Embed Size (px)
Citation preview
Throughput and Delay Analysis of the IEEE 802.15.3CSMAICA Mechanism Considering the Suspending
Events in Unsaturated Traffic Conditions
Xin LiuSoftware SchoolFudan UniversityShanghai, China
Abstract-Unlike in IEEE 802.11, the CSMA/CA trafficconditions in IEEE 802.15.3 are typically unsaturated. This paperpresents an extended analytical model based on Bianchi's modelin IEEE 802.11, by taking into account the device suspendingevents, unsaturated traffic conditions, as well as the effects oferror-prone channels. Based on this model we re-derive a closedform expression of the average service time. The accuracy of themodel is validated through extensive simulations. The analysis isalso instructional for IEEE 802.11 networks under limited load.
Keywords- CSMA/CA; IEEE 802.15.3; MAC; markov chain;performance analysis
I. INTRODUCTION
The IEEE 802.15.3 [1] is designed for high-rate multimediaapplications in wireless personal area networks (WPAN). It hasdefmed a hybrid MAC protocol based on the TDMA andCSMA mechanisms [2]. The performance analysis ofCSMA/CA is a key issue in IEEE 802.15.3. The correspondinganalysis of IEEE 802.11 [3] can be used as a reference.However, in IEEE 802.11 networks, all of the traffic istransmitted by the CSMA/CA mechanism; thus the trafficcondition is saturated in most cases. In contrast, in IEEE802.15.3 networks most of the traffic consisting ofsynchronous data is sent by the TDMA mechanism, and only asmall amount of traffic comprising commands andasynchronous data is transmitted by the CSMA/CA mechanism;hence the traffic condition is unsaturated frequently.
The modeling of CSMA/CA in IEEE 802.11 has been aresearch focus since the standards were proposed. The work in[4] gives the theoretical throughput limit of IEEE 802.11 basedon a p-persistent variant. However, it does not consider theeffect of contention window. In [5, 6] Bianchi analyzed thesaturated throughput of IEEE 802.11 DCF based on markovchains and stochastic processes. Based on Bianchi's model, [7]re-analyzes the throughput taking into account the frame retrylimit. Some of the subsequent research is diverted on theanalysis of IEEE 802.11e EDCF capturing the contentionwindow differentiation [8-10]. A key common assumption inthe above works is that each device always has a frame totransmit. This is unreasonable if the traffic load is limited, such
947
Wenjun ZengDept. of Computer Sciences
University of MissouriColumbia, USA
zengw@missourLedu
as in IEEE 802.15.3 networks. To our best knowledge, littleanalysis is available for unsaturated conditions except in [1114]. According to the specifications in [1, 3], whether or not thebuffer has a frame to send after a successful transmission, thestation will unconditionally back off. This was ignored in [1214]. Furthermore, with the assumptions of traffic arriving inPoisson process and the buffering of multiple frames [12, 13],the transition probability from states having different retrytimes to the buffer empty state should not be identical (whichunfortunately is assumed in [12, 13]) since the effectivearriving time interval of the next frame is different. In [12, 13],the arriving time interval of the next frame is counted from thearriving moment of the current frame to the successfultransmission moment of the current frame. It is different if thecurrent frame ends with different retry times. Consequently wetake the same assumption as in [11]: each device can bufferonly one frame and data arrives with a Poisson process. Thusthe effective traffic arriving interval of the next frame iscounted from the successful transmission moment of thecurrent frame and it is identical to the one-step state transitionperiod. Moreover related research on average service time inIEEE 802.11 includes [9, 13-16]. All of them failed to take intoaccount the suspending events during the back-off process. Inthis paper we extend the Bianchi's model by considering thesuspending events during the back-off process. Based on thismodel we re-derive the average service time in IEEE 802.15.3.
The paper is outlined as follows. Section II briefly reviewsthe IEEE 802.15.3 MAC mechanism. The extended analyticalmodel is presented in section III. Section IV validates themodel by comparing the analytical results with those obtainedthrough simulations. Finally, concluding remarks are given inSection V.
II. IEEE 802.15.3 ACCESS MECHANISM
A. IEEE 802.15.3 MAC Protocol
In IEEE 802.15.3, the basic component is device and thebasic network element is piconet. One device is required toassume the role of PNC (piconet coordinator). The time isdivided into superframes. The superframe is divided into threeparts as shown in Fig. 1: beacon frame, sent by PNC, used to
set time allocations and to communicate managementinformation for the piconet; contention access period (CAP),accessing the channel in CSMA/CA manner, used tocommunicate commands and/or asynchronous data if it ispresent in the superframe; channel time allocation period(CTAP), adopting the TDMA protocol, composed of channeltime allocations (CTAs), including management CTAs(MCTAs). CTAs are used for commands, isochronous streamsand asynchronous data connections. MCTAs are a type of CTAthat is used for communication between the DEVs and the PNC.
Superframe #m· 1 Superframe #m Superframe~m " l
the collision probability of a frame is constant and independentof the number ofretransmission.
We eliminate the assumption that at least one frame isalways available at each device. Furthermore we consider theeffect of frame errors introduced by channel noise. We also dosome simplifications in IEEE 802.15.3. PNC as a transmitter isnot considered since PNC has the absolute access prioritywithout the back-off process. The average frame delay of otherdevices caused by PNC insertion is limited to PNCtransmission time. The device's waiting time (SIFS duration) atthe beginning of CAP is approximated with BIFS for simplicity.
A. The Modified Markov Chain Model
Consider a piconet with n devices and a PNC. Assumeeach device can buffer one frame and there is a constantprobability q of at least one frame arriving per state, as
discussed in section I. Let bet) be the stochastic process
representing the back-off time counter and ret) be thestochastic process representing the back-off stage for a given
device at slot time t. We introduce the state {(O,b(t))e} as
the back-off process after a successful transmission if thebuffer remains empty. The subsequent buffer empty state isdenoted as {(-1,0)} . u is the probability of channel sensed
busy, and P, is the frame-error probability. Different from
previous models, the suspending probability S during back-offis supplemented. The modified markov chain model is depictedin Fig. 2.
Next we analyze the back-off and transmission process indetail. If the buffer has one frame to transmit, the device willenter the back-off process after BIFS idle duration and the O-th
back-off timer is CWo' Note that only when the channel is
idle for a can the back-off timer decrease; if the channel isoccupied, the back-off timer will suspend and stay in thecurrent state. The probability is 1-sand s respectively,where S is the suspending probability, namely the channelsensed busy probability U . The state transition period differs:if it is an idle slot, it lasts a ; if the slot is occupied, it can be asuccessful transmission slot, a failed transmission slot due toframe error or collision. Transmission is attempted when theback-off timer reaches zero. The transmission is unsuccessfulwith probability p due to collision or frame error; or it is
successful with probability 1- p . In the model p is thetransition probability from one row to the next row. In theformer case the next back-off and retransmission cycle beginsagain until the transmission reaches the retry limit. In the lattercase the device either has a new frame to transmit with
probability q, or enters the empty back-off process {(O,k)e}
with probability 1-q if the buffer remains empty after a
successful transmission. As to the state {(O,k)e}, if no frame
arrives, it switches to state {(O,k-l)e} or remains in the
current state because of suspending; if a frame arrives, it
CTA n
Channel timeallocation period
Figure I. IEEE 802.15.3 Piconetsuperframe
period
~m
Deacon ConrentionI---Y---"""T"""~-~-~-~---y-----l
III. ANANALYTICAL MODEL OF IEEE 802.15.3 CSMA/CA
In this section we present an analytical model of IEEE802.15.3 based on Bianchi's model [7]. We impose someassumptions similar to [7]: no hidden devices are considered;
B. IEEE 802.15.3 CSMA/CA Mechanism
The device first waits for back-off interframe space (BIFS)duration, from when the medium is determined to be idlebefore beginning the back-off algorithm. At the beginning ofthe CAP, the device may begin the back-off algorithm a shortinterframe space (SIFS) after the beacon transmission. Suppose
the device selects BO; as the back-off timer in the i-th back-
off process, then BO; =a x CW; , where CW; is the i-th
back-off window, CW; =rand[O, W; -1]
CWmin S W; S CWmax and a is the slot time. For the first
transmission attempt of a frame, i is set to zero and W; is set
to CWmin' With the retry count i increments, W; is doubled
up to CWmax after the m'-th collisions,
CWmax =CWmin X 2m' • Once W; reaches CWmax ' it will
remain at CWmax until it is reset. W; is reset to CWmin
either after every successful transmission or when retry count
reaches the retry limit m . The back-off timer BO; is
decremented only when the medium is idle for the entireduration of slot time; it is suspended when the channel is busy.The device resumes to continuously decrement the back-offtimer until the channel is measured idle for a BIFS. The devicemay transmit the frame at the moment that the back-off timerexpires. After correctly receiving a frame in the destinationdevice, a positive ACK is sent to notify the source device afterSIFS. If the ACK is not received, the source device assumesthe transmitted frame is collided, and then it schedules aretransmission and re-enters the back-off process.
948
s
,I-s
I-s
I-s (m '+ I,Wm, -I )
( I-s)( I-q/.-----L----..- - --{ (O,Wo-l)e
s(l-q)sq
I-s
I-s
s
t
s
(m ',2)
(m '+ 1,2)
s
s
s
(m, l)
(m ', I) .. I-sI-s
I-s
I-s
( I-p)q(m', 0)
(l -P)(l -q) p
(I-p)q(m '+ I,O)
(l-p)(l-q) p
PIq
(m.O)
Figure 2. A modified markov chain model for the back-off process in unsaturated traffic conditions
switches to state {(O,k)} or {(O,k-1)} similarly. The
transition probability is (1- q)s , (1- q)(1- s) , qs and
q(1- s) respectively. The transition probabilities for the
states {(O,k)e} and {(-1,O)} are identical: whether there is
a frame to come with the probability q , whether the channel is
sensed idle with the probability 1-u , whether thetransmission is successful with the probability 1- p . Fromthe above analysis, we can obtain the one-step transitionprobabilities.
{P{(i,k)I(i,k)}=s kE[I,W; -1] iE[O,m] (1)
P{(i,k -1) I(i,k)} = 1- s k E [I ,W; -1] i E [O,m]
1
P{(O,k)'I(O,k).}= s(1-q) kE[I,Wo-I]
P{(O,k-I).I(O,k).}=(1-s)(1-q) kE[I,Wo-I] (3)
P{(O,k) I(O,k)e} = sq k E [I ,Wo-1]
P{(O,k -1) I(O,k).} = q(1- s) k E [I,Wo-1]
P{(O,k) I(O,O)e} = qu kE[O,Wo-I]Wo
P{(1,k)I(O,O)e}=q(1-u)p kE[O,Jf;-I] (4)Jf;
P{(O,k)e I(O,O).} = q(1-~(1- p) k E [O,Wo-1]o
P{(-I,O)I(O,O)e} = I-q
P{ (O,k) I (i ,0)} = (1- p)q k e [O,Wo-I] i e [O,m -I]Wo
P{(O,k)el(i,O)}=(I-p)(I-q) ke[O,Wo-l] i e [O, m- l] (2)Wo
P{ (O,k) I (m,O)}=.!L k e [O,Wo-I]Wo
P{(O,k)eI (m,O)} = I-q k e [O,Wo- I]Wo
P{(O,k) I(-I,O)} = qu kE[O,Wo-I]Wo
P{(1,k)I(-I,O)}=q(1~u)P kE[O,Jf;-I] (5)1
P{(O,k)e I(-I,O)} = q(1-~(1- p) k E [O,Wo-1]o
P{(-I,O)I(-I,O)} = I-q
949
w = {CWrnin ·2i
i E [O,m']1 "CWrnin·2
m iE[m+l,m](6) E[Le ] be the average length of the longest frame payload
involved in a collision.
Pe is the probability that a frame encounters a collision.
The probability that a device transmits a frame in a slottime can be evaluated as:
Note that the above average frame delay is derivedprovided that this frame is not discarded, so the weighted
ffici b .c. T· peN = i) d h f hcoe ticient erore di IS c an t e sum 0 t e1-r'"
Tf is the average failed transmission time.
C. Frame Discard Probability
The frame discard probability Pd is the probability of
consecutive m +1 unsuccessful transmission attempts.
r, = pm+l (15)
D. Average Frame Delay
We denote as Td the average frame delay from the
moment the back-off process is initiated until the frame is
successfully transmitted. Let N e be the number of collisions
experienced before a successful transmission, Tdi be the
average frame delay at the condition that N e is i . Then Tdi
can be divided into four parts: i times back-off process, itimes failed transmission, i + I-th back-off process and thesuccessful transmission, then the average frame delay is:
{
I: = BIFS +PHYprelhdr +MAChdr +E[L]+8 +SIFS +ACK +8(14)
1;; = BIFS + PHYprelhdr +MAChdr +E[Lc]+8
I: = BIFS +PHYprelhdr +MAChdr +E[L]+8
m
LP(Nc =i)coefficients is ;=0 , equaling to 1.
1-r'"
T =~P(Nc=i).T.=~pi(I-P).[~1: -i.t +T](16)d LJ 1- m+l di LJ 1- m+l LJ b ]; f s
i=O P i=O P k=O
(9)
(8)
(11)P; = 1- (I - r )n
P; =u=s=I-(I-r)n-1
m
t =Lb;,o +Q(I-u)[b(o,o)e +b_l,o];=0
where P{ (iI' kl ) I(io, ko)} is the short notation of
P{r(t +1)= il,b(t +1)=kl Iret) = io,b(t) =ko}·
Combining equation (1)-(10), a nonlinear system with oneunknown T is formed. Due to the space limitation, we referthe readers to [7] for the detailed derivation process. Weconsider not only the unsaturated traffic condition but also thedevice suspending event, so the process to solve the equationsis much more complicated than previous models. We can fmdthe solution by using the symbolic math toolbox in MATLAB.
B. Throughput
~r is the probability that at least one transmission occurs.
~ is the probability that exactly one device transmits,
conditioned on the fact that at least one device transmits
Let bi,k ' bU,k)e and b_l,o represent the stationary
distribution and normalize them to 1, we can solve bo,o.
nr(l- r)n-lp=----
s ~r
nr(l- r)n-l
I-(I-r)n(12)
(17)
(18)
The normalized throughput in an error-prone channel is
= PsPtr (1- Pe ) · E[TL ] (13)Snorm (1- Ptr)O" +PtrPs(1- P, )Ts +P; (1- P,)Tc +PtrPsp:r.
If P, is zero, equation (13) agrees with [7] and [11].
E[~] is the average frame payload transmission time; T, '
T; and Te are the average times that the medium is sensed
busy due to a successful transmission, due to a collision anddue to transmission errors respectively. Let 8 be thepropagation delay, E[L] be the average frame length, and
Tbk is the back-off time during the k+ l-th back-off process.
Let Tstate be the one-step state transition period in Fig. 2,
Tdeere be the average time for the back-off timer to decrease by
1, namely the arriving time from state (k, j) to (k, j - 1) ,
N decre be the number of steps staying in state (k,j) before
jumping to (k, j - 1)
w: -Ir; =T ·Tdecre
950
Pis is the probability of exactly one transmission from the
n -1 remaining devices :
I. I
I
I
, I30 35 40
I
l
H.Wu model in [7]
12 c _ K.Duffy model in (11) f-----+--+---"-I,----- our model
.v simu lat ion
:: ;-~~~:=" '-~r-~--;--'--I
l ~---+~-----;; I20 I ~
18 I;ji 16
e 14 HI_+-_~_L,---~-r--+-+-+--~ I
unsaturated traffic model is based on the model in [II],whereas [II] did not take into account the effect of devicesuspending and did not address the average frame delay. [16]gave the mean and standard deviation of the frame delay insaturated traffic conditions using one-dimensional markovchain without considering the suspending events . We comparethe throughput analysis with [7] and [II] in Fig. 3 and comparethe average frame delay with [15] and [16] in Fig. 4 todemonstrate the effect of considering unsaturated trafficconditions and suspending events in performance modeling.All of the above works assume the channel is ideal, so the
frame error rate Pe in our model is set to zero for fair
comparison purpose.
In Fig. 3, the model in [7] assumes a saturated trafficcondition and q is set to 0.1 in [II] and our model. All curvesdemonstrate the same trend : with the increased number ofdevices the throughput increases and achieves a maximum andthen decreases . Once all of the bandwidth is occupied, thethroughput can not increase with the number ofdevices . On thecontrary the throughput will decrease with the increase of thecollision probability. Comparing the models in [7] and [II], wecan observe that the maximum throughput is reached with asmaller number of devices in the saturated traffic case than inthe unsaturated traffic case. The larger the q is, the earlier the
throughput becomes saturated.
As shown in Fig. 3, our analytical model matches the NS-2simulation results much better than the others. Whensuspending event is not considered, the device at the back offstate will jump faster to the state to transmit a frame thanotherwise. This means the probability to transmit a frame in agiven slot is larger when not considering the suspending event .If the network bandwidth is not occupied fully, largerprobability to transmit a frame results in larger throughput. Asthe network becomes saturated with the increased number ofdevices, a larger probability to transmit a frame will lower thethroughput. This suggests the performance analysis in [7] and[II] which ignores the suspending event during the back-offprocess is underestimated for large number ofdevices.
15 20 25Number ofde";ces
(19)
(21)
IEEE 802.15.3 PHY AND MAC PARAMETERSTABLE!.
Symbol Value Symbol Value
a (J.1S) 17.273 CWmin8
SIFS (J.1S) 10 CWmax64
BIFS (J.1S) 17.273 ACK(bytes) 10
PHYn rJJ.1S ) 17.455 b(J.1S) 1
ntv.; (J.1S) 0.727 L (bytes) 256
MAChdr (J.1S) 3.636 m 3
(n -1)T(1- Ty-2Pis =
Pc
After some algebra operations, (16) becomes
Tdecre=i:«: =l)~ . r.: + 'F.tatel1=0
= fs/(1-S)'(I+I)T = 'F.tate1=0 state 1- S
During the one-step state transition, the channel may be idleor occupied because of successful transmission, frame error orcollision by the remaining n -1 devices
Tstate = (1-U)a-+UPls(1-Pe)T, +uP,sPeTe +u(1- p's)Tc(20)
IV. NUMERICAL RESULTS
According to [1], the specific network configuration used inour simulations is listed in table I. The base rate is 22Mbps andthe data rate is 55Mbps. In order to verify the accuracy of theproposed model, the results obtained using the IEEE 802.15.3network in NS-2 are also plotted in the following figures .Related IEEE 802.15.3 simulation environment in NS-2 is setup by Mustafa [17]. The superframe size is set to 15microseconds and it consists of only the beacon frame andCAP to avoid the implication that CTAP may pose on the delaymeasurement.
T 2m'c w 2( m m') m+2~ = slate .{ minP P - P - P + P
2(l-s)(l- p m+
1) 1- p
-CW . p[I-(2p)m'+'] +2m'CW . (m-m' +2) (22)nun 1-2p nun
1 (m+l)pm-CW . -m-l}+T .p[-- ]+T
nun f 1 1 m+l S-p -p
Figure 3. Throughput for different number ofdevices
The models in [7] and [15] are both based on Bianchi'smodel but considering the retry limit in saturated trafficconditions. [7] derived the expression for the throughput and[15] derived the expression for the average frame delay. Our
Fig. 4 shows the average frame delay for different models.Again, our analytical model matches the NS-2 simulationresults much better than the others for both saturated and
951
4.5·· - - - - - - - - -- - -- - -- - -- - -;
Figure 4. Average frame delay for different number of devices
REFERENCES
[I] Part 15.3: Wireless medium access control (MAC) and physical layer(PHY) specifications for high rate wireless personal area networks(WPAN), IEEE Std 802.15.3, Sep. 2003
V. CONCLUSIONS
In this paper we propose an extended analytical model tostudy the performance of the IEEE 802.15.3 CSMAlCAmechanism . Both the back-off process after a successfultransmission in unsaturated conditions and the suspendingevent during the back-off process are considered. Theexpression for the average frame delay is re-derived based onthe modified model. The explicit analytical model has beenvalidated to be in agreement with the computer simulations.
[2] X. Shen, W. Zhuang, H. Jiang, and 1. Cai, "Medium Access Control inUltra-Wideband Wireless Networks", IEEE Tran. on VehicularTechnology, vo1.54, no.5, pp, 1663-1677, Sep. 2005
[3] Part 11: Wireless LAN Medium Access Control (MAC) and PhysicalLayer (PHY) Specification: Higher-Speed Physical Layer Extension inthe 2.4GHz Band, IEEE Std 802.11b, 1999
[4] F.Cali, M.Conti, E.Gregori, "Dynamic Tuning of the IEEE 802.11Protocol to Achieve a Theoretical Throughput Limit", IEEE/ACM Tran.On Networking, vo1.8, no.6, Dec. 2000
[5] G.Bianchi, "IEEE 802.11 Saturation Throughput Analysis", IEEEComm. Letters, vo1.2, no.12, Dec. 1998
[6] G.Bianchi, "Performance Analysis of the IEEE 802.11 DistributedCoordination Function", IEEE Journal on Selected Areas inCommunications, vol.l8, no.3, pp.535-547, Mar. 2000
[7] H.Wu, Y.Peng, K.Long, S.Cheng, 1.Ma, "Performance of ReliableTransport Protocol over IEEE 802.11 Wireless Lan: Analysis andEnhancement", in Proc. IEEE Infocom, New York, USA, pp.599-607,2002
[8] y'Xiao, "Performance analysis of IEEE 802.11e EDCF under satuarioncondition", in Proc. IEEE ICC, Paris, France, pp.170-174, June 2004
[9] J. Tantra, C. H. Foh, and A. Mnaouer, "Throughput and delay analysisof the IEEE 802.11e EDCA saturation", in Proc. IEEE ICC, Seoul,Korea, pp. 3450-3454, 2005
[10] L. Xiong and G. Mao, "Saturated throughput analysis of IEEE 802.11eEDCA", Computer Networks, vo1.51 , no.11, pp.3047-3068, Aug. 2007
[11] K. Duffy, D. Malone and DJ. Leith, "Modeling the 802.11 distributedcoordination function in non-saturated conditions", IEEE Comm. Letters,vo1.9, no.8, pp.715-717, Aug. 2005
[12] W.Lee, C.Wang, and K.Sohraby, "On use of traditional M1G/I model forIEEE 802.11 DCF in unsaturated traffic conditions", in Proc. IEEEWCNC, Las Vegas, USA, pp.1933-1937, Apr. 2006
[13] O.Rodolfo, B.Luis, P.Paulo, "Modelling Delay on IEEE 802.11 MACProtocol for Unicast and Broadcast Nonsaturated Traffic", in Proc. IEEEWCNC, HongKong, China, pp.463-467, Mar. 2007
[14] LJing, N.Zhisheng, "Delay Analysis of IEEE 802.11e EDCA UnderUnsaturated Conditions", in Proc. IEEE WCNC, HongKong, China,pp.430-434, Mar. 2007
[15] P. Chatzimisios, A. C. Boucouvalas, and V. Vitsas, "IEEE 802.11 framedelay - a finite retry limit analysis," in Proc. IEEE Globecom,SanFrancisco, USA, pp.950-954, Dec. 2003
[16] T.Sakurai, H.L.Vu, "MAC Access Delay of IEEE 802.11 DCF", IEEETran. on Wireless Communications, vol.6, no.5, pp.1702-1710, May2007
[17] R.Mangharam, M.Demirhan, R.Rajkumar and D.Raychaudhuri, "SizeMatters: Size-based Scheduling for MPEG-4 over Wireless Channels",SPIE Conference on Multimedia Computing and Networking, 2004
40353015 20 25Number of de"";ces
10
P.Chatzimisios model in [15]I
- T.Sakurai model in [16J ;a-: J"----a- our model, q=0.99 ,rr ..¥ ·· I-- /." " .
--:-- our rnodel.q-Oil ,2'" : .
I2,..,;--
" sim, saturated (q= l ) ..:~"..sim, unsaturated (q=0.1) r" ./-'
,;rr"'...,. .
/ ';:: -
-
-~¥~ ..,.,, '
.~~--- I/,":
,,~~.:7
I.'" if / " I~ / . '
-"/ , ,I~,""
r r r r r rI
0.5
3.5
4
.§. 3»,
'"~ 2.5Q)
E~ 2Q)
~~ 1.5«
unsaturated cases. In particular, let us compare the models in[IS] , [16] and ours in saturated conditions . As there existsuspending events, the back-off timer has more chance to stayin the current state. The larger the number of devices, thehigher probability to stay in the current state. The averageframe delay does not become saturated as suggested by theother two models with the increased number of devices evenfor a finite retry limit. This illuminates that there can not be toomany devices in a piconet in order to maintain a low framedelay.
952
