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PAPER

Adaptive Thresholds of Buﬀer to Solve the Beat-Down
Problem of Rate Control in ATM Networks
Harry PRIHANTO† , Student Member and Kenji NAKAGAWA† , Member

SUMMARY ABR service is currently standardized to handle applications of data traﬃc in ATM network. As a ﬂow control
method, the rate-based ﬂow control has been adopted and applied
to manage the ABR service. Several control methods have been
proposed, and the EPRCA is selected as one of the control methods by the ATM Forum. EPRCA is an excellent algorithm, butwhen the EPRCA is applied to the ATM network, several problems occur. One of the problems is the beat-down problem, which
gives unfair allocation of transmission rate to connections. We
propose a new control method which solves the beat-down problem. We will show that, by our proposed method, (i) the ACR
is given fairly to every connection compared to the conventional
method, and also (ii) the throughput is fair for both long-hop
and short-hop connections, (iii) the ACR is proportional to thethroughput, and ﬁnally (iv) the total throughput is larger thanthat of the conventional method. The fairness of the throughput
in (ii) is measured by the fairness index. In (iii), being proportional means that the allocated ACR is close to the throughput
and it is measured by the proportion index. The performance isevaluated by computer simulation.
key words: ow control, rate-based, ABR traÆc, EPRCA, beat-down problem, ATM network
1.

Introduction

To realize Broadband Integrated Services Digital Network (B-ISDN) which is intended to provide various
services in telecommunications, Asynchronous Transfer
Mode (ATM) is one of several data transfer technologies that are proposed and currently being developed[1]. In the ATM network, information is divided into
a ﬁxed length of data block, called cell. The ATM
technology can provide high speed and high eﬃciencyof the network because a simple data transfer protocol
and wide bandwidth of optical ﬁber media are used in
the network [2].
Several services are provided and deﬁned in ATM
networks. Five classes of service are deﬁned as Constant Bit Rate (CBR), real-time Variable Bit Rate
(rt-VBR), non-real-time Variable Bit Rate (nrt-VBR),
Available Bit Rate (ABR), and Unspeciﬁed Bit Rate
(UBR) [3]–[5]. The ABR service is designed to handle applications of data traﬃc in ATM network. Asa ﬂow control method, the ATM Forum has adopted
and applied rate-based ﬂow control to manage the ABR
service. The rate-based ﬂow control is a closed-loop
Manuscript received February 17, 1999.
Manuscript revised August 16, 1999.
†
The authors are with the Department of Electrical Engineering, Nagaoka University of Technology, Nagaoka-shi,
940-2188 Japan.

control. Each source uses feedback information from a
network to manage their transmission rate. A Resource
Management (RM) cell conveys feedback information
as explicit rate from switch to the source.
Several rate-based control methods have been proposed, e.g. EPRCA (Enhanced Proportional Rate Control Algorithm), CAPC (Congestion Avoidance using
Proportional Control), ERICA (Explicit Rate Indication for Congestion Avoidance), etc. [4], [6]. EPRCA isa favorite control method in the ATM Forum at thepresent time [7]. EPRCA is an excellent algorithm,
but when the EPRCA is applied in the ATM network,
several problems occur [4], [6]. One of the problems isthe beat-down problem, which gives unfair allocation oftransmission rate to connections [10], [11]. To solve thebeat-down problem, we propose a new control method
based on EPRCA. We use variable thresholds of buﬀer
to detect the congestion state of the switch.
We show through simulation results that our proposed method has better performance than conventional method. We will show that, by our proposed
method, (i) the ACR is given fairly to every connection
compared to the conventional method, and also (ii) the
throughput is fair for both long-hop and short-hop connections, (iii) the ACR is proportional to the throughput, and ﬁnally (iv) the total throughput is larger thanthat of the conventional method. The fairness of thethroughput in (ii) is measured by the fairness index. In(iii), being proportional means that the allocated ACR
is close to the throughput and it is measured by the
proportion index.
The rest of this paper is organized as follows. After describing ABR ﬂow control in Sect. 2, we discuss animplementation of EPRCA and its problems in Sect. 3.
We describe our proposed method in Sect. 4. We consider several network models and evaluate both performance of conventional and proposed method in Sect. 5.
Finally, the conclusion will be described in Sect. 6.
2.

ABR Flow Control

Flow control refers to the set of actions taken by the
network to avoid congestion conditions. Congestion isdeﬁned as a state of network elements in which the network is not able to meet the negotiated performance
objectives for already established connections [1]. The
ABR ﬂow control is operated between source end sys-

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Table 1
Lable
PCR
MCR
ACR
ICR
CCR
TCR
N rm

Fig. 1

RIF
RDF
CDF
ADTF
TBE
CRM
FRTT

Rate-based ﬂow control.

tem (SES) and destination end system (DES). The control is a closed-loop control because there are continuous feedback of control information between the network and the SES. Generally, the ABR ﬂow control
uses control information from the network to notify the
SES to set an appropriate rate. Each switch in the
network computes the appropriate rate that is called
explicit rate (ER) for all connections which are sharing the same link. The control information such as ER
is conveyed from the network to the SES by RM cells[3]–[5]. There are two directions of the RM cell ﬂow,
forward and backward, as shown in Fig. 1.

2.2 Control Mechanism
The basic mechanism of congestion control in ABR
service requires the cooperation of SES and DES to
the network to avoid congestion by controlling theirrates. Then the SES generates RM cells in every
N rm − 1 (= 31) data cells to probe network condition. RM cells travel from the SES to the DES andback to the SES which carry feedback information of
the network such as congestion state and rate allocation. The RM cell which travels from the SES to the
DES are called forward RM (FRM) cell, and backward
RM (BRM) cell from the DES to the SES. The RM

Default value
0PCR
10 cell/s
32
1/16
1/16
1/16
0.5 ms
16,777,215
TBE/N rm-

cell contains a current cell rate (CCR), PCR, ER, andother parameters required by the SES. Details of theRM cell conﬁguration can be found in [3].
The switch gives feedback information to the SES
in every RM cell arrival. There are three types of switch
to give the feedback information[3], [4], [8]:• “binary” switch, using explicit forward congestion
indication (EFCI) bit in the header of data cells to
indicate the congestion state.
• “relative rate marking” switch, using congestion
indication (CI) bit and no increase (NI) bit in the
payload of RM cell to notify the congestion state.
• “explicit rate (ER)” switch, using other ER ﬁeld in
the payload of RM cell to give the allocation rate.

2.1 ABR Parameters
In the ABR service, each SES negotiates several operating parameters with the network at the time of connection setup. The important parameters are peak cellrate (PCR), minimum cell rate (MCR), allowed cellrate (ACR), and so on. PCR is the maximum rate
for the SES to be allowed to transmit on the link. The
SES can also request the MCR, which is the guaranteed
minimum rate. During transmitting data, the SES isallowed to transmit at particular rate that is deﬁned
as ACR. The ACR value is dynamically changed between MCR and PCR depending on network condition.
At the connection setup or after long idle interval, theACR is set to the initial cell rate (ICR). The list ofparameters used in the ABR service are shown in the
Table 1 [3].

ABR parameters.

Extension
Peak cell rate
Minimum cell rate
Allowed cell rate
Initial cell rate
Current cell rate
Tagged cell rate
Number of cells between
forward RM cells
Rate increase factor
Rate decrease factor
Cutoﬀ decrease factor
ACR decrease time factor
Time buﬀer exposure
Missing RM-cell countFixed round-trip time

The ER switch is currently used to support ABR service. When a switch receives an RM cell, the switch
may reduce the ER value in FRM and/or BRM cell tothe calculated fair rate.
When the SES receives a BRM cell, the SES should
adapt its rate to the information carried in the RM cell.
If CI bit = 0, the SES can linearly increase its rate byrate increase factor (RIF), where RIF is determined atcall setup. The increasing rate can reach the ER value
in the RM cell but should never exceed the PCR. If CI
bit = 1, the SES must exponentially decrease its rateby using rate decrease factor (RDF), where RDF is also
determined at call setup. If the rate is still greater than
the returned ER, the SES must further decrease its rate
to the returned ER but should not be lower than the
MCR.
3.

Implementation and Problems of EPRCA

Several control methods have been proposed and the
EPRCA is chosen as one of the control mechanisms by
the ATM Forum [3]. The EPRCA is a closed-loop ratebased ﬂow control. The RM cells are used to transfer
information from the SES to the DES and vice versa.
The EPRCA is implemented at ER switch in order toachieve fairness of rate allocation [6].

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3.1 EPRCA
3.1.1 Switch Behavior
The basic features of EPRCA can be described as follows [3], [4], [6], [9]. In this algorithm all the connections
are assumed to share a common queue with two congestion thresholds QT and DQT . At every time an FRM
cell arrives, the switch computes the mean allowed cellrate (M ACR) using a running exponential weigth average as follows:
M ACR = (1 − α)M ACR + αCCR,(1)where α is averaging factor and generally is chosen to
be 1/16. The FRM cells sent by the SES contain adesired ER in the ER ﬁeld, the CCR ﬁeld set to the
ACR, and the CI bit set to zero. The switch monitors
its load by observing the queue length.
On arrival of BRM cell, when the queue length
in the switch buﬀer exceeds the threshold value QT ,congestion state is detected and only those connections
whose CCR values are above the f air share, computedasfair share = DP F × M ACR,

(2)

are asked to reduce their rates. The other connections
whose CCR value are below the f air share, have no adjustments. DP F is the down pressure factor of switch,and typically set to 7/8. Furthermore when the queue
length in the switch buﬀer exceeds the second threshold value DQT , the heavy congestion is detected andall the connections are asked to reduce their rates.
3.1.2 SES Behavior
The SES adjusts its transmission rate when the SES
receives BRM cells. If no congestion information is in
the BRM cell, the SES can increase their rate by using
the following equations to calculate their allowed cellrate (ACR):
ACR ← max[M CR, min(ACR +RIF × P CR, ER, P CR)].

(3)

But if BRM cell carries some congestion information,
the SES must decrease their rate with the following
equation:
ACR ← max(M CR, ACR − ACR × RDF ).

EPRCA in the network, such as unfairness problem [4],oscillation of ACR [6], beat-down problem [6], and etc.
In this paper we focus on the beat-down problem. According to [6], the beat-down problem occurs in thebinary switch when the switch manages several typeof connections which traverse through diﬀerent number of switches. The connections passing more switches(long-hop connection) have a higher probability of getting their RM cells marked than those passing fewer
switches (short-hop connection). Therefore the longhop connections are given the ACR which are smaller
than that of short-hop connections.
We deﬁne the beat-down problem as the diﬀerenceof average ACR between short-hop and long-hop connections is too large. According to our experiment,
the ER switch also have the beat-down problem when
EPRCA algorithm is applied [10], [11]. Then we try tosolve the problem by proposing a new method which
modiﬁes the EPRCA as described in the next section.
4.

Proposed Method

The beat-down problem occurs when there are various
connections which pass diﬀerent number of hops, if theswitch handles those connections in the same mannerwithout taking the number of hops into consideration.
We propose a new method to solve the beat-down problem. We modify the EPRCA algorithm with making
longer-hop connections more advantageous by applying
adaptive thresholds.
The proposed method is described as follows:• standard threshold
As the conventional EPRCA method, the proposed
method sets 2 threshold values QT and DQT at
the switch buﬀer to detect the congestion condition. The threshold values are set permanently inthe conventional method, but the threshold values
adaptively changed in the proposed method.
• adaptive threshold
Let h and d be integers. As shown in the Fig. 2, weconsider other threshold values QT1 , . . . , QTh , . . .
and DQT1 , . . . , DQTh , . . ., as well as the original
thresholds QT and DQT . QTh and DQTh are deﬁned as follows:
QTh = QT + h × d,

(4)

Default value of the ABR parameters are shown in the
Table 1.
3.2 Problems of EPRCA
Several problems can be found when we apply theFig. 2

Proposed method.

PRIHANTO and NAKAGAWA: BEAT-DOWN PROBLEM OF RATE CONTROL IN ATM NETWORKS365

DQTh = DQT + h × d.

(5)

In the following algorithm, h means the number ofhops that the FRM cell passed and d is the increment of threshold.
• RM cell structure
An RM cell contains the information from the SES
such as PCR, MCR, CCR, ER. We add the h-ﬁeld
for counting the number of passed switches of theRM cell in the up stream. Then the h value canbe used to decide which threshold value should be
used. The initial value of the h-ﬁeld is 0.
• switch behavior
When an FRM cell arrives, the switch computes
the MACR and fair share using Eqs. (1) and (2).
Then the switch reads the h value from the h-ﬁeldof the FRM cell and computes QTh and DQTh
by Eq. (5). The switch uses the QTh and DQTh
as thresholds instead of QT , DQT . If the queue
length Q of the switch buﬀer is below QTh , theswitch decides that there is no congestion and gives
PCR to all connections. If QTh < Q ≤ DQTh ,congestion state is detected and only those connections whose CCR values are above the fairshare
are asked to reduce their rates. Furthermore, if
Q > DQTh , the heavy congestion is detected andall the connections are asked to reduce their rate.
Then, the switch increases the h value of the FRM
cell by 1 and transmit it to the output link.
• source behavior
We use Eqs. (3) and (4) for increasing and decreasing rate, respectively. Other parameters are usedsimilarly as the conventional EPRCA method.
In the conventional EPRCA, long-hop connections
are given smaller ACR than short-hop connections. It isbecause the long-hop connections have a higher probability of decreasing rate than short-hop connections.
Therefore, we use adaptive thresholds to make the rateof long-hop connections not strictly be choked at theswitch. By making longer-hop connections more advantageous, we can solve the beatdown problem.
5.

Simulation and Evaluation

We make simulation models to show that the proposed
method provides better performance than the conventional method. We design several models to evaluate
the fairness of ACR distribution and the throughput ofeach connection, and so on.
5.1 Simulation Model
We consider simulation models with 2, 3, and 4
switches. The 2 switch model is shown in Fig. 3(a).
Each node contains 10 connections. The ﬁrst switch(SW1) accommodates 10 SES’s. 5 SES’s are terminatedFig. 3

Table 2
Parameter

Simulation models.

Simulation condition.
Value

PCR
MCR
N rm
RIF, RDF
α
DPF
QT, DQT
Switch buﬀer
d for proposed method
Load per SES
Simulation time

150 Mbps
1.5 Mbps
32 cells
1
, 1
16 16
1
16
7
8

5, 10 cells
35,40,45,50 cells
5 cells
0.06-0.12
1,000,000 cell times

to the ﬁrst DES as short-connection (S1) and the otherconnections go to the next switch (SW2). New SES’s
come to the SW2 as short-hop connection (S2), they
are terminated to the last DES. Other 5 SES’s as along-hop connection (L) travel from SW1 to SW2 andterminate to the ﬁnal DES. The EPRCA is applied in
the models and we use default EPRCA parameters as

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Fig. 4

Average ACR in conventional method, 2 switch model.

Fig. 7

Average ACR in proposed method, 2 switch model.

Fig. 5

Average ACR in conventional method, 3 switch model.

Fig. 8Average ACR in proposed method, 3 switch model.

Fig. 6

Average ACR in conventional method, 4 switch model.

Fig. 9Average ACR in proposed method, 4 switch model.

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shown in the Table 1. We assume that the EPRCA
is applied in a local area network (LAN). Because thenode distances are so short, then we can assume thatthe transfer delay can be ignored.
It is important to decide an appropriate value of
QT and DQT for preventing a beat-down problem. If
we set the QT and DQT too small, the network decides that the congestion occurs very frequently, thenthe connections are choked and the throughput will go
down. On the other hand, if the QT is too large, thenetwork misses the congestion, then the total ACR exceeds the link capacity. Furthermore, if the DQT is toolarge, the beat-down problem becomes worse. This isbecause the connections can update their f air shares
many time before the queue length reaches DQT , so
the diﬀerence of the f air shares between a short-hop
and a long-hop connections enlarges. As our experiment results, we set QT and DQT value to 5, 10 cells
respectively as the best condition of EPRCA method.
Other parameters are shown in the Table 2.
Similarly to 2 switch model, 3 and 4 switch models
contain long-hop and short-hop connections. 5 SES’s
from the ﬁrst node travel through all nodes to the ﬁnal DES. New 5 SES’s enter to each node and leave
immediately for the corresponding DES. We call them
short-hop connections. The simulation models can beshown in Figs. 3(b),(c).

Fig. 10

Average ACR for 2 switch model.

5.2 Comparison of ACR Allocation

Fig. 11

Average ACR for 3 switch model.

The average ACR is deﬁned as the distributed ACR
to each connection (SES) averaged over the simulation
time. The results are shown in Figs. 4–9. We set thresholds of switch buﬀer QT = 5 cells, DQT = 10 cells.
The buﬀer size of each switch is variable from 35 to 50
cells. The average load of each SES is 0.1, then the
total oﬀered load of 10 SES’s is 1.0.
The beat-down problem appears as depicted inFig. 4. The long-hop connection (L) is given smaller
ACR value than the short-hop connections (S1, S2).
This is because the long-hop connection passes many
switches, so it has a high probability to meet the congestion at one of the switches. On the other hand, theproblem are solved when we apply the proposed method
as shown in the Fig. 7. Because of the advantage of L
connections, they can get more ACR than the conventional method.
Similarly, for 3 switch model we have the same phenomenon. See Figs. 5 and Figs. 8. In the conventional
method, the beat-down problem appears, especially at
the short-hop connection S3. The S3 has the highest
ACR among connections. We can solve the problem byapplying the proposed method. Each connection has
almost the same ACR values as seen in Fig. 8.
In the 4 switch model, we can also see that thebeat-down problem still occurs in the conventional
method, Fig. 6. The problem can be solved by applying

the proposed method as shown in Fig. 9.
According to the results, the conventional method
distributes higher ACR than the proposed method toshort-hop connections, especially to the last short-hop
connections, i.e., S2 in Fig. 4, S3 in Fig. 5, and S4 in
Fig. 6. On the other hand, by the proposed method,
the ACR are distributed fairly to every connection.
Now we evaluate the ACR which are given to each
SES versus oﬀered load. Figure 10, Fig. 11, and Fig. 12
show the average ACR of each connection at 2, 3, and4 switch models, respectively. We ﬁnd that the large
ACR are distributed when the oﬀered load is low. The
ACR are choked at the high oﬀered load because theheavy congestion is detected. The proposed method
shows better performance by appropriate ACR allocation when oﬀered load become high. For the highoﬀered load ≥ 0.7, the proposed method allocates the
ACR to long-hop and short-hop connections fairly compared to the conventional method. Because the longhop connection is applied higher threshold QTh and
DQTh , the ACR of the long-hop connection is not easy
to be choked.
5.3 Comparison of Throughput
Next, let us investigate the comparison of throughput

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Fig. 12

Average ACR for 4 switch model.

Fig. 15

Throughput for 4 switch model.

Table 3 Fairness Index for 2 switch model.
Oﬀered load
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Conventional 1.00 1.19 1.40 1.48 1.50 1.59 1.62
Proposed
1.00 1.10 1.21 1.28 1.27 1.28 1.30

Table 4 Fairness Index for 3 switch model.
Oﬀered load
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Conventional
Proposed

Fig. 13

Throughput for 2 switch model.

Throughput for 3 switch model.

1.20
1.16

1.68
1.26

2.16
1.27

2.22
1.30

2.33
1.28

2.37
1.27

Table 5 Fairness Index for 4 switch model.
Oﬀered load
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Conventional 1.00 1.21 1.71 2.61 2.88 2.89 2.91
Proposed
1.00 1.20 1.58 1.71 1.75 1.74 1.82

5.3.1

Fig. 141.00
1.00

Fairness Index

We here deﬁne the f airness index as the ratio of the
maximum throughput among connections to the minimum throughput. If the fairness index is close to 1.0, we
can say that the throughput of every connection is fair.
We calculate the fairness indices for the conventional
and proposed methods and show them in Tables 3, 4,
and 5. We see from these tables that the fairness index
of the proposed method is smaller than that of the conventional method. The fairness between the long-hop
and short-hop connections is improved by the proposed
method.
5.4 Allocation of ACR Proportional to Throughput

performance between the conventional EPRCA and the
proposed method. We deﬁne the throughput as the average transmitted information rate during the simulation. Figure 13, Fig. 14, and Fig. 15 show the throughput of each connection at 2, 3, and 4 switch models,
respectively. We see that the diﬀerence of the throughputs between long-hop and short-hop connections by
the proposed method is smaller than that by the conventional method. We will examine the diﬀerence numerically with the following fairness index.

We deﬁne the proportion index as the ratio of theaverage ACR over all the connections to the averagethroughput. If the proportion index is close to 1.0, we
can say that the ACR is allocated proportionally to thethroughput for every connection. We show in Table 6
the proportion indices in the case of the oﬀered load
is 0.9. We see that the proportion index of the proposed method is smaller than that of the conventional
method. The ACR is proportionally allocated by thePRIHANTO and NAKAGAWA: BEAT-DOWN PROBLEM OF RATE CONTROL IN ATM NETWORKS

369
Table 6model
Conventional
Proposed

Table 7

Proportion Index.

2 switch
1.41
1.19

3 switch
1.72
1.05

4 switch
2.41
1.31

Total throughput at each switch on average.

model
Conventional [Mbps]
Proposed [Mbps]

2 switch
94.07
94.69

3 switch
91.47
94.66

4 switch
89.23
92.12

proposed method.
5.5 Total Throughput at a Switch
Total throughput at a switch is deﬁned as the sum of
the throughputs of all the connections which enter tothe switch. We calculate the total throughputs at eachswitch and take the average over all switches and show
the average values in Table 7 in the case of the offered load is 1.0. We see that the total throughputs ofthe proposed method are larger than the conventional
method, either in the 2, 3, or 4 switch models. Although the throughputs of short-hop connection in the
proposed method are smaller than that in the conventional method, the throughputs of long-hop connection
are larger. As a result, the total throughput at a switch
becomes larger than that of the conventional method.
6.

[5] R. Jain, et al., “Source behavior for ATM ABR traﬃc management: An explanation,” IEEE Commun. Mag., vol.34,
pp.50–57, Nov. 1996.
[6] A. Arulambalam, et al., “Allocating fair rates for available
bit rate service in ATM networks,” IEEE Commun. Mag.,
vol.34, pp.92–100, Nov. 1996.
[7] A. Pitsilides, et al., “Eﬀective control of traﬃc ﬂow in ATM
networks using fuzzy explicit rate marking (FERM),” IEEE
J. Sel. Areas Commun., vol.15, no.2, pp.209–225, Feb. 1997.
[8] T. Kubo, “Traﬃc issues in ATM LAN—Principle and practice,” IEICE Trans. Commun., vol.E81-B, no.5, pp.840–848,
May 1998.
[9] M. Hashmani, et al., “ABR congestion control in ATM networks and proposal of EPRCAM,” IEICE Trans. Commun.,vol.E81-B, no.11, pp.2064–2071, Nov. 1998.
[10] H. Prihanto and K. Nakagawa, “Problems in enhanced
proportional rate control algorithm (EPRCA),” IEICE
Shinetsu-Shibutaikai, Oct. 1997.
[11] R. Soelistijorini, “A study of rate-based ﬂow control in
ATM networks,” Bachelor Thesis, Nagaoka University ofTechnology, March 1998.
[12] H. Saito, et al., “Performance issues in public ABR service,”
IEEE Commun. Mag., vol.34, pp.40–48, Nov. 1996.
[13] H.B. Chiou and Z. Tsai, “An age priority packet discarding
scheme for ATM switches on internet backbone,” IEICE
Trans. Commun., vol.E81-B, no.2, pp.380–391, Feb. 1998.
[14] D.H.K. Tsang and W.K.F. Wong, “A two-level ﬂow control
scheme for ABR traﬃc in ATM networks,” IEICE Trans.
Commun., vol.E79-B, no.11, pp.1633–1640, Nov. 1996.

Conclusion

When the original EPRCA is applied in the switch,several problems occur. The beat-down problem is oneof the problems that appears not only in the binary
switch but also in the ER switch. We show the problem by simulation models. Then we proposed a newalgorithm based on the EPRCA to solve the beat-down
problem. By the simulation, the average ACR is allocated fairly either to long-hop and short-hop connections. We ﬁnd that the throughputs are fair forboth long-hop and short-hop connections. Moreover,the proposed method allocates the ACR proportionallyto the achieved throughput. We ﬁnd also that the total
throughput at each switch is larger than the conventional method.
References[1] L.G. Cuthbert and J.-C. Sapanel, “ATM the broadband
telecommunications solution,” IEE, London, 1994.
[2] F. Bonomi and K.W. Fendick, “The rate-based ﬂow control
framework for the available bit rate ATM service,” IEEE
Commun. Mag., vol.9, no.2, pp.25–39, March/April 1995.
[3] The ATM Forum, “Traﬃc Management Speciﬁcation version 4.0,” ftp://ftp.atmforum.com/pub/approved-specs/aftm-0056.000.pdf, April 1996.
[4] R. Jain, “Congestion control and traﬃc management in
ATM networks: Recent advances and a survey,” Computer
Networks and ISDN System, vol.28, pp.1723–1738, 1996.

Harry Prihanto
was born in Jakarta,
Indonesia, on 6 December, 1966. He received the B.Eng. degree in electronics
from Yamanashi University in 1992 andthe M.Eng. degree in electronics from Nagaoka University of Technology in 1996.
In 1992, He joined the Association for
Overseas Technical Scholarship (AOTS)
training program at the Data Transmission Laboratories, NEC Co. Ltd. Japan.
In 1993, he joined with the Directorate
for Engineering Science, Agency for the Assessment and Application of Technology (BPPT), Jakarta, Indonesia. Since 1996
he has been a Doctorate student at the Department of Electrical Engineering, Nagaoka University of Technology. His researchinterests include network management and B-ISDN traﬃc management. He is a student member of IEEE. He is also a memberof Indonesian Society on Electrical, Electronics, Communication
and Information (IECI) and Institute for Science and Technology
Studies (ISTECS).

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Kenji Nakagawa
was born in Yamanashi, Japan, on 28 January, 1957. Hereceived the B.S., M.S., and D.S. degrees
in mathematics from Tokyo Institute ofTechnology in 1980, 1982, and 1986, respectively. In 1985, he joined the Basic Research Laboratories, NTT (Nippon
Telegraph and Telephone Corp.). Since
1992, he has been an associate professorof Nagaoka University of Technology. His
research interests include information theory, statistics, and queueing theory. Dr. Nakagawa is a memberof the Society of Information Theory and its Application, theIEEE, and the Mathematical Society of Japan.