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VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 1 (2015) 45-54
A Contribution to Performance Analysis Approach of the IEEE 802.11 EDCA in Wireless Multi-hop Networks
Minh Trong Hoang*, Minh Hoang, Duc Cong Le
Posts and Telecommunications Institute of Technology, Hanoi, Vietnam
Abstract
The IEEE 802.11e standard has been introduced to support service differentiation for wireless local area networks. In wireless multi-hop networks, the performance of IEEE 802.11e EDCA has to confront with some practical problems such as unsaturation traffic and hidden node problem. Hence, this problem has attracted numerous studies in recent years, in which several investigations use analytic model to evaluate the performance due to its accuracy aspect. However, the accuracy and complexity of analytical model depends on a range of assumed parameters. The complexity caused by the introduction of realistic conditions in wireless multi-hop networks is the major challenge of current studies in this field. To overcome this challenge, this paper proposes an analytical model which covers full specification of IEEE 802.11e EDCA. To reduce the complexity, the model is simplified by decomposing the problem in two models based on Markov chain that can be easily solved by numerical method. The proposed model is presented in the theoretical aspect as well as numerical results to clarify its accuracy.
© 2015 Published by VNU Journal of Science.
Manuscript communication: received 01 December 2014, revised 29 January 2015, accepted 10 February 2015 Corresponding author: Minh Trong Hoang, hoangtrongminh@ptit.edu.vn
Keywords: IEEE 802.11e EDCA, Virtual collision, Multi-hop network, Hidden node, Markov chain.
1. Introduction
The IEEE 802.11 has become ubiquitous and gained widespread popularity for wireless multi-hop networks. To adapt the quality of service requirements of multi-media applications, the IEEE 802.11e Enhanced Distributed Channel Access (EDCA) has been standardized [1]. EDCA provides differentiated, distributed access to the wireless medium for node based on eight user priorities which are mapped into four Access categories in MAC layer. Three characteristic parameters of access categories are Contention Window (CW),
Arbitrary Inter-Frame Space (AIFS) and
Transmission Opportunity (TXOP).
In the recent years, a large body of work has appeared in the literature to investigate performance of IEEE 802.11e EDCA through analytical models. Most of them focused on the impacts of the parameter differences on network performance. However, due to very high complexity of presenting an analytical model which addresses all the features and details of the standard, the models are limited or ignore some important specifications to simplify the modeling. Many analytical models of IEEE 802.11e are extended from Bianchi
model for IEEE 802.11 Distributed
45
46 M.T. Hoang et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 1 (2015) 45-54
Coordination Function (DCF) [2]. They fall into two cases: Saturations and unsaturation conditions. Under saturated condition the authors in [3, 4] proposed analytical models to capture AIFS and contention window differentiation to analyze the throughput and delay of the IEEE 802.11e. However, the impact of AIFS differentiation is not covered. The proposed analytical model in [5] use the AC-specific EDCAcycle time for predicting the EDCA saturation performance but it can not clarify the impact of the contention window.
Under unsaturated condition, the authors in [6] used frame transmission cycle approach to consider the difference of AIFS. The model analyzes WLAN based on IEEE 802.11e EDCA in detail; however it is not applicable to multi-hop networks. The proposed analytical models used renewal reward approach to extend a saturation model of single cell IEEE 802.11e to comfort with both unsaturated and saturated conditions [7, 8]. In [9], internal collisions in each node, concurrent transmission collisions among nodes, differences of CWs among ACs, and effects of contention zone are considered. However, these models in [7, 8] do not count to the hidden node problem, and the model in [9] focus only on throughput analysis in multi-hop string topology. It is clear that, the lack of input factors in analytical model can lead to its inaccuracy in the performance analysis problem [10].
To our best knowledge, there isn’t any analytical model considering fully of parameters of IEEE 802.11e EDCA with realistic conditions including contention window, AIFS, virtual collision, hidden nodes and unsaturated condition in multi-hop
networks. Hence, in this paper, a novel
analytical model enhanced from our previous work is proposed to overcome these previous limitations to analyze throughput and access delay multi-hop network performances [11]. The remains of this paper is structured as follows: In Section 2, the proposed analytical model is presented in full details. Main numerical results and our discussions are adopted in Section 3. The conclusion is drawn in Section V with the indication of our future work.
2. Analytical Model
To capture quality of service and priority characteristics of IEEE 802.11e EDCA, we used our previous analytical model with some modifications [11]. We specialized the node state model to AC sub-node state model which different between ACs by EDCA parameters. We also propose the channel state model and transmission probabilities to take AIFS, CW values difference and virtual collision into account. In the following subsections, we describe our assumptions and the analytical model in detail.
2.1. Assumptions and Notations
Considering an IEEE 802.11e EDCA based network containing n nodes distributed as a two-dimensional Poisson process with density γ. The network works on single radio single channel mode with error-prone condition. Every node has four ACs defined in the standard and homogeneous physical characteristics. Assume M is the average number of nodes in the area A, the probability of finding n node in area A is
p(n,M )= n! e M ,M =g.A
M.T. Hoang et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 1 (2015) 45-54 47
The problem of hidden nodes is illustrated in Figure 1. In which, node i transmits to node j with the present of hidden node k in the same time. The hidden area AH depends on distance between transmitter and receiver (x), and then
the average number of nodes in hidden area isMH =g AH (x). Some main notations in this
paper are represented in Table 1. Figure 1. A hidden node scenario.
DR
Table 1. Notation of parameters in our model
Index Parameters
1 Radius of transmission range 2 Radius of sensing range
3 Density of node’s distribution function
4 Average number of nodes in node’ sensing range
5 Average number of nodes in node’ transmission range 6 The average number of node in the hidden area
7 Network throughput
8 Duration of a PHY slot 9 Arrival rate (lambda)
10 Maximum retry limits (short:4, long:7)
11 Prob.{ a node (4 ACs) transmits a packet in a time slot}
12 Prob.{ successful transmission in a time slot}
13 Bit error rate (BER)
Notation
t
Rs g
M N MH
Th s l
m pt ps
pb
According to the principle of CSMA/CA mechanism, all ACs follow an exponential back-off scheme that a discrete back-off value which is chosen uniformly from zero to CW and reduced by one when the medium is free for a slot time. When back-off counter of an AC reduces to zero, the first packet in the AC's queue is transmitted. These transmitting probabilities will be explored using two simple Markov chains to model criteria of IEEE 802.11e operation. In which, a node is considered as four individual sub-nodes interplaying under internal virtual collision handler called AC sub-node. For convenience, we denote four access categories in IEEE 802.11e standard as ACj , j = (1,2,3,4); from
lowest to highest priority. The packet transmission of each AC sub-node depends on actions of other ACs in the same node and other node in the same carrier sense area at the same
time. We define the probability of AC j sub-node transmitting a packet in a time slot by p(j) , which becomes p'( j) when count to virtual
collision, and completing transmission with probability p(j) . In a similar way, pt and ps are
probabilities of a node which transmits and
successfully transmits a packet in any AC, respectively. Also define a virtual slot E( j) [T]
whose duration depends on what event belong to anyAC happens duringthe slot.
48 M.T. Hoang et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 1 (2015) 45-54
2.2. AC Sub-node State Model TRTS/CTS = AIFS( j) +TRTS +d + SIFS . (5)
An AC sub-node is modeled by Markov chain as shows in Figure 2. Steady states of an AC sub-node state model includes four states:
idle, defer, failure and success, which are denoted as π( j) ,π( j) ,π( j) ,π( j) respectively.
The transition probability of a node changes from defer state to success state with Basis access scheme is
p( j) (x)= p( j) (Nt , p( j) )1 pData
´ p( j) (M , p ,T( j) )1 pAck (6) Basic
And with RTS/CTS scheme is
p( j) (x)= p( j) (Nt , p( j) )1 pRTS 1 pData
´p( j) (Mh, pt ,T( j)CTS )1 pCTS 1 pAck (7)
Finally, we have
p( j) = f (x)p(sj) (x)dx = 2xp( j) (x)dx (8) 0 0
Figure 2. Markov chain for AC sub-node state model.
The transition probability from defer to
success state for an AC sub-node depends on
with the assumption each node transmits to
a random receiver in its transmission area with equal probability of density function f (x) depends on distance x, f (x) = 2x,0< x < R .
three factors: successful sending ( p( j) ), The transition probability of AC sub-node successful receiving ( p( j) ) and no error occurs changes from defer state to idle state is
during transmission time. We consider a network with imperfect channel which has
packet error probability ppacket , ppacket =1 (1 pbit )Lpacket for both control and
( j)
( j) ( j)
p( j) = m( j) (9) 0 else
where m( j) is service rate at an AC sub-node;
data packets (notation as pRTS/CTS , pData ). We its value is calculated in Section 3.
have
p( j) (M, p( j) )= p¢( j)(1 n=2
pt )n ´ p(,n M) (2)
The transition probabilities of AC sub-node changes from defer to failure and from defer to
defer state are p( j) = p( j) p( j)
T( j) ¥
p( j) MH , pt ,T( j) =n=0 (1 pt ) ´ p n,MH (3)
where T( j) is vulnerable time, MH is average number of nodes in the hidden area as shown on Figure 1.
The duration times of two types of IEEE 802.11e access mechanisms are
TBasic = AIFS( j) +TDATA +d + SIFS , (4)
( j) ( j) ( j) dd t di
From Figure 2, we have some constraints to calculate the stable probabilities of AC sub-node state:
( j) ( j) ( j) ( j) ( j) ( j) s d ds f d df
( j) ( j) ( j) ( j) ( j) i d di i ii
( j) ( j) ( j) ( j) ( j) ( j) ( j) d d dd i id f s
piij) + pid ) =1, pdi ) + pdd) + pdf ) + pds) =1.
With some basic calculus, we have the
M.T. Hoang et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 1 (2015) 45-54 49
steady states probabilities of the node state
model are:
PI =1 pt np(,n M ); n=1
(12)
( j) ( j) di
i p( j) 2 p( j) p( j) p( j) id
π( j) = ( j) 1 ( j) p( j) ;
dd di ( j) id
PC = (1 npt (1 pt )n 1 (1 pt )n )p(n,M ); n=2
(13)
PD =1 PC PS j=1.PSj) (14)
( j)
s
2
( j) ds
( j) ( j) dd di
( j) ; (11) di
( j) id
The transition probability from idle state to each success state comprises two probabilities:
successful transmitting ( IS1 ) and successful
( j)
f 2
( j) df
( j) ( j) dd di
( j) . di
( j) id
receiving ( IS2 ) for the given AC j :
P( j) = np( j) (1 pt )n P(,n M ) n=1
(15)
2.3. Channel State Model
The channel around node (i) is modeled by
using four-state Markov chain as in Figure 3.
P( j) = np( j) (1 pt )n P(,n MA )
n=1 (16)
in which, p( j) is the successful transmission probability from node k in annulus AA to a
node in the intersection area I (Figure 1), p( j) is π( j) examined in AC sub-node state
model as
( j) ( j) ( j) IS IS1 IS2
(17)
From these probabilities and the
Figure 3. Markov chain for channel state model.
We denote steady states and their durations by πI ,πC ,πS ,πD , andT ,T ,TS ,TD ,
respectively. Furthermore, the success state is
relationship on Figure 3, the idle steady state probability is
4
( j)
I I II C CI D DI ( j) SI j=1
=πI II +1 πI (18)
derived from 4 sub-states denoted as Thus, stable state probabilities of channel
S( j) , j = (1,2,3,4) corresponding to four ACs.
The transition probabilities between channel states in channel state model is illustrated in the figure and there are some transition probabilities equal to 1,
P I = P I = PIj) =1.
The transition probabilities II , IC and ID
of channel around node are acquired by similar
model are
πI = 2 1PI ; πC = 2 I PI ;πD = 2 I PI ;
( j) πS = π ( j) ; π ( j) = IS .
j=1 II (19)
2.4. Derivation of Analytical Problem
Contrast to Bianchi’s approach that based
arguments as in [11]: on the non-linear equations for unknown
50 M.T. Hoang et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 31, No. 1 (2015) 45-54
probabilities called collision probability and
transmission one, we propose relationship
p¢( j) = p( j)Õ1 k> j
p(k) . (23)
between probability of transmission and their successful probability from our two models as described in previous sections.
The event a packet of AC j is sent from the AC’s queue to virtual collision handler happens when node i changes from idle state to defer state (pid ) and channel around a node is idle (P(j) ) and back-off process is finished (P( j) ).
We have
p( j) = p( j) ´P( j) ´P( j) (20)
The probability that channel around a node is idle is different between ACs due to the disparity in the AIFS value and can be obtained from steady state probabilities of channel model in (19):
( j)
P( j) = I I 4
( j) ( j) ( j) ( j)
I I C C D D ( j) S
= T( j) 4 j=1 (21) ( j) ( j) ( j) ( j) ( j)
I IC C ID D IS S j=1
Thus, the probability of a node containing four ACs transmits a packet of any ACj , j = (1,2,3,4) to the channel around it in a
time slot is
pt = p¢( j). (24) j=1
2.5. Remarks
As described in the previous subsections, the analytical model is decomposed by two state models namely AC-node sub state model and channel state model respectively. By the decomposition, the main IEEE 802.11e EDCA features is exactly captured under realistic conditions. To evaluate its accuracy, the network performance such as throughput and access delay is examined by numerical simulation as bellows.
3. Numeric Results and Discussions
We use MATLAB to calculate throughput and delay performance from our proposed
The probability of back-off counter reduced model. Analytical results will be examined
to Zero in a given time slot ( p( j) ) depends on the average contention window at ith attempt and failure steady state probability of AC sub-node as formula
CW( j)π( j) i
P(O) = ( j) , CWavr = i=0 m (22)
avr ( j)
i 0