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Designing Efficient Explicit-Rate Switch Algorithm with Max-Min Fairness
for ABR Service Class in ATM Networks
Hiroyuki Ohsaki, Masayuki Murata and Hideo Miyahara
Department of Informatics and Mathematical Science
Graduate School of Engineering Science, Osaka University
oosaki@ics.es.osaka-u.ac.jp
Abstract — A rate-based congestion control algorithm regulates
cell emission rate of source end systems based on feedback infor-
mation from the network. It was standardized by the ATM Forum
for application to an ABR (Available Bit Rate) service class. In
the standard, two types of congestion notification methods of the
switch are specified: EFCI marking and explicit-rate marking. In
this paper, we focus on explicit-rate marking switch. We propose
our enhancements on a recently proposed switch algorithm called
as the max-min scheme. The main objective of our enhancements
is to control the queue length of the switch for preventing cell loss
and achieving full link-utilization. We show effectiveness of our
switch algorithm by simulation experiments.
I. INTRODUCTION
A rate-based congestion control algorithm is a closed-loop control
method suitable for data transfer applications. In the rate-based
congestion control algorithm, cell transmission rates of source
end systems are regulated according to congestion information re-
turned by the network. The ATM Forum has adopted it as the
congestion control mechanism for the ABR (Available Bit Rate)
service class, and has finished its standardization [1]. In the stan-
dard, behavior of source and destination end systems (i.e., termi-
nals) are specified in detail. Congestion notification methods from
the network (i.e., ATM switches) to source end systems are also
specified. Thesource end system periodically sends a forwardRM
(Resource Management) cell per data cells, and the desti-
nation end system sends it back to the corresponding source end
system as a backward RM cell. The switch notifies its conges-
tion to source end systems by marking an EFCI (Explicit Forward
Congestion Indication) bit of data cells or a CI (Congestion In-
dication) bit of RM cells. Since it uses one-bit information, the
switch utilizing the EFCI bit or the CI bit is often referred to as
a binary-mode switch. In the standard, the switch is allowed to
explicitly designate the cell transmission rate by modifying an ER
(Explicit Rate) value of the RM cell. This sort of switch is called
as explicit-rate switch.
While its implementation is rather complex, the explicit-rate
switch has a potential to achieve much better performance than
the binary-mode switch. A typical operation of the explicit-rate
switch is to compute an appropriate bandwidth allocation for ev-
ery connection based on, for example, the bandwidth available to
ABR connections and the degree of congestion. The switch then
updates the ER valueofforward and/or backward RM cells. When
the source end system receives the backward RM cell, it updates
its (Allowed Cell Rate) as
Thus, bandwidth allocation for all connections can be finished
within one round-trip time if
is set to be a large value. Oth-
erwise, the source end system needs more RM cells to increase
its
to . The brightness of the above equation is that the
source end system does not necessarily know the switch type (i.e.,
binary-mode or explicit-rate switch). In other words, effectiveness
of the explicit-rate switch is highly dependent on the determina-
tion method of the ER value.
In the ATM Forum, several switch algorithms with explicit-rate
marking have been proposed through standardization process of
the rate-based congestion control algorithm [1, 2]. These include
EPRCA (Enhanced Proportional Rate Control Algorithm) [3],
CAPC (Congestion Avoidance using Proportional Rate Con-
trol) [4], APRC2 (Adaptive Proportional Rate Control) [5] and
ERICA (Explicit Rate Indication for Congestion Avoidance) [6].
Each algorithm has its own advantagesand disadvantages in terms
of, for example, effectiveness, robustness, fairness and configura-
tion simplicity. We first summarize a recently proposed switch al-
gorithm called as the max-min scheme [7]. A strong point of this
algorithm compared with others is that it can satisfy max-min fair-
ness for any network configuration; that is, total throughput of the
network is maximized while fairness among connections is main-
tained [8]. However, its defect is in lack of adaptability to changes
in the network (e.g., connection addition/disconnection) as will be
demonstrated in Section III. Thus, we propose our enhancements
to the max-min scheme to improve its stability and efficiency. We
also evaluate its performance through simulation experiments by
comparing with other explicit-rate switch algorithms.
The rest of this paper is organized as follows. In Section II, we
introduce the max-min scheme and propose our enhancements.
Section III is devoted to performance evaluation of explicit-rate
switch algorithms. Finally, in Section IV, we conclude our paper
with a few remarks.
II. DESIGNING EXPLICIT RATE SWITCH
ALGORITHM
We start this section with an introduction of the max-min scheme
proposed by Tsang et al. in [7] with reviewing its advantages and
disadvantages. We next propose our enhancements to the max-
min scheme, and explain how the defects of the original max-min
scheme are resolved.
A. Max-Min Scheme
The max-min scheme maintains an information table at the switch.
An entry of the table is listed in Table 1. In this table, cor-
responds to the VC identifier of the connection. and
remember ER values written in the latest forward and backward
RM cells, respectively. is the current bandwidth allocation to
this connection, and a constrained flag indicates whether this con-
nection is constrained or not by other switches; if this flag is true,
it means that this connection cannot achieve its fair share of the
bandwidth at the switch. The constrained flag is used to allocate
bandwidth according to the max-min fairness. At every receipt of
forward and backward RM cells, the switch updates the associated
entries and recomputes the bandwidth allocation for the connec-
tion as follows.
name constrained
type integer float float float boolean
Table 1: Information table at the switch.
Suppose that the switch receives a forward RM cell. The switch
first checks whether the ER value in the RM cell is different from
. If different, it implies that the bandwidth allocation for
this connection has been changed at other switches, and that the
bandwidth allocation should be recomputed. Hence, the switch
replaces with the ER value in the RM cell, and updates the
constrained flag by comparing
with the allocated bandwidth
. Then, the following calculation of the bandwidth allocation
is performed.
Let
be the fair share of the bandwidth for unconstrained
connections (i.e., the constrained flag is false). is computed
as
(1)
where is the available bandwidth to the ABR service class,
and is of the th connection. and are sets of
constrained and unconstrained connections, respectively.
represents the number of unconstrained connections. The switch
updates the constrained flag of each connection for , and as-
signs to of unconstrained connections. Namely, the con-
strained flag and are determined as follows.
constrained
true
false
(2)
if constrained
otherwise
(3)
The above process is repeated until there is no change in con-
strained flags. Finally, the ER value of the RM cell is updated
as
(4)
Refer to [7] for more detail of the switch algorithm.
B. Our Enhancements to Max-Min Scheme
In this subsection, we propose enhancements to the max-min
scheme. The objective of our enhancements is to eliminate defects
of the max-min scheme without losing its advantages. Advan-
tages of our enhanced max-min scheme over the original max-min
scheme are: (1) controllability of the queue length, (2) an effective
(Transient Buffer Exposure) [1] allocation mechanism, (3)
robustnessagainst background traffic, (4) fairness achievement in-
corporating and , and (5) interoperability. Details of
our enhancements are described below.
The first enhancement is to control the queue length to a de-
sired level. This mechanism is intended to prevent cell loss and
to achieve full link-utilization as well as small cell delay. In our
enhanced max-min scheme, the switch allocates the bandwidth to
connections according to the current queue length. More strictly,
the allocation of the ER value in Eq. (4) is changed as
where is a bandwidth adjustment function, and is a cur-
rent queue length. The bandwidth adjustment function, ,is
a monotonically decreasing function having the following charac-
teristics.
is a target queue length at the switch buffer. and
are upper and lower bandwidth adjustment factors. For example,
when the queue length is zero, the switch allocates times
larger bandwidth than the available bandwidth to the ABR service
class. On the other hand, when the queue length is greater than
, the switch reduces the bandwidth allocation. By introduc-
ing this mechanism, the queue length is managed to be kept at
. Namely, if the queue length is below , the switch tries
to increase its queue length by allocating more bandwidth. If the
queue length is over , the switch tries to decrease its queue
length. Hence, the queue length is restored at even when the
switch gets overloaded or under-loaded.
The second enhancement for the max-min scheme is to sup-
port various fairness definitions with and . To take
account of and , the equation for computing the fair
share, Eq. (1), is further extended as
where and are selected according to a desired fairness crite-
rion.
In our enhanced max-min scheme, the available bandwidth to
the ABR service class is computed at the switch by monitoring
the number of arriving CBR and VBR cells within a fixed inter-
val. More specifically, by letting be the bandwidth monitoring
interval and be the number of CBR and VBR cells received
during , the available bandwidth is computed as
We next explain our mechanism to allocate for a new
connection. Let us assume that there are active connections
on the link, and th connection starts cell emission at
. At the connection setup time, the switch determines
for this connection as
where is a reserved buffer capacity for th connection, and
is the buffer size of the switch. is an estimated round-
trip delay of the RM cell including processing delays, which is
signaled at connection setup [1]. The buffer reservation, ,is
valid until the source end system receives the first backward RM
cell from the network; that is, is canceled at .
Thus, the buffer reservation for th connection is given
by
Given from the network, the source end system computes
(Initial Cell Rate) [1]. By employing this mechanism, buffer
overflow caused by activation of a new ABR connection can be
completely avoided. Another possibility of buffer overflow is
when background traffic suddenlyincreases its bandwidth require-
ments. In what follows, we investigate an appropriate setting of
control parameters satisfying two objectives — preventing cell
loss and achieving full link utilization — even with background
traffic.
From now on, we analyze the maximum and minimum of the
queue length by assuming infinite buffer capacity. To analyze the
worst case, we assume that all connections are not constrained
at other switches, and that all source end systems always have
cells to transmit. We further assume that the network is in steady-
state; the queue length is equal to because of the queue control
mechanism of our enhanced max-min scheme. Let denote
the number of active connections. We introduce and
( ) as the propagation delays between the th source
end system and the switch, and between the switch and the cor-
responding destination end system. The bandwidth of the link is
denoted by
.
When the amount of the background traffic is increased from
to ( )at = , the switch immediately recomputes
new bandwidth allocations and notifies them to source end sys-
tems via the ER values of RM cells. In this case, the bandwidth
allocation for each connection is changed from
to . Since the RM cell containing a new explicit-
rate arrives at the th source end system after the arrival rate
of the background traffic is changed, cells are excessively injected
into the network. Thus, the envelope of the queue length is given
by
where is the bandwidth allocated for the th connec-
tion. The backward RM cell having the new bandwidth allo-
cation of are received by the th source at
, where is the propagation delay from
the switch to the source end system and is a delay for the
next RM cell at the switch. Thus, is given by
otherwise
The maximum queue length, , is obtained as
Hence, to prevent buffer overflow, should be chosen to satisfy
.
The queue decreases when the amount of background traffic
is decreased. When the amount of background traffic is changed
from to ( )at , the envelope of the queue
length is simply given by replacing in Eq. (5) with .As
with the previous case, the minimum queue length is given by
Thus, full link utilization can be achieved by setting to satisfy
.
In our enhanced max-min scheme, three control parameters —
, , and — are newly adopted for fulfilling high per-
formance in exchange for configuration simplicity. However, the
threshold value, , can be configured according to the above
analysis.
In the original max-min scheme, the destination end system
must reset the ER value in the RM cell to
. It requires an
additional hardware to maintain values of active connec-
tions at the destination end system, and does not follow the ATM
Forum standard. In our enhanced max-min scheme, such a mech-
anism is eliminated; the destination end system simply sends back
the RM cell.
III. PERFORMANCE EVALUATION
A. Simulation Model
SW1
SW2
SES1
SES2
SES3
SES4
DES1
DES2
DES3
DES4
Source End System
Destination End System
ATM Switch
Fig. 1: Our Simulation Model.
Figure 1 shows our simulation model, which consists of two inter-
connected explicit-rate switches and four ABR connections with
identical propagation delays. In the following simulation, the link
bandwidth, , is fixed at 353.7 cell/ms assuming a 150 Mbit/s
link. The propagation delay of each link (source–switch, switch–
switch or switch–destination) is fixed at an identical value denoted
by . A round-trip delay between source and destination end sys-
tems is, therefore, . We use two values of : 0.01 ms (about
2 km) as LAN environments and 1.00 ms (about 200 km) as WAN
environments. Thus, the round-trip delay is 0.06 ms for LAN en-
vironments or 6.00 ms for WAN environments.
At each switch, its buffer size, , is set to 300 Kbyte (5,796
cells). We assume persistent sources; all source end systems al-
ways have cells to transmit. In other words, we assume that
(Current Cell Rate) of the source end system is always equivalent
to . For other parameters, we use the values proposed in [1].
B. Addition and Departure of ABR Connections
In this subsection, we compare three explicit-rate switch algo-
rithms: ERICA, the max-min scheme and our enhanced max-min
scheme. The main objective of this section is to evaluate the influ-
ence of connection addition and departure. So we add four con-
nections to the network at different starting points, = 0, 20, 40
and 60 ms, and remove them from the network at
= 300, 280,
260 and 240 ms, respectively. Forcomparison purposes, the
determination algorithm of our enhanced max-min scheme is not
used. Instead, we set the initial cell rate,
,tobe in all
schemes.
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300
Cell Rate (cell/ms)
Time (ms)
VC 1
VC 2
VC 3
VC 4
0
50
100
150
200
250
300
350
400
450
500
0 50 100 150 200 250 300
Queue Length (cell)
Time (ms)
SW 1
SW 2
Fig. 2: Effect of connection addition/disconnection in ERICA for
ms and target utilization of 0.95.
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300
Cell Rate (cell/ms)
Time (ms)
VC 1
VC 2
VC 3
VC 4
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300
Queue Length (cell)
Time (ms)
SW 1
SW 2
Fig. 3: Effect of connection addition/disconnection in ERICA for
ms and target utilization of 0.95.
We first show simulation results for ERICA in Figs. 2 and 3
for different propagation delays, = 0.01 and 1.00 ms, respec-
tively. A target utilization and a load averaging interval are set
to be 0.95 and 100 cell time. In ERICA, the target utilization is
used to limit the bandwidth allocation for ABR connections; that
is, target utilization of the bandwidth is shared by ABR
connections, and the rest of the bandwidth is not allocated to ab-
sorb the rate fluctuation. The load averaging interval is an inter-
val for monitoring the current traffic load at the switch. Readers
should refer to [6] for details of ERICA.
Each graph shows s of source end systems and queue
lengths of switches. As can be found from these figures, the queue
length grows when the new connection is activated (around =
20, 40 and 60 ms), and the maximum queue length is about 470
cells in the LAN environment. Since the target utilization is less
than 1.0, the buffered cells are gradually processed and the queue
length diminishes. In simulation, the queue length is decreased
in about 30 ms, and the maximum queue length is limited even
with several new connections. In the WAN environment, how-
ever, many cells are lost due to buffer overflow as can be found
from Fig. 3. The number of lost cells was 59,927 cells during
the simulation run. It can also be found that fairness among con-
nections is not fulfilled. This problem also occurs in EPRCA++,
which is the previous version of ERICA [9]. Buffer overflow can
be avoided by setting the target utilization to be a much smaller
value. However, it should be noted that setting a small value of
the target utilization causes lower utilization of the bandwidth.
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300
Cell Rate (cell/ms)
Time (ms)
VC 1
VC 2
VC 3
VC 4
0
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250 300
Queue Length (cell)
Time (ms)
SW 1
SW 2
Fig. 4: Effect of ABR connection arrival/departure in max-min
scheme for ms.
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300
Cell Rate (cell/ms)
Time (ms)
VC 1
VC 2
VC 3
VC 4
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 50 100 150 200 250 300
Queue Length (cell)
Time (ms)
SW 1
SW 2
Fig. 5: Effect of ABR connection arrival/departure in max-min
scheme for ms.
In Figs. 4 and 5, we next show simulation results of the orig-
inal max-min scheme for = 0.01 and 1.00 ms. From the fig-
ures, it can be found that cell loss can be prevented even in the
WAN environment, and that the maximum queue length is much
smaller than the one obtained by ERICA. It is because the max-
min scheme can adjust of the new connection to the correct
value in one round-trip time. However, the serious problem of the
max-min scheme is that each connection cannot increase its
even when some connections are terminated. Namely, max-min
fairness is not satisfied after = 240 ms. This is due to a deadlock
problem of the max-min scheme explained as follows.
constrained
1 4 353.7 88.4 88.4 true
Table 2: Information table at SW1 before VC4 terminates.
constrained
1 4 88.4 353.7 88.4 true
Table 3: Information table at SW2 before VC4 terminates.
Tables 2 and 3 show information tables maintained at SW1 and
SW2 before VC4 terminates at = 240 ms. Note that all connec-
tions have the same entry. When VC4 terminates, the switch tries
to reallocate the available bandwidth. Since there are three active
connections, the switch computes the fair share, ,as
(= 117.9 cell/ms) according to Eq. (1). However, the minimum of
and is 88.4 cell/ms at both SW1 and SW2, all connec-
tions are regarded as constrained. Consequently, the bandwidth
allocation for each connection is still limited to 88.4 cell/ms (see
Eqs. (2) and (3)).
Another problem of the max-min scheme is that the queue
length is settled at a high level. It becomes more apparent in the
WAN environment as shown in Fig. 5. In the figure, the maxi-
mum queue length is about 4,700 cells, and cells would be lost if
one more connection is added to the network. In other words, it
takes long time for the queue length to be decreased because the
max-min scheme tries to fully utilize the available bandwidth even
though the queue length is almost full.
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300
Cell Rate (cell/ms)
Time (ms)
VC 1
VC 2
VC 3
VC 4
0
20
40
60
80
100
120
140
160
180
0 50 100 150 200 250 300
Queue Length (cell)
Time (ms)
SW 1
SW 2
Fig. 6: Effect of ABR connection arrival/departure in enhanced
max-min scheme for ms.
We next show simulation results of our enhanced max-min
scheme in Figs 6 and 7 for = 0.01 and 1.00 ms, respectively.
In these figures, is chosen according to our analysis presented
in Subsection II-B: in these cases, = 138 in the LAN envi-
ronment and = 1,189 in the WAN environment. Bandwidth
adjustment factors, and , are set to be 0.2 and 0.5, respec-
tively.
It can be found from these figures that the maximum queue
length is quite small, and that the queue length is stabilized at .
It can also be found that the queue length is decreased quickly
once the queue length exceeds . It is owing to the mechanism
of our enhanced max-min scheme to control the queue length. Our
enhanced max-min scheme frequently updates the bandwidth al-
location compared with the original one. However, frequent com-
putation of the bandwidth allocation would be indispensable when
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300
Cell Rate (cell/ms)
Time (ms)
VC 1
VC 2
VC 3
VC 4
0
500
1000
1500
2000
2500
3000
0 50 100 150 200 250 300
Queue Length (cell)
Time (ms)
SW 1
SW 2
Fig. 7: Effect of ABR connection arrival/departure in enhanced
max-min scheme for ms.
the background traffic coexists in the network.
IV. CONCLUSION
In this paper, we have focused on the explicit-rate marking switch,
which utilizes the ER value in the RM cell for allocating band-
width to each connection. We have proposed our explicit-rate
switch algorithm, which is an enhanced version of the max-min
scheme. Through simulation experiments, we have evaluated the
performance of our switch algorithm, and have shown that our
switch algorithm achieves better efficiency and stability compared
with other switch algorithms.
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