives some future areas ofstudy.
II. G UIDELINES FOR ROUTER BUFFER SIZING
A. Normal (bandwidth-delay product) discipline
The traditional guideline for setting the buffer size basedon the bandwidth-delay product is described in [6]. We callISBN # 1-56555-317-9

this guideline the normal discipline. In what follows, we
introduce the fundamental reasons for the normal discipline.
For a detailed explanation, please refer to [6].
The changes in the congestion window size of a TCP
connection in the congestion avoidance phase can be modeled
as additive-increase and multiplicative-decrease (AIMD) in
versions of TCP such as Reno [13] and NewReno [14].
Figure 1 presents the typical behavior of a single TCP-Reno
flow passing through a single-bottlenecked-router network.
The top graph shows the time evolution of the queue length at
the bottleneck router buffer, and the bottom graph shows thechanges in the congestion window size of the TCP connection,
where Bmax is the buffer capacity. We assume the bottleneck
link bandwidth is C. From time t1 , the sender starts filling thebuffer until a packet is dropped because of the full buffer (attime t2 ). About one RTT later, the sender receives duplicate
ACKs. Then, the sender retransmits the lost packet, and halves
its window size from Wmax to Wmax /2 (at time t3 ). Before
the time t3 , the sender is allowed to have Wmax outstanding
packets. But after time t3 , the sender is only allowed to have
Wmax /2 outstanding packets. So, the sender must stop sending
packets until it receives Wmax /2 ACK packets. This means
the number of packets in the buffer decreases while the senderstops sending packets (from time t3 to time t4 ). After time t4 ,the sender increases it’s window size, so the number of packets
in the buffer again increases after time t5 .
If the buffer goes empty before time t5 comes, the routercannot send packets onto the bottleneck link at a constantrate, so the link utilization becomes less than 100%. While
the router’s buffer is not empty, the sender’s ACKs arrival
rate equals the bottleneck link bandwidth C. So, the senderstops sending packets for (Wmax /2)/C seconds to wait for
Wmax /2 ACK packets. On the other hand, the buffer is
emptied after Bmax /C seconds. Therefore, if Bmax /C isless than (Wmax /2)/C, the buffer is emptied. That is, thefollowing condition should be satisfied to avoid the buffer
becoming empty:
Bmax ≥ Wmax /2(1)

The amount of data packets that exist on the bottleneck link
can be shown as C × RT T where RT T is the average RTT
value of TCP connections passing through the link. If Wmax /2
is larger than C × RT T , we can keep the bottleneck link fully
utilized. Therefore, we require the following condition to besatisfied:
Wmax /2 = C × RT T
(2)
Finally, Equations (1) and (2) lead to
Bmax ≥ Wmax /2 = C × RT T

(3)

In summary, if Bmax ≥ C ×RT T is satisfied, the buffer nevergoes empty, and we can take full advantage of the bottleneck
link capacity.
In a backbone network, many TCP flows share the bottleneck link. However, the above discussion still holds true if
the flows are synchronized. When N TCP flows exist at the110

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BufferOccupancy

1RTT

Bmax

t1
Cogestion
Window Sizet2 t3 t5

time

t3 t4

time

Wmax
Wmax
2

Fig. 1.

Fig. 2.

The time evolution of the congestion window and the queue length

bottleneck link, we can consider that an individual flow has abandwidth of C/N [15-18]. This means that each flow needs
more than C/N × RT T for the buffer capacity. Therefore, thebuffer capacity needed can still be shown as follows:(C/N × RT T ) × N = C × RT T

(4)

B. Square-root discipline
In [8], the authors propose decreasing the router buffer size
to the bandwidth-delay product of the network divided by thesquare-root of N , which is the number of concurrent TCP
connections passing through the bottleneck router, when n issufficiently large (typically larger than 500). In this paper, wecall this guideline the sqrtN discipline.
The window sizes of TCP connections usually change
synchronously when the number of concurrent connections issmall and their RTTs are almost equal [15-18]. This means
when a certain connection halves its window size, the others
do the same simultaneously [15]. This is because of the natureof the drop-tail buffer at the bottleneck link, which causes
bursty packet losses when the buffer overflows.
However, flows are not synchronized in many cases. For
example, small variations in RTTs or processing times are
sufficient to prevent synchronization [19]. The absence ofsynchronization has been demonstrated in real networks [9,20]. Even if flows do not have a diversity of RTTs, they
can become asynchronous when there are more than 500
concurrent flows [8]. In what follows, we briefly introduce therequired buffer size when TCP flows are not synchronized. For
details, please refer to [8].
The queue occupancy Q(t) of N flows at time t canbe derived by using the congestion window size of eachconnection Wi (t):

 N

(5)
Q(t) = max 0,
Wi (t) − (RT T × C)
i=1

Since the average value of the sum ofthe congestion window
Nsize of all flows is obtained as W = i=1 Wi (t), the averagequeue occupancy Q is given by:
Q = max(0, W − (RT T × C))(6)

Q > 0, the average congestion window size of each flow, Wi ,can be calculated from Equation (6) as follows:
Wi = W /N =RT T × C + Q
RT T × C + Bmax≤
N
N

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(7)

Network topology for simulations

The standard deviation of distribution of the change in thecongestion window size, σwi , can be described by the following equation, based on the assumption that the change in thesum of the window size of all connections follows the normal
distribution:1
σwi = √ Wi(8)
3 3
For a large number of flows, the standard deviation of the sumof the windows, σwi , is given by√
σ w ≤ N σ wi
(9)From Equations (7) - (9) the standard deviation of the queue
occupancy, Q, is shown as:
RT T × C + Bmax
1 RT T × C + Q√√
σQ = σw ≤ √
≤
3 3
N
N
(10)
Therefore, we obtain the following lower bound for the link
utilization:
⎞
⎛
√
B
3
3
max
⎠
(11)
U til ≥ erf ⎝ √max
2 2 RT T ×C+B√
N

For example,
if there are 10000 concurrent flows, U til ≥√erf ( 32√32 )  0.9899 when we set Bmax = RT√TN×C . This
result means that we can achieve 98.99% of the link utilization
with the buffer whose size is the bandwidth-delay productdivided by the square-root of the number of flows, that is,
Bs = RT√TN×C . In [8], the effectiveness of the sqrtN discipline
is confirmed by the simulations and the experiments, butattention is given mainly to the long-lived TCP flows. For
accommodating short-lived flows, it is only stated that small
buffers are needed from the aspect of the maintenance of link
utilization. It is a straightforward expectation that when weuse a smaller buffer, the packet loss ratio increases, which isalso shown in [8]. However, there is no description of how
the packet loss ratio influences the performance of short-lived
traffic.
Then, in the following sections, we clarify the influence ofa small size of buffer on short-lived flows through extensive
simulations.
III. E VALUATION ENVIRONMENT
A. Network and traffic model
We evaluate the performance of the two disciplines forbuffer sizing using ns-2 [21] simulations. The network model

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100

Link utilization [%]

80

60

6

40 sqrtN - Packet loss ratio

4

20

2
normal - Packet loss ratio

00
100 200 300 400 500 600 700 800 9001000
Number of hosts(a) P2P traffic

Component

Probability Density Function

80

File Sizes - Body−(lnx−µ) /2σ√p(x) = exσ 2πFile Sizes - Tailp(x) = αkα x−α+1

Inactive OFF Timesp(x) = αkα x−α+1

Parameters

Link utilization [%]µ = 9.357
σ = 1.318
k = 133K
α = 1.1
k=1
α = 1.5

Table I shows the parameters of the SURGE model. For
both traffic models, we change the traffic volume by changing
the number of sender/receiver terminals (N ).

IV. S IMULATION RESULTS AND DISCUSSIONS
A. Basic performance
Figure 3 shows the change in the link utilization and packet
loss ratio when the number of hosts N is changed, where allsender hosts use the P2P traffic model (Figure 3(a)) and the
Web traffic model (Figure 3(b)). We set C=100 Mbps and
D=90 msec.
Figure 3(a) shows that when the buffer size is determinedby the normal discipline, high link utilization can be obtained
regardless of the number of hosts. This is simply because thelarger buffer size brings the lower packet loss ratio. However,ISBN # 1-56555-317-9

sqrtN - Utilization

8

60

6

40

4
normal - Packet loss ratio

20

sqrtN - Packet loss ratio

2

0
0
100 200 300 400 500 600 700 800 9001000
Number of hosts

B. Metrics for the performance evaluation
We observe the behavior of the packet at the bottleneck
link router. We calculate the link utilization from the numberof packets that pass per unit time, and the packet loss ratio
from the number of lost packets and the number of packets
that arrive at the router. For the Web traffic, we check the filetransfer time, which is the time from the beginning of the filetransmission to the reception of the ACK packet corresponding
to the last packet. The packet loss ratio for each file transfer isalso derived to check the relationship between the transferredfile size and packet loss ratio.

10

normal - Utilization

Packet loss ratio [%]

100

2

8

sqrtN - Utilization

TABLE IS UMMARY S TATISTICS FOR M ODELS USED IN SURGE [22]210normal - Utilization

Packet loss ratio [%]for simulations is depicted in Figure 2. The model consistsof sender/receiver terminals (S1 to SN and R1 to RN ), twointermediate routers, and links interconnecting terminals androuters. The link between the two routers is a bottleneck linkwith a D msec propagation delay and C Mbps bandwidth.
The links between the terminals and routers have a 5 msec
propagation delay and bandwidth equal to the bottleneck link
if not notified. We change N , C, D, and the access link
bandwidth in the simulations and investigate the performanceof the two buffer sizing disciplines.
We use two kinds of traffic models: P2P traffic and Web
traffic. In the P2P traffic model, the sender terminals havean infinite amount of data and continue sending the data
by using an FTP-like protocol. In the Web traffic model,on the other hand, the sender terminals determine their data
(file) sizes and data transfer intervals based on the Scalable
URL Reference Generator (SURGE) model [22]. SURGE isa realistic Web workload generation tool that mimics a set ofreal users accessing a server.

(b) Web traffic

Fig. 3.

Influence of buffer size to link utilization and packet loss ratio

when the sqrtN discipline is used, the link utilization decreases
when the number of hosts becomes small (less than 800 hosts).
This degradation is as much as 20% of the bottleneck link
bandwidth, especially when the number of multiplexed flows
is small. Furthermore, we can recognize the larger packet loss
ratio, regardless of the number of flows, compared with thenormal discipline. However, we conclude that the assertion in[8] is correct because the link utilization is almost 100% when
there is a large enough number of hosts (concurrent flows).
That is, when we have sufficiently many co-existing persistentflows, we can reduce the buffer size without degradation of
the link utilization.
In Figure 3(b) for Web traffic, we can observe that the link
utilization with the sqrtN discipline is also lower than thatwith the normal discipline when short-lived TCP flows are

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accommodated. We should note here that the link utilization
with the sqrtN discipline becomes degraded in under-utilized
networks; even when the link utilization with the normal
discipline is around 60-80%, the sqrtN discipline further
degrades the link utilization. We also note that the packet
loss ratio with the sqrtN discipline does not decrease to zeroeven when the number of hosts is small, whereas that of thenormal discipline becomes zero when the number of hosts
is less than 700. This is mainly due to the bursty natureof short-lived Web traffic. That is, the small buffer with thesqrtN discipline cannot absorb the bursts of packets from theshort-lived TCP connections in the slow-start phase of theirpacket transmission. However, the link utilization becomesalmost 100% when the number of hosts is sufficiently large.
Therefore, the assertion in [8] is also confirmed even withshort-lived Web traffic.
In the following, we investigate whether the conclusion in[8] remains true even when the network environment changes,
and we check the characteristics of the sqrtN discipline interms of the performance of each TCP flow passing throughthe router.

22

Packet loss ratio [%]

18
16
14
12
10
8
6
4
0

18
normal-900node
normal-1200node
normal-1500node
sqrtN-900node
sqrtN-1200node
sqrtN-1500node

16
Data transfer delay [sec]We next discuss whether the normal discipline or the sqrtN
discipline should be applied when the network environmentchanges. This section gives the guidelines for sizing a routerbuffer for future high-speed networks.
1) Traffic volume: Figures 4 and 5 depict the change ofthe packet loss ratio and data transfer delay as a functionof the transferred file size when the number of hosts, corresponding to the traffic volume, is changed. We utilize the
Web traffic model for each sender host, and set C=100 Mbps
and D=20 msec (Figure 4) and 90 msec (Figure 5).
Figures 4(a) and 5(a) show that the packet loss ratio withthe sqrtN discipline is always higher than that with the normal
discipline. This is confirmed by Figure 3 in the previous
subsection. We also point out that the packet loss ratio with thesqrtN discipline increases as the transferred file size decreases
when D=20 msec, whereas that with the normal discipline
remains almost constant. This is because TCP connections
with a small data size have a strong bursty nature in theirpacket transmission, and the smaller buffer with the sqrtN
discipline cannot absorb the burstiness.
However, the difference in the packet loss ratio does notaffect enough the data transfer delay. From Figures 4(b)and 5(b), we can observe that effect of the high packet loss
ratio with the sqrtN discipline to the data transfer delay issmall when D=20 msec, whereas it causes a larger transfer
delay when D=90 msec. This is because the RTT valuesof the TCP connections become small when the propagation
delay is small, and this feature brings quick detection of thepacket losses and their retransmission. Consequently, the sqrtN
discipline conceals the bad effect in the increase of packet
loss ratio. On the other hand, when the RTTs are large, as in
Figure 5, the higher packet loss ratio brings the larger datatransfer delay, as we expected.

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes](a) Packet loss ratio

B. Effect of the change in network environment

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normal-900node
normal-1200node
normal-1500node
sqrtN-900node
sqrtN-1200node
sqrtN-1500node

20

14
12
10
8
6
4
2
0
0

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes](b) Data transfer delay

Fig. 4.

Effect of transferred data size (D=20 msec)

2) Access link bandwidth: Figures 6 and 7 show thechange of the packet loss ratio and data transfer delay as afunction of the transmitted file size when we change the accesslink bandwidth. We set C=100 Mbps, N =1500, D=20 msec
(Figure 6) and 90 msec (Figure 7).
From both figures, we can observe that the packet loss ratio
increases when the access link bandwidth increases. This isbecause the bursty nature increases and some of the bursty
packet transmissions cannot be absorbed at the router buffer.
However, the characteristics of the two disciplines wouldchange drastically if we changed the propagation delay of thebottleneck link (D). When D is small (in Figure 6), the two
disciplines have almost the same value for the packet loss
ratio, and this causes an almost identical trend in the datatransfer delay in Figure 6(b). When we increase D, however,

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12

20

Packet loss ratio [%]

10
8

15

Packet loss ratio [%]normal-900node
normal-1200node
normal-1500node
sqrtN-900node
sqrtN-1200node
sqrtN-1500node

6
4

10
normal-256Kbps
normal-4Mbps
normal-64Mbps
sqrtN-256Kbps
sqrtN-4Mbps
sqrtN-64Mbps

5

2
0

0
0

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

0(a) Packet loss ratio(a) Packet loss ratio

20

18
normal-900node
normal-1200node
normal-1500node
sqrtN-900node
sqrtN-1200node
sqrtN-1500node

16
14

normal-256Kbps
normal-4Mbps
normal-64Mbps
sqrtN-256Kbps
sqrtN-4Mbps
sqrtN-64Mbps

16Data transfer delay [sec]18
Data transfer delay [sec]20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

12
10
8
6
4

14
12
10
8
6
4
2

2
0

0
0

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

0(b) Data transfer delay
Fig. 5.

(b) Data transfer delay

Effect of transferred data size (D=90 msec)

Fig. 6.

the sqrtN discipline has a quite larger value for the packet
loss ratio compared with the normal discipline (Figure 7(a))
and the data transfer delay is affected by the difference in thepacket loss ratio. This is because, when D is large, the buffer
size in the normal discipline increases significantly, which canabsorb the bursty packet arrivals from the TCP senders.
3) Bottleneck link propagation delay: We investigate last
the effect of the propagation delay of the bottleneck link.
Figure 8 shows the change of the packet loss ratio and thedata transfer delay when the bottleneck link propagation delay
is changed to C = 100 Mbps and N = 1000.
From this figure, we can also observe the higher packet
loss ratio in the sqrtN discipline regardless of the propagation
delay and transferred data size (Figure 8(a)). However, it does
not always degrade the data transfer delay (Figure 8(b)). In
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20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

Effect of the bandwidth of the access link (D=20 msec)

particular, when either the propagation delay or the transferreddata size is small, the data transfer delay remains almost thesame as that in the normal discipline. When the propagation
delay is small, the detection and retransmission of the lost
packets in the network can be carried out in a small amountof time, which overcomes the increase in the packet loss ratio.
When the transferred data size is small, on the other hand, theeffect of the packet loss ratio becomes small, as described in
the mathematical analysis in [4].
4) Bottleneck link bandwidth: Figure 9 shows the change
in the packet loss ratio as a function of the bottleneck
link bandwidth when we set D=20 msec (Figure 9(a)), and
D=90 msec (Figure 9(b)). Here we set N =1500.
It can be seen that the link utilization with the sqrtN
discipline is smaller than that with the normal discipline. Es-

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20

25
normal-256Kbps
normal-4Mbps
normal-64Mbps
sqrtN-256Kbps
sqrtN-4Mbps
sqrtN-64Mbps

20
Packet loss ratio [%]Packet loss ratio [%]15

normal-10ms
normal-50ms
normal-90ms
sqrtN-10ms
sqrtN-50ms
sqrtN-90ms

10

5

15

10

5

0

0
0

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

0(a) Packet loss ratio(a) Packet loss ratio

18

20
normal-256Kbps
normal-4Mbps
normal-64Mbps
sqrtN-256Kbps
sqrtN-4Mbps
sqrtN-64Mbps

1412normal-10ms
normal-50ms
normal-90ms
sqrtN-10ms
sqrtN-50ms
sqrtN-90ms

18
Data transfer delay [sec]Data transfer delay [sec]

16

10
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6
4
2

16
14
12
10
8
6
4
2

0

0
0

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

0(b) Data transfer delay
Fig. 7.

20 40 60 80 100 120 140 160 180 200
DataSize [KBytes](b) Data transfer delay
Fig. 8.

Effect of the bandwidth of the access link (D=90 msec)

pecially, in Figure 9(a), the sqrtN discipline loses up to about
10% of the link bandwidth utilization when the bottleneck
link bandwidth is large. These results mean that the sqrtN
discipline would hinder the utilization of link bandwidth in
the under-utilized network, whereas it can maintain the link
utilization in the congested network. The main reason for thisresult is that the packet loss ratio in the sqrtN discipline neverdecreases to zero, even when the bottleneck link bandwidthis sufficiently large. This is one of the negative effects of asmaller-sized buffer at the bottleneck link.
C. Summery
When buffer’s size is determined by using a sqrtN discipline, if there are many flows, the utilization of the bottleneck
link almost equal to the case of a normal discipline. but about
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20 40 60 80 100 120 140 160 180 200
DataSize [KBytes]

Effect of the bottleneck link propagation delay

the packet loss ratio of each flow, it becomes higher, andif the case where transferred data size nor a bottleneck linkpropagation delay are small, data transfer delay also becomeslarge.
When network load is high, the influence of increasing theamount of traffic is not so large. but when network load is low,
since the packet loss ratio does not fall, even if a bottleneck
link bandwidth is large, compared with a normal discipline,
the utilization of the link and a data transfer performance
deteriorate.
From these things, sqrtN discipline is useful in a network
which includes enough hosts in order to enlarge bottleneckload and small data occupies the greater part of the flow and/or
the bottleneck link propagation delay is short.
However, on the present Internet, much traffic with large

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normal - Utilization

Link utilization [%]80

8sqrtN - Utilization
60

40

20

and short-lived traffic flows. However, we revealed that thesqrtN discipline would degrade the performance of each TCP
flow passing through the bottleneck link in terms of packet
loss ratio and file transmission delay, and it can maintain eachflow’s performance only when the file transfer size is around50-100 Kbytes or when the propagation delay between thesender and the receiver hosts is significantly small.
In the future, we will investigate the effect of pacing TCP
on the buffer sizing problem. Furthermore, we will intensively
study the conditions in which TCP connections sharing thebottleneck link behave synchronously, which would significantly affect the buffer sizing.

10

6

sqrtN - Packet loss ratio

normal - Packet loss ratio

4

Packet loss ratio [%]100

2

R EFERENCES
00
200 300 400 500 600 700 800 900 1000
Bottleneck Link BandWidth [Mbps](a) Effect of the bandwidth of the bottleneck link (D=20 msec)

normal - Utilization

Link utilization [%]80

8sqrtN - Utilization

60

40

20

10

6

4
sqrtN - Packet loss ratio
normal - Packet loss ratio

Packet loss ratio [%]

100

2

0
0
200 300 400 500 600 700 800 900 1000
Bottleneck Link BandWidth [Mbps](b) Effect of the bandwidth of the bottleneck link (D=90 msec)

Fig. 9.

Packet loss ratio

data sizes, such as P2P, is also flowing. Moreover, as for flows
other than TCP, such as UDP, the increase in a packet loss ratio
has big influence on communicative quality, and a backbone
network are designed so that an average utilization of the link
may become low. From these things, It is conjectured to havea bad influence on the performance of TCP to use a sqrtN
discipline under the present environment .
V. C ONCLUSION
In this paper, we compared the performance of the above
two disciplines for router buffer sizing, and we especially
focused on the performance of TCP connections traversing
the router. Through extensive simulations, we confirmed thatthe sqrtN discipline can maintain utilization of the bottleneck
link when there is enough traffic volume for both long-lived
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