Low Latecy Radom Access with TTI Budlig i LTE/LTE-A Kaijie Zhou, Navid Nikaei Huawei Techologies Co., Ltd. Chia, zhoukaijie@huawei.com Eurecom, Frace, avid.ikaei@eurecom.fr Abstract To reduce the uplik chael access latecy i LTE/LTE-A, we propose a Trasmissio Time Iterval (TTI) budlig scheme for the radom access procedure. With the proposed method, a UE seds multiple preambles i cosecutive subframes i order to icrease the success rate of radom access ad hece to reduce the latecy. We itroduce a Semi-Markov model to accurately model ad aalyze the radom access mechaism with TTI budlig. With this model, we formulate the access latecy as a fuctio of the umber of TTI budles ad select the optimal value which miimizes the chael access latecy. The proposed Semi-Markov model is validated agaist simulatio ad the performace of the TTI budlig method is also evaluated. We fid that chael access latecy ca be sigificatly reduced whe the preamble collisio rate is ot high. Keywords LTE, Radom Access, TTI budlig, Semi-Markov Model. I. INTRODUCTION Low-latecy protocols ad access methods are becomig crucial to improve the spectral efficiecy ad to lower the eergy cosumptio i ed-devices, especially i view of emergig applicatio scearios foud i machie-to-machie commuicatio, olie iteractive gamig, social etworkig ad istat messagig. However, the majority of wireless systems, icludig LTE/LTE-A, are desiged to support a cotiuous flow of iformatio, at least i terms of the timescales eeded to sed several IP packets, such that the iduced sigalig overhead is maageable. While these systems are iteded mostly for dowlik-domiat ad bursty traffic, emergig applicatio scearios are of geerally differet characteristics [], amely: uplik domiat packets, periodic ad evet-drive packets, small ad low duty cycle packets. Such applicatios do ot ecessarily eed a icrease i the maximal data rate though part of the 4G-5G requiremet [2], they rather call for a efficiet support for low-latecy, potetially coordiated, chael access, ad i particular for small to verysmall packets. We argue that i 4G/4G+ system, this represets a opportuity to limit the modificatios i the physical layer ad redesig the access ad trasmissio protocols to obtai the desired features. Curretly, to reduce the sigalig overhead for the uplik schedulig, a UE ca use radom access chael for uplik chael access (see Ref. [3] i case of machie-to-machie commuicatio). More specifically, to apply for uplik trasmissio resources from enb, a UE seds the schedulig request (SR) message through radom access, which provides a chael access latecy of 4 ms i the best case (see Fig. ). However, if the radom access fails, UE has to backoff before startig aother radom access. This sigificatly icreases the chael access latecy, which may ot be desirable for the iteractive ad/or realtime applicatios that require fast reactio time to a evet. A lot of efforts has bee give to improve the performace of radom access, with particular attetio to machie-tomachie commuicatio (small low duty cycle packets). I Referece [4], a self optimizatio method for radom access is proposed, which pre-computes the radom access parameters (offlie approach) to guaratee the chael access latecy. Differet backoff schemes for radom access are aalyzed i [5]. Based o this method, a dyamic widow assigmet method is desiged, ad as a result, the performace of radom access is greatly improved compared to the fixed widow scheme. Referece [6] suggests a fast collisio resolutio method for radom access. This method utilizes the timig advace iformatio of the statioary UEs to idetify UEs ad hadle collisios betwee UEs. To icrease the success rate of the radom access, we propose a TTI budlig scheme for the trasmissio of preambles. I the proposed method, a UE seds multiple preambles i several subsequet TTIs (i.e. subframes), by which a radom access is successful if at least oe of the preambles is correctly received by a enb without a collisio. We use a semi-markov model to aalyze the radom access with the TTI budlig scheme. With this model the access latecy is derived as a fuctio of the umber of TTI budles, ad hece the optimal TTI budlig umber which miimizes the access latecy is foud. The idea of TTI budlig is ot ew ad itroduced i LTE Rel. 8 to improve the uplik coverage for VoIP applicatio [7]. The method allows a UE to sed multiple VoIP packets through a budle of several subsequet TTIs before receivig the HARQ from the servig enb, which elimiates the latecy caused by the packet retrasmissios ad thus improves the QoS for VoIP applicatio [8]. The remider of this paper is orgaized as follows. Sectio II provides a backgroud iformatio o the radom access mechaism i LTE/LTE-A ad presets the basic idea of the proposed TTI budlig scheme. Radom access model with TTI budlig ad the assumptios are explaied i Sectio III. The method ad how the optimal umber of TTI budles is calculated are detailed i Sectio IV. Sectio V presets the model validatio ad simulatio results. Fially, Sectio VI provides the cocludig remarks. II. RANDOM ACCESS IN LTE/LTE-A AND THE TTI BUNDLING SCHEME Fig. depicts the procedure for the cotetio based radom access i LTE/LTE-A [9]. Firstly, a UE seds a radomly
selected preamble whe the backoff couter becomes zero. Secodly, if the preamble is correctly received by enb, the enb seds the radom access respose (RAR) iformatio durig the RAR widow. Thirdly, UEs decode the RAR message. If a UE fids its preamble idetifier i the RAR message, it seds a L2/L3 message, for example schedulig request SR (L2 message) or RRC coectio request (L3 message). It has to be oted that multiple UEs sed L2/L3 message o the same resource if they select the same preamble i the first step (preamble collisio), which results i that the L2/L3 message might ot be correctly received by enb. Fially, the enb seds the cotetio resolutio to ackowledge the correctly received L2/L3 message. Assumig that the time used to decode preamble, RAR, ad L2/L3 message is 3ms, the total latecy is aroud 4 ms i the best case (o preamble collisio ad o wireless chael error). However, if the iitial radom access fails, a UE has to backoff for certai time before startig a ew radom access attempt. Time ms 2 ms 3 ms 6 ms 7 ms UE 9 ms 0 ms 4 ms 5 ms enb 2 ms 3 ms 4 ms 5 ms 6 ms 0 ms ms 3 ms 4 ms TTI budlig Corrupt due to wireless chael error Fig.. Time ms 6 ms 9 ms 4 ms UE Cotetio based radom access i LTE enb 2 ms 5 ms 0 ms 3 ms To improve the success rate i radom access, we propose a TTI budlig scheme as show i Fig.2. With the proposed scheme, a UE seds several radomly selected preambles i cosecutive subframes to perform multiple radom access attempts, which is referred to as TTI budlig for radom access. Here we cosider the multiple radom access i cosecutive subframes as a radom access roud. It is obvious that if oe of these preambles i a radom access roud is correctly received by enb ad without collisio, the radom access roud is successful, which elimiates the time that a UE has to wait for to start aother radom access whe the iitial radom access fails. It seems that icreasig the umber of budlig TTIs yields higher successful probability for a radom access roud ad thus reduces latecy. However, this is ot always true as the preamble collisio rate icreases with the umber of budlig TTIs. This is because each UE has to trigger more trasmissios whe budlig larger umber of TTIs, which i tur could reduce the success rate of a radom access roud ad accordigly icreases the latecy. Therefore, the optimal selectio of TTI budlig umber i o-trivial. The maximum legth of the backoff time is sigaled by the enb ad ca vary from 0 to 960 ms. Fig. 2. III. Cotetio based radom access with TTI budlig RANDOM ACCESS WITH TTI BUNDLING MODEL AND ASSUMPTIONS To fid the optimal umber of TTI budles, a mathematical model is eeded to aalyze the radom access mechaism. The existig radom access models are based o a multichael slotted ALOHA [0]- [], where the delay ad throughput of the radom access procedure ca be derived. However, they caot be used to aalyze the beefits of the TTI budlig scheme as they do ot cosider the backoff procedure after a usuccessful trasmissio ad the waitig state for a radom access respose. We apply the Semi-Markov process to model the radom access i LTE/LTE-A ad to aalyze both the regular radom access as well as the radom access with the TTI budlig. I the proposed model, the followig assumptios are made. Collisio: We assume that each packet collides with a costat ad idepedet probability. The assumptio is feasible whe the backoff widow ad umber of UE are large [2]. Packet Trasmissio: Regardless of the packet size, all the packets i a UE s buffer ca be set by oe uplik trasmissio. This assumptio is reasoable as a UE ca provide a buffer status report for the enb scheduler through the L2/L3 message (see Fig. ). Note that durig the radom access, it is possible that ew packets are geerated. With this assumptio, these ew packets are delivered with precedet packets. Therefore, whe a UE re-starts at the iitial state, there is o packet i its buffer. Moreover, due to the memoryless characteristic, the probability that a packet arrives i oe subframe is ot chaged. Traffic Model: The packet arrival is Poisso distributed. This is a simplifyig assumptio, for aalytical purposes, but ca be relaxed later (ot cosidered i this paper). Radom Access opportuity: The radom access chael is available i every subframe, which is related to radom access resource cofiguratio idex 4 specifed by 3GPP [3]. Fig. 3 shows the proposed Semi-Markov process model for radom access with TTI budlig, where there are three types of state: idle, backoff, ad radom access.
Idle Fig. 3. S 0,E Radom access p 0 /W S,R S,0 S, S, -2 S, - S i-,r p i- / S i,r p /W 2 p i /+ p M- /W M S M,R S i-,0 S i-, S i,0 S i, S M,0 S M, Backoff Semi-Markov process model for radom access with TTI budlig Idle state S 0,E meas there is o packet i the UE s buffer. Backoff state S i,j, i [, M], j [0, ], meas that the UE i the ith backoff stage ad the backoff couter is j, where M is the trasmissio limit ad is the maximum backoff couter size for ith backoff stage. Radom access trasmissio state S i,r, i [, M], meas that a UE is performig multiple radom access attempts, i.e., sedig preambles or L2/L3 messages, ad waitig for the respose from enb, such as RAR or cotetio resolutio message. A UE trasfers betwee states as follows. Whe a UE is at state S 0,E, if a packet arrives i oe subframe the UE selects a radom backoff couter j over [0, W ] ad trasfers to state S,j to start the first backoff. Otherwise it remais at state S 0,E. Whe a UE is at state S i,j, i [, M], j [0, ], it trasfers to S i,j after ms. Whe a UE is at state S i,r, i [, M ], it trasfers to state S 0,E if a cotetio resolutio idicatig a successful radom access is received. I cotrast, it trasfers to state S i+,j ( j is radomly selected over [0, + ]) to start aother radom access roud if the, [, N], radom accesses i oe radom access roud all fail, where is the umber of budlig TTIs ad N is the limit of TTI budlig umber. Whe a UE is at state S M,R, whether the radom access attempts i this roud are successful or ot, it trasfers to state S 0,E whe the radom access roud eds. IV. OPTIMAL TTI BUNDLING FOR RANDOM ACCESS Followig the model preseted i the Fig. 3, we deote the probability that a packet arrives durig oe subframe (ms) as p 0, the state trasitio probability from S 0,E to S,j, j [0, W ], is p 0 /W. Similarly, we deote p i, i [, M ], as the usuccessful probability for the ith radom access roud, therefore the state trasitio probability from S i,r, i [, M ] to S i+,j, j [0, + ] is p i /+. Deotig π i,j as the statioary probability for state S i,j (the probability that UE remais at a give state), it ca be calculated as: p 0 π,w = π 0,E W p 0 π,j = π 0,E + π,j+, j [0, W 2]. W π i,w = π,r p, i [2, M] π i,j = π,r p + π i,j+, i [2, M], j [0, 2]. () With the first ad secod equatios i equatio system (), we have: π,j = (W j) p 0 W π 0,E, j [0, W ]. (2) π,r = p 0 π 0,E. (3) By the use of the third ad fourth equatios i equatio system (), we get π i,j = ( j) p π,r, i [2, M], j [0, ]. (4) π i,r = p π,r, i [2, M]. (5) The sum of the all state s statioary probabilities is, which yields: = π 0,E + π i,r + W = π 0,E + p j π 0,E + = π 0,E + p j π 0,E + Therefore, we have π 0,E = π i,j (6) W + 2 j π i,r p j π 0,E. + M p j + M + 2 p. (7) j Now let us calculate the state trasitio probabilities. Assumig the packet arrives followig Poisso distributio with arrival rate λ, the probability that a packet arrives i oe subframe is p 0 = e λ. Oe radom access roud is usuccessful if all the radom access attempts i this roud are usuccessful, therefore p i = p F,i where p F,i is the usuccessful probability for oe radom access i the ith radom access roud. A usuccessful radom access is caused by erroeous trasmissio for the preamble or the usuccessful delivery of the L2/L3 message. More specifically, the usuccessful delivery of the L2/L3 message is also caused by two subcases: () collisio of the preamble, which leads to the failure
for the L2/L3 message delivery, ad (2) the L2/L3 is corrupted due to wireless chael error. I the later case, the preamble is correctly received by the enb without ay collisios, however the L2/L3 caot be successfully decoded by the enb due to the wireless chael error. With the above aalysis, we have p F,i = p E,i + ( p E,i )p c + ( p c )( p E,i )p N HARQ ES. (8) I the above equatio p c is the collisio rate for a preamble; p E,i is the error probability caused by wireless chael for a preamble i the ith radom access roud; p ES is the error rate to sed the L2/L3 message which cotais SR ad N HARQ is the maximum umber of HARQ trasmissios. Sice the L2/L3 message cotaiig SR is of very small size, therefore its error rate p ES is very small (less tha 0.) ad hece p N HARQ ES 0 cosiderig that N HARQ is usually larger tha 2. With this result, we have p F,i p c + p E,i p c p E,i. From the perspective of oe UE, collisio happes whe there are other UEs selectig the same preamble, therefore N u ( ) Nu p c = τ i ( τ) Nu i ( ( ) i ). (9) i N p I the above equatio N u is the total amout of UE; τ is the probability that a UE seds a preamble i oe subframe; N p is the umber of available preambles for radom access. Now let us calculate the state holdig time for this Semi- Markov process model. It is obvious that the state holdig time for S 0,E ad S i,j, i [, M], j [0, W ] is ms. For the UE at S i,r, i [, M], the calculatio for state holdig time is less obvious. We deote the duratio that starts at the ed of a preamble trasmissio ad eds at the time istat whe receivig the RAR message for that preamble as T RAR ad the time used to decode the RAR message as T D. Therefore, the SR message is set T RAR + T D ms after the preamble s trasmissio if the RAR message is received (o wireless error for the trasmitted preamble). As stated above, whe the UE is at S i,r, i [, M], the state trasitio happes whe oe radom access is successful or all the radom access i oe radom access roud fail. Hece, we calculate the state holdig time for three cases: ) The jth, j [, ], radom access i the ith, i [, M], radom access roud is successful. The probability for the first case p S i,j is or k= p k p j F,i ( p F,i), i > (0) p j F, ( p F,), i =. () Whe a radom access succeeds, the UE trasfers to the iitial state S 0,E after decodig the cotetio resolutio message. Deotig T CR as the average duratio which starts at time istat whe a UE seds the SR message ad eds at the time istat whe a UE decodes the cotetio resolutio message, the state holdig time for the first case is Ti,j S = j + T RAR + T D + T CR 2) Noe of the radom access i the ith, i [, M], radom access roud is successful, ad the UE receives the RAR message from enb for the last trasmitted preamble. I this case, a UE seds the L2/L3 message. However, as the radom access is usuccessful, it caot receive the cotetio resolutio message. This UE will trasfer to the iitial state S 0,E whe the cotetio resolutio timer expires. Therefore, the state holdig time for the secod case is T R = + T RAR + T D + T timer where T timer is the duratio for cotetio resolutio timer. The probability for this secod case whe i > is p R i = k= p k p F,i P RAR,i. (2) Whe i =, the probability for the secod case is p R = p F, P RAR,. (3) where P RAR,i, i [, M], is the probability that the collisio happes for a radom access i the ith radom access roud ad UE receives the RAR message. The P RAR,i is calculated by equatio (4). I equatio (4) r i,j+ is the detectio rate for the preamble i the ith radom access roud whe j + UEs (oe UE plus j cotedig UEs) sed the same preamble. If r i,j+ for j, i.e., a preamble ca mostly be detected whe it is set by multiple UEs, the P RAR,i p c. 3) Noe of the radom access i the ith, i [, M], radom access roud is successful, ad the UE does ot receive RAR for the last radom access. I this case, after sedig the last preamble the miimum time that a UE will stay at state S i,r is T W, i.e., the miimum state holdig time for state S i,r is T W, where T s the duratio which starts at the time istat whe a UE seds a preamble ad eds at the last subframe of RAR widow. Besides that, if this UE has received the RAR for a radom access i this roud (ot the last radom access i this roud), it caot trasfer to the iitial state S 0,E util the cotetio resolutio timer eds, which may exted the state holdig time. Deotig the time istat whe a UE seds the jth, j [, ], preamble as t j ad assumig the RAR is received by UE for this preamble, its cotetio resolutio timer eds at t j +T RAR +T D +T timer. Therefore, for a preamble trasmissio which ca exted the UE s state holdig time at state S i,r, i [, M], its trasmissio time istat t j should satisfy the followig the coditio t j + T RAR + T D + T timer > t + T W (5) where t is the time istat whe a UE seds the last preamble. Sice t = t j + ( j) where is the idex of the last preamble set i a radom access roud ad j is the idex of the jth preamble set i a radom access roud, the above calculatio is rewritte as j + T RAR + T D + T timer > + T W. (6) We ca fid the miimum preamble idex j satisfyig the above formula, which is deoted as z. Therefore, whe a UE ca trasfer from state S i,r to aother state is determied by the status whether RAR is received for the kth preamble, k [z, ]. Specifically, a UE trasfers from state S i,r to aother state whe the kth preamble s cotetio resolutio timer eds if the followig
P RAR,i = N u = ( ) N u τ ( τ) Nu ( ) ( ) j ( ) j r i,j+. (4) j N p N p coditios hold: (a) RAR is received for this preamble; (b) the radom accesses are usuccessful for the preambles set before it; (c) o RAR messages are received for the preambles set after it. Accordigly, the state holdig time is ad its probability p N i,k is or T N i,k = k + T RAR + T D + T timer (7) p j p k F,i P RAR,iP k NRAR,i, i > (8) p k F, P RAR,P k NRAR,, i = (9) where P NRAR,i, i [, M], is the probability that o RAR is received i oe radom access of the ith radom access roud. The RAR is ot set to a UE if the trasmitted preamble set by oe UE (or multiple UEs) is ot correctly detected by enb, therefore we have equatio (20). It is also possible that o RAR is received for all the radom accesses whose idex are larger tha z. The the state holdig time is Ti, N = + T W ad its probability p N i, is or p j p z F,i P z+ NRAR,i, i > (2) p z F,i P z+ NRAR,i, i = (22) If r i,j+ for j, i.e., a preamble ca mostly be detected whe it is set by multiple UEs, we have P NRAR,i ( p c )p E,i. With the above results, the average holdig time T i,r, i [, M], for state S i,r is T i,r = ps i,j T i,j S + pr i T R + T i,j N ps i,j + pr i +. (23) Whe a UE is at state S i,r, i [, M], the average duratio which is used for sedig preambles is T i,t X = ps i,j j + pr i + ps i,j + pr i +. (24) Therefore, the proportio of time that a UE is sedig a preamble, i.e., the probability that a UE seds a preamble i oe subframe, is where T = π 0,E + τ = W π i,r T i,t X T π i,j + (25) π i,r T i,r. (26) is the average holdig time for all the states. It ca be see that equatios (25) ad (9) comprise a equatio system with two ukows p c ad τ, which ca be solved by the use of umerical method. Provided that the i [, M] radom access roud is usuccessful, the the duratio that UE stays at state S i,r is the latecy itroduced by this radom access roud. Deotig the latecy i this case as d i, it is calculated by d i = pr i T R + p R i T N i,j +. (27) If a radom access is successful at the first radom access roud, o latecy is caused by the subsequet radom access rouds. Therefore, we have T = 0. However, if a radom access is successful at the ith radom access roud, the latecy caused by the precedet usuccessful radom access is T i = d j, i [2, M]. (28) Now let us calculate the access latecy for radom access which is defied as the duratio that starts at the time istat whe a UE wats to trigger a radom access ad eds at the time whe that UE receives a cotetio resolutio message idicatig the radom access is successful. Assumig the radom access is succeed i the jth trasmissio of the ith radom access roud, the access latecy icludes () the duratio of i W j 2 which is used for backoff, (2) the duratio of Ti,j S which is the time used for the successful radom access i the curret roud, ad (3) the latecy T i which is used for the precedet usuccessful radom access rouds. With above aalysis, the average chael access latecy caused by radom access is calculated by d = + p (j ) i=2 F, ( p F, ) M p i k= p kp (j ) ( W 2 + T S,j) F,i ( p F,i ) M p i ( i k= W k 2 + T S i,j + T i ). (29) The optimal TTI budlig umber which miimizes the access latecy is arg mi subject to d < N (30) where N is the limit of TTI budlig umber. The L2/L3 message is set T RAR + T D ms after the first preamble s trasmissio if the preamble is correctly received by enb. As a UE caot sed a L2/L3 message as well as a preamble at the same time, the maximum budlig TTI umber N should be o larger tha T RAR + T D. Sice we do ot have a closed form of d i the term of, therefore the above optimizatio problem ca oly be solved by exhaustive search.
P NRAR,i = N u =0 ( ) N u τ ( τ) Nu ( ) ( ) j ( ) j ( r i,j+). (20) j N p N p For some power costraied devices, the optimal TTI budlig umber obtaied from the above equatio might be adjusted to achieve a trade-off betwee the power cosumptio ad the latecy costrait. A. Simulatio Parameters V. RESULTS The simulatio parameters are show i Table I. Here the total umber of available preambles is assumed to be 20. While the total umber of available preambles i LTE is 64, this assumptio allows us to study the behaviour of the proposed method uder a high collisio rate regime. I additio, this assumptio is also related to the sceario where the available preambles are divided ito multiple (o- )overlappig sets to cotrol the collisio across multiple applicatios, e.g. oe for huma type commuicatio ad the other for the machie type commuicatio [4]. Two packet arrival rates are cosidered: λ = /00 ad /50 packet/ms, which correspod to the iteractive ad/or realtime applicatio scearios (e.g. realtime machie-to-machie commuicatio ad olie iteractive gamig). I case of o collisio, the preamble detectio rate is assume to be e i similar to [3], where i [, M] idicates the ith preamble trasmissio. Whe a preamble are set by multiple UEs, it ca always be correctly decoded, r i,j+ for j. This assumptio is quite typical i LTE. If a preamble is set by two UEs, two peaks appear at the enb side. The probability that either peak ca be decoded by enb is relatively low. TABLE I. SIMULATION PARAMETERS Parameter Value Descriptio T RAR 5 ms Time elapsed betwee the preamble trasmissio ad the receptio of RAR message T D 3 ms Time used to decode a RAR message T CR 8 ms Time elapsed betwee the trasmissio of a SR ad the receptio of a cotetio resolutio message T W 5 ms Time elapsed betwee the preamble trasmissio ad the last subframe of RAR widow T timer 24 ms Duratio of cotetio resolutio timer M 5 Trasmissio limit for radom access N p 20 Number of available preambles for radom access N 8 Max TTI budlig umber, i [, 5] 30 Backoff Widow Size B. Model Validatio To validate the proposed method, we compare the simulatio results with the aalytical results obtaied usig equatio (29) i Fig. 4. To validate the applicability of the modellig approach for both regular radom access ad radom access with TTI budlig, simulatios are performed with ad 2 TTI budles (i.e. = ad = 2). As show i Fig. 4, the aalytical results match the simulatio results validatig the modellig approach. C. Optimal TTI budles ad The Iduced Latecy Fig. 5 depicts the optimal TTI budlig umber uder differet umbers of UE ad packet arrival rates. It ca be Fig. 4. Latecy (ms) 00 90 80 70 60 50 l=/00, =2, aalytical l=/00, =2, simulated l=/50, =2, aalytical l=/50, =2, simulated l=/00, =, aalytical l=/00, =, simulated l=/50, =, aalytical l=/50, =, simulated 40 500 600 700 800 900 000 Number of UE Compariso of simulatio ad aalytical results see that the optimal TTI budlig umber o-icreases as the umber of UE ad the packet arrival rates icrease. The reaso for this pheomeo is that, the preamble collisio rate grows with the umber of UEs ad the packet arrival rate. Therefore, whe the umber of UEs ad/or packet arrival rate become large, a UE should budle smaller (or same) umber of TTI to reduce the collisio rate. Moreover, we also fid that the TTI budlig umber scales with the packet arrival rate i that higher packet arrival rate limits the umber of budles. This is reasoable sice the packet collisio rate icreases with packet arrival rate. Therefore, smaller TTI budlig should be used to cotrol the collisio. Fig. 5. Number of budlig TTI 0 9 8 7 6 5 4 3 2 l=/00 l=/50 500 600 700 800 900 000 Number of UE Optimal umber of budlig TTI Fig. 6 compares the latecy obtaied usig the results show i Fig. 5 to the latecy without the TTI budlig scheme. It ca be iferred that the latecy is greatly reduced util the average umber of simultaeous chael access is less tha the umber of available preambles, e.g. with λ = /50 ad 000 users, there will be 20 radom chael access attempts per subframe. Thus, the achievable latecy gai is also depedet o the umber of available preambles. From the figures, it ca be see that there are two regimes. I the first
regime, the preamble collisio rate is ot very high, ad thus budlig multiple TTIs greatly icreases the successful rate of the radom access procedure. For example whe λ = /00, =, ad N u = 500,the collisio rate is 0.22 ad the first radom access roud successful rate is 0.50 ad the resulted latecy is 6ms. Whe the TTI budlig umber icreases to 8, though the collisio rate icreases to 0.36, the first radom access roud successful approximately equals which reduces the latecy to 33ms as show i Fig.6. I the secod regime, the preamble collisio rate is high, thus budlig multiple TTIs further icreases the preamble collisio rate. As a result, the radom access success rate could ot be improved. For example whe λ = /50, = ad N u = 800, the collisio rate is 0.48; the first radom access roud successful rate is 0.33 ad the latecy is 85ms. Whe the TTI budlig umber icreases to 2, the preamble collisio rate jumps to 0.65 ad the successful rate for the first radom access roud oly icreases to 0.45 which slightly reduces the latecy to 8ms (see Fig.6). Therefore, to reduce the radom access chael access latecy whe the preamble collisio rate is high, the TTI budlig is applicable oly whe more preambles ad/or more PRACH resources ca be (dyamically) allocated to lower the collisio rate. VI. CONCLUSION I this paper, we propose a TTI budlig method to reduce the uplik chael access latecy i LTE/LTE-A. With TTI budlig, a UE seds oe or multiple preamble(s) i oe radom access roud to icrease the radom access success rate. To fid the optimal TTI budlig umber which miimizes the chael access latecy, we apply a Semi-Markov model to formulate the access latecy as a fuctio of TTI budlig umber. The proposed model is validated through simulatios ad performace of the proposed TTI budlig scheme is also evaluated. We fid that the TTI budlig scheme ca sigificatly reduce the uplik latecy whe the preamble collisio rate due to simultaeous chael access is ot high while the latecy improvemet vaishes as the preamble collisio rate icreases. ACKNOWLEDGEMENT The research leadig to these results has received fudig from the Europea Research Coucil uder the Europea Commuity Seveth Framework Programme (FP7/204-207) grat agreemet 62050 for FLEX project. Fig. 6. Latecy (ms) 00 90 80 70 60 50 40 l=/00,with TTI budlig l=/00,without TTI budlig l=/50,with TTI budlig l=/50,without TTI budlig 30 500 600 700 800 900 000 Number of UE Latecy compariso with ad without TTI budlig Fig.7 shows the chael access latecy uder differet TTI budlig umber whe λ = /00 ad /50, ad N u = 500. It ca be observed that the latecy ca icrease if the umber of budles is ot optimally selected (see the curve for λ = /50). Latecy (ms) 70 65 60 55 50 45 40 35 l=/00, N u =500 l=/50, N u =500 30 2 3 4 5 6 7 8 TTI budlig umber REFERENCES [] N. Nikaei, M. Laer, K. Zhou, P. Svoboda, D. Drajic, M. Popovic ad S. Krco, "Simple Traffic Modelig Framework for Machie Type Commuicatio," 203. [2] Ericsso, "5G Radio Access: Research ad Visio," White paper, Ericsso, 203. [3] 3GPP TR 37.868, "RAN Improvemets for Machie-type Commuicatios," V..0.0., Oct., 20. [4] M. Amirijoo, F. Guarsso, F. Adre, "Radom Access Chael Self-Optimizatio i 3GPP LTE," IEEE Trasactios o Vehicular Techology, No.99, pp., Feb. 204. [5] Ju-Bae Seo, Leug, V.C.M, "Back to Results Desig ad Aalysis of Backoff Algorithms for Radom Access Chaels i UMTS-LTE ad IEEE 802.6 Systems," IEEE Trasactios o Vehicular Techology, vol. 60, No. 8, pp. 3975-3989, Oct. 20. [6] K.S. Ko, M.J.Kim, etal., "A Novel Radom Access for Fixed-Locatio Machie-to-Machie Commuicatios i OFDMA Based Systems," IEEE Commu. Lett., vol.6,no.9, pp.428-43, Sept. 202. [7] 3GPP TDoc R2-072630, HARQ operatio i case of UL Power Limitatio, Ericsso, Jue 2007. [8] R. Susitaival, M.Meyer, "LTE coverage improvemet by TTI budlig," Proc. IEEE VTC Sprig, April, 2009, pp.-5. [9] 3GPP TS 36.32, Evolved Uiversal Terrestrial Radio Access (E- UTRA); Medium Access Cotrol (MAC)," V.2.0.0, Ja., 204. [0] E.Osipov, L.Riliskis, A. Eldstal-Damli, M.Burakov, M.Nordberg, Mi Wag, "A improved model of LTE radom access chael", Proc. IEEE VTC Sprig, April, 204, pp.-5. [] Michael Burakov, "A LTE Radom Access Chael Model for Wireless Sesor Network Applicatios", MSc Thesis, Lules uiversity of techology, 202. [2] Giuseppe Biachi, "Performace Aalysis of the IEEE 802. Distributed Coordiatio Fuctio", IEEE Joura o Selected Areas i Commuicatios, Vol. 8, No. 3, pp. 535-547. [3] 3GPP TS 36.2, "Evolved Uiversal Terrestrial Radio Access Network (E-UTRAN); Physical Chaels ad Modulatio," V 2.0.0, Dec., 203. [4] 3GPP TS 36.300, " Evolved Uiversal Terrestrial Radio Access (E- UTRA) ad Evolved Uiversal Terrestrial Radio Access Network (E- UTRAN)," V. 0.4.0, Ju. 20. Fig. 7. Latecy uder differet umber of TTI budles