This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
Throughput Model of IEEE 802.11e EDCF with
Consideration of Delay Bound Constraint
Jae-Han Lim
Ji-Hoon Yun
Seung-Woo Seo
Telematics and USN Research Division
ETRI
161 Gajeong-dong, Yuseong-gu
Daejeon 305-700, Korea
Email: ljhar@etri.re.kr
School of Electrical Engineering and
Computer Science
Seoul National University
Seoul 151-742, Korea
Email: sjeus@ccs.snu.ac.kr
School of Electrical Engineering and
Computer Science
Seoul National University
Seoul 151-742, Korea
Email: sseo@snu.ac.kr
Abstract— In this paper, we present an accurate throughput
model of the IEEE 802.11e enhanced distributed coordination
function (EDCF). Compared to the previous models, we newly
consider a delay bound by predicting an effective retry limit
and applying the retry limit to our model. To support this,
the accurate description of the performance in a non-saturation
condition is necessary, which is achieved by newly considering a
queue length and a queue limit in the Markov chain. Simulation
results show that our model is accurate in predicting the system
throughput.
I. I NTRODUCTION
In recent years, IEEE 802.11 [1] has been a dominant
technology for providing high-speed wireless internet access
due to the simplicity in deployment and low cost. However, IEEE 802.11 cannot satisfy the increasing demand of
quality-of-service (QoS) which is required for multimedia
applications. Consequently, the IEEE 802.11e standard [2] is
specified to enhance the legacy IEEE 802.11 medium access
control (MAC) protocol. This new standard defines the hybrid
coordination function (HCF) in order to support QoS at the
MAC layer. The HCF is composed of two access mechanisms,
the enhanced distributed coordination function (EDCF) and
HCF controlled channel acess (HCCA). The EDCF is the
contention-based channel access mechanism, while the HCCA
is the polling-based channel access function. In this paper, we
aim at proposing the accurate analytical model of the EDCF.
Based on the throughput model introduced by Bianchi
[3], some previous investigations have been conducted for
modeling of the EDCF, the basic MAC protocol of IEEE
802.11e [2]. In [4], Kong and Tsang extended [3] to analyze
the saturation throughput performance of the EDCF. In [5],
Paal and Olav developed a model which considered a nonsaturation condition. In [6], Tantra and Foh proposed a model
to find the throughput and MAC delay under statistical traffic
when the maximum queue size is only one. However, the
previous models lack the consideration of a delay bound.
In this paper, we introduce a new throughput model of
EDCF under a non-saturation condition. In our model, the
delay bound which is specified in the IEEE 802.11e standard
[2], is newly considered. According to the delay bound, an
effective retry limit is predicted and applied to the throughput
model for accurate analysis. To support this, the accurate
description of the performance in a non-saturation condition
is necessary, which is achieved by newly considering the
followings in Markov chain: (1) queue length (the number of
frames in the queue and server of each AC) and (2) queue limit
(the maximum number of frames which can be stored in the
queue and server of each AC). To the best of our knowledge,
this is the first attempt to consider a delay bound, queue length
and queue limit in a throughput model.
The rest of paper is organized as follows. In the next section,
we will briefly describe the DCF and the EDCF. Subsequently,
we propose the throughput model of EDCF with consideration
of the delay bound constraint. In section IV, we verify the
accuracy of our model through ns-2 simulation. Finally, we
conclude our paper in section V.
II. OVERVIEW OF DCF AND EDCF
A. Distributed Coordination Function
The basic MAC protocol in IEEE 802.11 is DCF, which
decides when to access the channel in a distributed manner.
DCF employs the carrier sense multiple access with collision
avoidance (CSMA/CA) mechanism. When a station generates
a frame for transmission, it should sense if the channel is idle
for distributed interframe space (DIFS) time plus backoff time.
The backoff time is equal to a unit slot time multiplied by a
backoff counter, which is selected randomly between zero and
a contention window (CW). If the channel is sensed idle for
DIFS time, a backoff countdown is started and the backoff
counter decreases by one. If the channel is sensed busy in the
middle of the backoff countdown, the countdown process is
stopped until the channel is sensed idle for at least DIFS time.
When the backoff counter reaches zero, the station initiates a
frame transmission.
If a destination station successfully receives a frame, the
destination station responds with transmitting an acknowledgment frame (ACK) after short interframe space (SIFS) time.
If the sender does not receive ACK within ACK timeout due
to the transmission failure of ACK or the original frame, the
sender regards the frame transmission as a failure and doubles
its CW and increments its retry count by one. If the retry count
978-1-4244-2075-9/08/$25.00 ©2008 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
Select backoff
number 7
Station 1
7 6 54 3 2
DIFS
Busy Channel
Busy Channel
2 1 0
DIFS
Data
Pi,e(K)
(From P 0,0,0,0 )
P i(2-k)
Pi(0)
P i,e(k)
Pi(k)
( To queue k )
(To queue k)
∑ L ≥Q Pi,e(L)
(From P 0,0,0,0 )
∑ L≥ Q-k+1 Pi (L)
Pi(K-k+1)
( From queue k)
(From queue 1 )
ACK
SIFS
Pi,e(1)
(From P 0,0,0,0 )
(From queue k)
Pi (0)
(From queue k)
(To queue Q-1 )
Pi (k-K+1)
∑ L ≥1P i(L)
(To queue k)
(To queue Q )
Select backoff
number 5
Station 2
Busy Channel
DIFS
1
Select backoff
number 10
1
9 8
0
DIFS
5 4 32 1 0
Data
K
Q
K,0,0,0
0,0,0,0
Busy Channel
K,M,0,0
ACK
SIFS
<IEEE 802.11 DCF channel access procedure >
Pi (k-K+1)
Pi (K-k+1)
(From queue length k
(1≤k≤K+1))
Pi,e(K)
(From P 0,0,0,0)
(To queue length k
(K-1≤k≤Q ))
AIFS[AC] =
SIFS +
AIFSN[AC] *
aSlotTime
0~15
Select backoff
number 6
Station 1
Freeze
K,0,0,AIFSN i
K,0,0,AIFSN i
6 5 4 3 2 1
AIFS[AC]
Freeze
AIFS[AC]
1 0
Pb
Busy
medium
1-Pi
1-P b
K,0,0,0
K,0 ,W 0-2,AIFSN i
Pb
K,0 ,W0 -1,AIFSN i
Pb
1-P b
K,0,1,0
qi
1-P b
K,0,W 0 -2 ,0
1-qi
K,0,W 0 -1 ,1
Pi/W 1
0~7
AIFS[AC] =
SIFS +
AIFSN[AC ] *
aSlotTime
Station 2
Freeze
Select backoff
number 5
5 4 3 2 1 0
AIFS[AC]
Select backoff
number 3
Busy medium
AIFS[AC]
Pi/W j
3 21
K,j,0,AIFSN i
Freeze
K,j,1,AIFSN i
1
<IEEE 802.11e EDCF channel access procedure >
K,j ,Wj -1,AIFSN i-1
1
qi
qi
1
qi
qi
1
1
1
Fig. 1. IEEE 802.11 DCF and IEEE 802.11e EDCF channel access procedure
K,j ,W j-2,AIFSN i-1
1
1
1
1
K,j,1, AIFSN i-1
K,j,0 ,AIFSN i-1
K ,j,W j-1,AIFSN i
K,j ,W j-2,AIFSN i
1
1
qi
K,j,1,A i
K,j,0,A i
Pb
1-qi
1-qi
K,j,W j -1,A i
K,j,W j -2,A i
qi
1-qi
1-qi
qi
Pb
reaches the retry limit which is specified in the IEEE 802.11
standard[1], the frame will be dropped.
K,j,0,1
1-qi
1-qi
Pb
K,j,1,1
1-q i
1-Pi
K,j,W j -1,1
K,j,W j -2,1
1-q i
1-qi
1-Pb
K,j,0,0
1-q i
K,j,1,0
1-Pb
1-Pb
K,j,W j -2,0
Pi/W j+ 1
B. Enhanced Distributed Coordination Function
Based on the legacy 802.11 DCF, EDCF is devised in
order to support QoS. Therefore, the operation of EDCF is
similar to that of DCF. For example, both DCF and EDCF use
CSMA/CA as a medium access control mechanism. However,
there are some differences between DCF and EDCF. Firstly
EDCF stations support up to four queues. Each queue is an
independent backoff entity which contends for the right to
access the channel. In addition, each queue is related to a
specific access category (AC).
Secondly, different levels of services are provided to each
AC by setting different parameters according to AC : arbitration interframe space (AIFS), the minimum CW (CWmin),
the maximum CW (CWmax) and transmission opportunity
(TXOP) limitation. Each AC can have different AIFS which
is calculated by
AIF S[AC] = SIF S + AIF SN [AC] × σ
1-qi
1-qi
qi
(1)
where AIFSN[AC] is a AIFS number and σ is a unit slot time.
As AC has smaller AIFS, AC can finish their AIFS deferring
and backoff countdown earlier. In this sense, the AC of higher
priority AIFS has smaller AIFS.
The CWmin and CWmax can be set differently for different
ACs in order to provide differentiated services. In EDCF, the
AC of a higher priority has smaller CWmin and CWmax since
the AC with smaller CWmin and CWmax tends to have shorter
backoff countdown delay. Each AC can have a different TXOP
limit in order to provide differentiated services. The TXOP
limit is the maximum time interval during which a particular
station has the right to access the channel without contention.
As TXOP limit of AC is longer, AC can transmit more frames,
which means higher priority.
Pi/W M
K,M,0,AIFSN i
K,M,0 , AIFSN i
Pb
1
Fig. 2.
K,M,0,0
1-P b
Pb
K,M ,W M -2,AIFSN i
K,M ,W M -1,AIFSN i
Pb
K,M,1,0
1-P b
1-P b
qi
K,M, W M -2 ,0
1-qi
K,M,W M -1 ,1
Markov chain for the backoff procedure of ACi in 802.11e EDCF
Thirdly, the backoff countdown of EDCF is different from
that of DCF. The first backoff countdown in EDCF occurs
at the last slot of AIFS deferring, while DCF starts the first
backoff countdown after DIFS deferring is over. Moreover, a
frame transmission in EDCF is initiated after a slot time from
the moment when a backoff counter becomes zero, while DCF
initiate a frame transmission right after a backoff countdown
is over. The above-mentioned difference between the EDCF
and DCF backoff countdown procedures is described in Fig.1.
Finally, an internal collision can happen among the ACs
of the same station in EDCF. We call this internal collision
a virtual collision. When a virtual collision happens, the AC
with a higher priority can transmit, whereas all the other ACs
act as if a collision occurs on the channel.
III. M ATHEMATICAL A NALYSIS
A. Accurate Description of EDCF Backoff Procedure in NonSaturation Condition
In the model, we assume that there are N stations in a
network and each station has L access categories (ACs) and
a frame arrival follows the Poisson process. We model the
backoff procedure of each AC as the finite state 4-dimensional
Markov chain under the assumption that pi (the transmission
failure probability of the i-th access category ACi ), Pb (the
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
channel busy probability during backoff countdown) and qi
(the channel busy probability of ACi during AIFS deferring)
are independent of the backoff procedure, as shown in Fig. 2.
Each state of the Markov chain consists of 4 parameters,
(k, j, h, l), where k is a queue length, j is a backoff stage, h
is a backoff counter, and l is the remaining number of slots
in AIFS deferring. When ACi enters a new backoff stage j,
(j)
(j)
h takes its value in [0, Wi − 1] where Wi is the contention
(j)
window size of a backoff stage j. Wi is expressed as
0 ≤ j ≤ mi
2j ·(CWmin,i + 1),
(j)
Wi =
(2)
mi
2 ·(CWmin,i + 1), mi < j ≤ Mi
where mi is the maximum number of retransmissions of ACi
using different CWs and Mi is the retry limit of ACi .
The performance in a non-saturation condition is influenced
by the probability of an empty queue. In order to calculate
this probability accurately, we should consider the fact that
the transition probability to the state where the queue is
empty depends on the queue length of the previous state.
In the previous model [5], only two queue states, empty
or non-empty, are considered implicitly without considering
the above-mentioned fact. However, our model considers the
point, which [5] misses by adding a new parameter (a queue
length) to the state of the Markov chain. Moreover, we newly
consider the finite queue limit, which shows the effect of queue
overflow. Therefore, our model is more accurate in predicting
the performance in a non-saturation condition.
All the state transition probabilities of the Markov chain are
expressed by pi , qi , Pb , pi (k), and pi,e (k), which we obtain
in the following. A transmission failure happens due to either
real or virtual collision, and pi is expressed as
L
L
pi = 1 − (1 − τl )N −1 · (1 − τl )
l=1
L
(1 −
l>i
Ai − Al N
) ,
Ul
1 ≤ i ≤ L.
(4)
Ui =
pji
· (1 − pi ) ·
(j)
Wi
+
i
pM
i
·
(M )
Wi i .
(5)
j=0
During the backoff countdown of ACi , all the other ACs can
access the channel if their backoff counter becomes zero earlier
1 We
2A
i
assume that the priority of AC becomes higher as i increases.
is defined as AIF SNi − AIF SNL .
L
(1 − τl )N .
(6)
l=1
We assume that frames arrive every service interval. The
service interval is defined as an expected service time when
the queue is not empty, or as an expected slot time when the
queue is empty. The above assumption does not have an effect
on the system throughput due to the Chapman-Kolmogorov
equation [7], which is valid for all processes having a Markov
ian property.3 pi (k) and pi,e (k) are the probabilities which
k frames arrive during the expected service time and the
expected slot time, respectively. They are expressed as
pi (k) = (λi · E[Service])k · e−(λi ·E[Service]) /k!
pi,e (k) = (λi · E[ST ])k · e−(λi ·E[ST ]) /k!
(7)
where E[Service] and E[ST ] are the expected service time
and the slot time, respectively and are expressed by
Ui
· (E[ST ] + Pb σ) + Tbusy
2
L
E[ST ] = (1 − Pb ) · σ +
Ps,l · Ts,l + Pc · Tc,i
E[Service] =
(8)
l=1
where Pb σ means that ACi experiences an additional unit
time slot σ for every busy slot in a backoff countdown. Ps,i
and Pc are the probabilities of the successful transmission of
ACi and collision, respectively. They are expressed as
Ps,i = N · τi · (1 − pi )
P c = Pb −
L
Ps,l .
(9)
l=1
l>i
where Ui is the average contention window size and is
calculated as
M
i −1
Pb = 1 −
(3)
where τl is the transmission probability of ACl in a slot.
During the AIFS deferring of ACi , the other ACs of
higher priority1 can finish their backoff countdown and start
transmission. This situation happens when the ACs of higher
priority select their backoff counter less than Ai − Al . 2 Then,
qi is expressed as
qi = 1 −
than ACi ’s, and we have Pb as
Tbusy is the expected busy time regardless of a reason and Ts,i ,
Tc,i are the channel busy times due to successful transmission
and collision, respectively. They are expressed as
Tbusy = Ts,i = Tc,i = Tdata,i + SIFS + Tack,i + AIFSi (10)
where Tdata,i and Tack,i are the transmission times of a data
frame and an ACK frame, respectively, in ACi . 4
Let bk,j,h,l be the steady probability of state (k, j, h, l).
Since the transmission attempt of ACi happens at state
(k, j, 0, 0), τi is described as
τi =
Qi
Qi
Mi Mi (
bk,j,0,0 ) =
(
pji · bk,0,0,0 )
j=0 k=1
(11)
j=0 k=1
where Qi is the maximum queue size of ACi .
3 The arrival process of our model is assumed to be Poisson process which
has a Markovian property.
4 We only consider the basic mode throughput in this paper. However, we
can easily extend the model to the RTS/CTS mode by adding RTS/CTS
overhead to Te , Ts and Tc .
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
TABLE I
PARAMETER SETTINGS FOR NUMERICAL RESULTS
Parameters
AC1
CWmin
31
15
CWmax
255
127
AIFSN
3
2
1000
The total delay St,i (Mi , Di ) required for a successful transmission from the frame arrival to the (Mi + 1 )-th transmission
attempt in ACi is obtained by
AC2
Payload(byte)
1000
BasicRate(Mbps)
1
1
DataRate(Mbps)
11
11
Queue limit
15
15
Delay bound(ms)
none
20
St,i (Mi , Di ) = Sm,i (Mi ) + Sq,i (Mi , Di )
(13)
where Sm,i (Mi ) is the medium access delay required for a
successful transmission after Mi unsuccessful transmission
attempts in ACi , and is obtained by
Sm,i (Mi ) =
M
i −1
(j)
(j)
(Mi)
[Ci + Fi ] + Ci
+ Ts,i
(14)
j=0
(j)
Since the maximum number of frames that can be served
during the service interval is one, the previous queue length5
should be equal to or less than the current queue length plus
one. Moreover, we should consider the number of frames
arriving and leaving during the service interval in order to
calculate the current queue length from the previous queue
length. To be specific, when the previous queue length is
not zero, the current queue length is less by one than the
sum of the previous queue length and the number of frame
arrivals, since a frame leaves the queue every service interval.
On the other hand, when the previous queue length is zero,
the current queue length is equal to the sum of the previous
queue length and the number of frame arrivals, since no frame
leaves the queue. Therefore, bk,0,0,0 can be obtained by using
the following equation and the normalization condition.
bk,0,0,0 =
=
w
0 −1
h=0
k+1
M
i −1
·[
c=1
+ pi,e (k) · b0,0,0,0 ,
(j)
Wi
(15)
2
Sq,i (Mi , Di ) is the queueing delay of the frame which is not
dropped before a backoff process and is expressed as
ri (Di )
[(k − 1) · a b c bk,a,b,c ]
(16)
Sq,i (Mi , Di ) = k=1 r (D ) i
i
λi · k=1
[ a b c bk,a,b,c ]
(j)
Ci = (E[ST ] + Pb σ)
where ri (Di ) is the maximum number of frames which are
not dropped before a backoff process in the queue of ACi and
expressed as
(17)
ri (Di ) = Di · λi We obtain Mi∗ for each AC so that the below conditions
are satisfied:
bk,0,h,AIF SNi
(k+1−c)
pi
where Ci is the channel access delay due to backoff and
(j)
AIFS deferring in a backoff stage j, Fi is the busy time due
(j)
to the j-th unsuccessful transmission attempt. Fi is equal to
(j)
Tbusy and Ci is expressed as
(1 − pi ) · bc,j,0,0 + bc,Mi ,0,0 ]
j=0
Mi∗ = arg(M in
L
|Di − St,i (Mi , Di )|)
l=1
0 ≤ k ≤ (Qi − 1).
(12)
where b0,0,0,0 is the probability of an empty queue.
B. Effect of Delay Bound Constraint on Markov Chain
If a data frame is not successfully transmitted within its
delay bound, the data frame is discarded since it is already outof-date. In other words, the transmission attempt which does
not satisfy the delay bound of the data frame never happens.
Therefore, we can show the effect of the delay bound of ACs,
which is the main contribution in our model, to the system
throughput in the following manner: (1) find the maximum
number of transmission attempts Mi∗ for ACi (i=1,· · · ,L),
with which the medium access and queueing delay of a data
frame does not exceed the delay bound Di , (2) substitute Mi∗
for the retry limit value of the throughput model.
5 The queue length is changed every service interval since we assume that
frames arrive every service interval. Therefore, we define the previous queue
length as the queue length in the previous service interval.
Mi ≤ dot11Long(Short)RetryLimit
St,i (Mi∗ , Di ) ≤ Di .
(18)
Finally, we substitute Mi∗ for the retry limit value of the
backoff process which is explained in the previous section,
in order to obtain the accurate value of the non-saturation
throughput T hi
Ps,i E[Pi ]
(19)
T hi =
E[ST ]
where E[Pi ] is the expected frame length of the ACi .
IV. N UMERICAL R ESULTS AND M ODEL VALIDATION
To validate the model, we compare the numerical results
of the model with the simulation results using ns-2 [8]. We
use the parameters of IEEE 802.11b. In the validation, ten
stations which have two ACs are considered: AC2 with a
higher priority and AC1 with a lower priority. The effect of
channel errors is not considered and RTS/CTS mechanism is
not employed. The parameter settings for each AC are listed
in Table. I.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
5
Simulation
Proposed model
3
20ms delay bound for AC2
2
5.0
Throughput (Mbps)
4.5
4.0
3.5
AC1
0
0
2
4
6
8
10
Traffic load per AC (Mbps)
Fig. 4. Comparison of the system throughput from the analytical model
and the simulation according to traffic load when the delay bound of 20ms is
considered for AC2
4.5
Simulation
Proposed model
4.0
Throughput (Mbps)
Simulation
Proposed model
Paal&Olav model
AC2
1
3.5
5.5
No delay bound for AC2
4
Throughput (Mbps)
Fig. 3 shows the comparison of the system throughput
between our model and the model of [5] when the effect
of a delay bound is not considered6 . As depicted in Fig. 3,
we concentrate on the traffic load of each AC from 1Mbps
to 5Mbps in order to show the results in the non-saturation
condition. In this figure, we can observe that our model is
more accurate in predicting the system throughput than the
model of [5]. This is because our model reflects the effect of
queue length and queue limit which the model of [5] misses.
In Fig.4 and Fig.5, a delay bound is not considered for
AC1 and the delay bound of 20ms is considered for AC2 . In
these two figures, analytical and simulation results are added
when delay bounds are not considered for AC1 and AC2 . Fig.4
shows the system throughput when the traffic load of each AC
varies from 1Mbps to 10Mbps. On the other hand, Fig.5 shows
the system throughput according to the number of stations. In
Fig.5, we fix the traffic load of each AC to 3Mbps at a different
number of stations in order to validate our model in the nonsaturation condition. As can be seen in Fig.4 and Fig.5, our
analytic model shows accurate throughput results compared to
the simulation.
Fig.6 shows the system throughput when the delay bound of
AC2 varies from 20ms to 140ms and the delay bound of AC1
is not considered. In Fig.6, we can observe that throughput
prediction of our model closely follows the simulation results.
No delay bound for AC2
20ms delay bound for AC2
AC2
3.0
2.5
2.0
1.5
3.0
AC2
2.5
1.0
AC1
2.0
AC1
0.5
4
1.5
6
8
10
12
14
16
18
20
22
Number of stations
1.0
0.5
0.0
0
1
2
3
4
5
Traffic load per AC (Mbps)
Fig. 3. Comparison of the system throughput of the various models according
to traffic load when there is not the effect of delay bound
V. C ONCLUSION
In this paper, we propose an accurate throughput model of
the IEEE 802.11e enhanced distributed coordination function.
Compared to the previous models, we newly consider a delay
bound by predicting an effective retry limit and applying the
6 We only consider the model of [5] for comparing with our model in
non-saturation condition, since [4] considered saturation condition and [6]
considered the queue whose size is only one.
Fig. 5. Comparison of the system throughput from the analytical model and
the simulation according to number of stations when the delay bound of 20ms
is considered for AC2 and the traffic load of each AC remained 3Mbps at a
different number of stations.
retry limit to our model. The consideration of a delay bound is
based on the accurate description of a non-saturation condition,
which is achieved by newly considering a queue length and a
queue limit in the Markov chain.
The model is validated through ns-2 simulation. Simulation
results show that our model is accurate in predicting the system
throughput when a delay bound is considered. Moreover, even
when the effect of a delay bound is absent, simulation results
show that our model is more accurate in predicting the system
throughput than the other model [5] which considers a nonsaturation condition.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
3.4
Simulation
3.2
Proposed model
Throughput (Mbps)
3.0
2.8
2.6
AC2
2.4
2.2
AC1
2.0
1.8
1.6
20
40
60
80
100
120
140
Delay bound of AC2 (ms)
Fig. 6. Comparison of the system throughput from the analytical model and
the simulation when the delay bound of AC2 varies from 20 to 140 and the
delay bound of AC1 is not considered.
ACKNOWLEDGMENT
This work was supported by the IT R&D program of
MIC/IITA. [2006-S024-02, Development of Telematics Application Service Technology based on USN Infrastructure]
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Access Control (MAC) Enhancements for Quality of Service (QoS)”,
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