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A Novel Mechanism for Contention-based Initial Ranging in IEEE 802.16e Networks Jing Chi Philippe Martins Marceau Coupechoux ENST & CNRS LTCI ENST & CNRS LTCI ENST & CNRS LTCI 46, rue Barrault 75013 Paris, France 46, rue Barrault 75013 Paris, France 46, rue Barrault 75013 Paris, France Email: jing@enst.fr Email: martins@enst.fr Email: coupechoux@enst.fr Abstract—The paper proposes a Waiting-time Dependent In- of the back-off window (BW) size based on the network creasing rate Adapted Backoff (WDIA) algorithm to improve the size. In [3], a distributed backoff algorithm is proposed to contention efﬁciency in the IEEE 802.16e. A contention model is maximize the throughput by computing the optimal value ﬁrst proposed to analyze the frame-based behavior of contention resolution in 802.16e network. We introduce the concept of of CW for each station. However, the optimization is based reduced overlapping between back-off windows of contending on estimating the number of active stations that is inaccu- stations and we adopt an adaptable increasing rate. An initial rate under a distributed contention manner. In [4], collision ranging scenario is constructed to evaluate the effectiveness of history based BW adjustment is proposed to randomize the WDIA. The simulation results show that the WDIA algorithm transmission timing and minimize the collision probability. achieves better performance than Truncated Binary Exponential Backoff (TBEB) algorithm in terms of number of retransmissions, Authors focus on periodic ranging. However periodic ranging access delay and resource utilization. is performed using periodically granted bandwidth and not using contention-based ranging unless no grant is received I. I NTRODUCTION when T4 (35s as maximum deﬁned in 802.16e) expires. In In 802.16e, the uplink frame consists in three parts: con- [5], authors propose a Markov chain based analytical model tention interval for initial ranging (IR), contention interval for to study initial ranging performance. They point out that a bandwidth request (BR), and data transmission interval for ﬁxed size of initial BW, as proposed in the standard, neglects user trafﬁc. These parts are allocated by the base station (BS). the effect of varying network load and deﬁne a new adaptive At network entry, subscriber stations (SS) contend for resource algorithm based on the number of contending SSs. Again, this on the IR interval in order to access the network. As in many number is difﬁcult to estimate in practice. cellular networks, this random access is based on a traditional In our work, we propose a contention model of initial slotted Aloha in conjunction with a back-off algorithm. ranging in 802.16e and give the direct relation between Changes to the allocation of the contention interval per- contention performance and back-off window overlapping. formed by BS can reduce the collision probability of user Based on the analysis, we introduce the concept of reduced access, but also reduces the amount of resources dedicated to overlapping between BWs of contending SSs to improve user data trafﬁc. A better solution is improving the contention contention performance. The way BWs are adjusted is based efﬁciency within a relative stable contention interval, while on the time duration requests have already waited, the so called maintaining sufﬁcient resources for data trafﬁc. waiting time (WT). And the load of contention is used for In this paper, a Waiting-time Dependent and Increasing rate optimizing the BW instead of the contending number of SSs Adapted (WDIA) back-off algorithm is proposed to improve since it can be estimated under our separated BW mechanism. the contention performance (collision rate, access delay and The rest of the paper is organized as follows. In Section II, resource utilization) of IEEE 802.16e networks. Waiting-time we summarize the procedure of initial ranging and point out Dependent Back-off (WDB) has been originally proposed for the limitations of contention resolution in 802.16e. Section WLAN [1] and is extended in this paper to the IR process in III presents the contention model and gives direct relation WiMAX. Focusing on contention performance, the Request- between contention performance and backoff window overlap- Response mechanism based IR is considered rather than the ping. Section IV proposes our algorithm WDIA and Section CDMA ranging code mechanism. Although presented here for V evaluates the improvements of WDIA. Finally, conclusions IR, WDIA is such a novel algorithm for contention resolution are drawn in Section VI. that can also be used for other types of contention-based uplink accesses, including periodic ranging, handoff ranging II. IEEE 802.16 E C ONTENTION - BASED I NITIAL R ANGING and bandwidth request. Bianchi [2] has given a simple and accurate framework for As speciﬁed in IEEE 802.16e [6] Initial Ranging is the the analysis of back-off based MAC protocols but focused third step in initialization process for entering and registering on IEEE 802.11 DCF networks. He concluded that maximum a new SS to the network. It is a primary and vital procedure performance can be achieved by adaptively tuning the value for a SS to access the network and setup connection. It is 1 Downlink Frame TTG Uplink Frame also representative since the periodic and handover ranging or bandwidth request have similar process. Preamble DL-MAP Initial Bandwidth UL-Burst We give some basic notations in initial ranging: FCH UL-MAP Ranging Request 1…… N • BW: Back-off window with a range of type [0,Wr -1], …… Wr is reset after each transmission. Its initial/maximum value is BOs and BOe . • BOs and BOe : back-off start/end deﬁned in IEEE 802.16e standard. It is the initial/maximum back-off …… …… window size for initial ranging contention, speciﬁed by BS SS1: Case 1 RNG-REQ RNG-RSP BS and expressed as a power of 2. • BO: back-off number randomly chosen from its window SS2: Case 2 Failed, range [0,Wr -1] whenever a backoff process begins. RNG-REQ, RNG-REQ, max retries SS3: Case 3 collided retry collided • r : Request (REQ) retry counter. • rmax : The maximum number of contention retries deﬁned Fig. 1. Illustration of contention resolution. in IEEE 802.16e. • TU CD : The time interval of two consecutive UCD mes- sage which is periodically broadcasted by the BS. can be set between 20 and 200 ms according to the standard: The ranging process is shown in Fig. 1, and the cases of this causes a much longer waiting time than the ACK timeout three SSs experiencing success or collisions are illustrated. in IEEE 802.11. The typical T3 value of 200 ms equals 10 Initial ranging is started once a SS that tries to enter the frames with 20 ms duration. The back-off counter (BO) is network, receives a UCD message after the DCD message decremented by the number of TO. In each frame, NT O TOs to be synchronized with the BS for the ﬁrst time. The UCD is deﬁned by BS. If BO < NT O , the SS transmits the request Interval is deﬁned in 802.16 with a maximum value of 10s, in the current frame, else it has to wait for TO in subsequent and this value is not changed in 802.16e. A SS enters the frames and try to transmit when its BO reaches 0. contention process by setting its internal BW before sending a The MAC layer packet delay is decomposed into four types ranging request (RNG-REQ). The initial BW value is speciﬁed of defer time: the defer time TpreT O before a TO comes (the as BOs in the UCD message sent by BS. The SS shall back-off process is not yet started); the defer time T 3 before randomly select the backoff (BO) value within its BW, and having a negative response from the BS (and so entering an- defer that number of contention transmission opportunities other BO process); the defer time of a backoff; the defer time (TO) before transmitting the RNG-REQ [6] [7]. A TO provides from the time instant request is successfully transmitted until the required bandwidth for RNG-REQ transmission. the instant RNG-RSP is received (if the RNG-RSP is received After the transmission, the SS waits for a RNG-RSP mes- in the next frame after a successful request transmission, this sage. Once received, the contention resolution completes as the duration is approximately the frame duration Tf ). In Fig. 2, we case of SS1 shown in Fig. 1. If no response has been received can see in case of SS1, the request is successfully transmitted within T3 (response reception timeout), the SS shall consider without collision. The delay consists of TpreT O and Tf . In case the contention transmission as lost. Then the SS increases its of SS2, we can see after each collision the SS experiences a BW by a factor of two, as long as it is less than the maximum T 3 and a back-off defer equals to T 3/Tf + BO/NT O + 1 BW (BOe ). The SS shall randomly select a number within frame duration before next transmissions. It is clear that the its new BW and repeat the deferring process described above. collision has a huge impact on the global access delay. The contention resolution ends when the RNG-RSP is received or the retry counter r reaches the maximum number allowed B. Lower Resource Utilization [6] [7]. This is the case of SS2 and SS3. In IEEE 802.16e, the SS is allowed to send RNG-REQ only This mandatory contention resolution is based on a trun- during the initial ranging interval with limited number of TOs cated binary exponential back-off (TBEB) algorithm to avoid in each frame. Thus, this constraint induces higher collision possible re-collision. TBEB limitations in terms of efﬁciency rate and a fast deterioration as the number of contending and latency have been extensively studied for IEEE 802.11 SSs increase. In worst case, due to the contention failure, the systems in the literature [2], [3]. However, in IEEE 802.16 BS cannot allocate the dedicated resource to unregistered SS networks the contention process is frame-based and the back- although it has enough bandwidth. So the bandwidth allocation off is triggered by T3 timeout (much bigger than the ACK depends heavily on the performance of contention. timeout in IEEE 802.11). Thus its limitations are further C. Higher Collision Rate studied. The upper bound of BW is controlled by the TBEB but the A. Deteriorated Delay lower one is always zero. So, overlapping between back-off As shown in Fig. 2, in 802.16e, the contention process intervals of contending SSs can be quite high. The random BO is not started until a UCD message is received. The back-off selection in the overlapped BW induces a bigger collision rate for retransmission is not started until T3 timer expires. T3 since the same BO may always be selected even from a bigger 2 Frame UCD interval of contending SSs is simulated and shown in Fig. 4. It is not Frame UCD proper to model the contention as a stochastic process with UCD a constant SS arrival rate and steady transition probability T preTO 1st BO BS diagram, while most existing work do. In our model the N SSs Tf successful transmission probability increases as the number arrival RNG-REQ RNG-RSP SS1: Case 1 of contending SSs and the contention intensity decreases. T3 2nd BO SS2: Case 2 In each retry stage r > 0, the SSs are grouped by their RNG-REQ RNG-REQ prior collisions and the SSs collided in the same TO are Collided Retry SS3: Case 3 assigned to a same group. The SSs in the same group start their next back-off at the same time, while the SSs from different Fig. 2. Initial ranging model. groups start the back-off with a time differ related to their last contention. As shown in Fig. 2, the back-off for retry BW range. The effect of BW overlapping on collision and is not started until T3 expires. With assumption (3), in our delay is modeled and simulated in context of WLAN [1]. And model, omitting a small-probability collision type we analyze this effect is bigger in frame-based context of IEEE 802.16e the successful transmission probability considering only the as analyzed below. impacts from SS in the same retry stage. III. M ODEL OF C ONTENTION R ESOLUTION IN S INGLE A. Successful Transmission Probability C HANNEL The collision occurs when more than one SS transmit the Most of the existing studies on contention use a Markov request in the same TO. The collision probability for a random model and calculate the transition probability diagram to every SS i in rth retry is deﬁned as: steady-state following the analysis in IEEE 802.11. Their i i model are based on an assumption of constant request arrival Pc,r = 1 − Ps,r , (1) and related with the distribution of request arrivals. It is i Ps,r is the successful transmission probability for a random not realistic in initial ranging process of IEEE 802.16e. And SS i in rth retry. If the back-off is started at the same TO, it is complicated to derive the primary factors that lower i Ps,r is the probability the other SSs choose a different BO contention performance [4] [8]. Our model gives the direct value than SS i. As in 802.16e the n SSs started contention relation between successful transmission probability and back- simultaneously at the instant a TO arrives, thus the SSs with off window overlapping. It is then easier to be applied to the same BO value collide. [0, Wr -1] is the back-off window improve contention performance by optimizing the back-off for an SS in r transmission stage. The probability that SS i window. choose value k from [0, Wr -1] is derived as: Concerning the timeout triggered, frame-based characteris- 1 tic of TBEB in 802.16e, we assume that: P i (BO = k) = , (2) Wr 1. N SSs have arrived in the network during a UCD interval. The user arrival rate is below 20/s so n < 100. The successful transmission probability for ﬁrst transmission 2. During one UCD interval all the n SSs can ﬁnish IR. is derived as: 3. Collisions happen between the SSs in the same retry stage. The collisions happen between the SSs in different retry W0 −1 i 1 1 n−1 1 n−1 stages occurs with a small probability that can be omitted. Ps,0 = (1 − ) = (1 − ) , (3) W0 W0 W0 These assumptions are useful for deriving the primary k=0 factors that lower contention performance. In Section V we From equation (3), it is clear Ps,0 is the minimum value present simulation results to show that these assumptions are of Ps,r , not only because W0 is the minimum value of BW, reasonable. but also because the overlap of the BW between the SSs is As shown in Fig. 2, the n SSs start to transmit RNG-REQ the whole BW (W0 ) and the number of contending SSs (n) is immediatly after receiving a UCD message for the ﬁrst time. the biggest. These in all increase the collision probability. It Thus all the SSs arriving in the same UCD interval start IR also indicates that the worst case of contention happens in the process at the same time and set their retry counter r as 0. beginning part, which particularly needs improvements. So the distribution of RNG-REQ arrivals has no effect on When r > 0, for the retransmission back-off, the number of the contention. It also indicates that contention within a UCD contending SSs in rth contention is nr . The SSs are grouped interval only happens among the n SSs and does not involve by their prior collisions and the SSs collided in the same TO the new arrived SSs in this UCD interval since their contention are assigned to a same group. We use mr to represent the process are not started until receiving a UCD message. With number of groups in rth contention, and nj to represent the r mr j assumption (2) contention does not involve the contending number of SSs in group j, j ∈ (1, mr ), nr = j (nr ). SSs in prior UCD interval since their IR is ﬁnished. Thus Only the SS in the same group enters the next back-off within one UCD interval the number of contending SSs is not simultaneously with the same BW Wr . While the SSs from constant but decreasing from n. The decrement of the number different group start the back-off with a time differ of ∆r−1 3 BW(r-1) BW(r) 100 j ,1 Number of Current Contending SSs j ,1 Wr r 1 r 1 80 T3 60 T3 40 SS i in group 1 group j 20 Fig. 3. Illustration of BW and ∆j,1 . r−1 0 0 1 2 3 4 5 6 7 Retry Stage (which is related to their last contention), if Wr − ∆r−1 > 0 Fig. 4. Contending SSs in rth retry stage their BW overlap is Wr − ∆r−1 or else the overlap is 0. Their relations is shown in Fig. 3. To simplify the formula, we use 100 group 1 to denote the group SS i belongs. The time differ of Ps7 Ps6 SS i and a SS from group j is derived as: 80 Ps2 Ps5 Successfull probability ∆j,1 ∈ (1, Wr−1 − 1), (j = 1), r−1 (4) 60 Ps4 Ps1 Based on the analysis above, the successful transmission probability in rth (r > 0) retry is derived as: 40 Ps3 20 Wr −1 Ps0 i 1 1 n1 −1 Ps,r = (1 − ) Wr Wr 0 10 20 30 40 50 60 70 80 90 100 k=0 Number of SS j,1 mr ∆r−1 −1 Wr −1 1 1 1 nj Fig. 5. Comparison of model and simulation. ( + (1 − ) r) Wr Wr Wr j=1 k=0 k=∆j,1 r−1 mr the SS arrives at the network. BO is a function of WT and r. 1 n1 −1 ∆j,1 Wr − ∆j,1 1 nj For each retransmissions, the SS slides the lower bound of the = (1 − ) r ( r−1 + r−1 (1 − ) r) l Wr Wr Wr Wr BW, Wr , according to its own WT with a determinist function. j=1 δ The size of BW, Wr , increases with a tunable multiplicative 1 nr > (1 − ) , factor. As shown in the Fig. 6, the overlapping between two Wr l BW is reduced by changing the Wr . It is so expected that the We use Ps,r to denote the average value of successful collision probability is reduced. transmission probability of nr SSs. nr = n r−1 (1 − Ps,r ) is monotonic decreasing. We assume the average value of nj B. Mathematic Model and Parameter Setting r is nj = Wr−1 −1 , as ∆j,1 conforms a uniform distribution r nr r−1 Inheriting the essence of WDB mathematic model [1], within [1, Wr−1 − 1]. BO function contains two addends: a deterministic function From equation (4) we can see in 802.16e, the overlap l δ Wr (W T ) and a random function RandInt[0, Wr ]. In Fig. 6, of BW affects the collision and the successful transmission the determinist function is the curve of lower bounds and probability. This inspired us to design an algorithm to improve the random function is represented by the successive intervals contention performance by reducing the overlap. δ δ named Wr . RandInt[0, Wr ] is a random integer generated δ Our model gives a simple method to analyze the contention from uniform distribution between 0 and Wr . The functions process in initial ranging. The direct relation between success- are given by: ful transmission probability and backoff window overlapping T3 l is given. In Fig. 4, we shows the decrement of contending SSs. Wr (W T ) = W T (mod ). (5) Tf In Fig. 5, the dash line shows the Ps,r derived from our model. The solid line shows the mean value of Ps,r calculated from δ BOs if r = 0 simulation of TBEB. The comparison of numerical results and Wr = δ (6) αWr−1 if r = 0 simulation results show the accuracy of model. The maximum α is a tunable integer for the increasing rate of BW after each differ of the two is 5.3%. collision. It provides ﬂexible adjustment for the mathematic IV. WDIA A LGORITHM model to be applied under different performance requirements A. Method description and network conﬁgurations. As a consequence, the back-off value after r retries is obtained as follows: The basic ideas of WDIA algorithm is illustrated in Fig. 6. l δ Waiting time (WT) is tracked for each SS from the instant BO = Wr (W T ) + RandInt[0, Wr ]. (7) 4 TABLE I BW Random Function PARAMETERS OF SIMULATIONS . Deterministic Function Parameter Value W4 PHY OFDMA W3 Bandwidth 10 MHz Lu Duplexing mode TDD W2 Frame duration 20 ms L W1 T3 200 ms W4l Ll W3l DCD interval 5s W2l W1l UCD interval 5s WT(ms) IR TO per frame 3 rmax 16 Fig. 6. Illustration of BW adjustment in contention process. λ 10 per s Let us now make two remarks on the above model. 50 1) WT-dependent Overlap-restricted BW: WT is used to 40 Percent of Collisions differentiate the lower bounds of BW for each SS. Each SS l slides its own BW to the offset Wr (W T ), which is calculated 30 before starting a back-off. The offset value is set to be smaller 20 l than the number of TO within T3 so that Wr (W T ) will not be too big to induce time waste. This overlap-restricted BW 10 reduces the probability of choosing the same BO thus the 0 collision rate is reduced. 0 10 20 30 40 50 60 70 80 90 100 Number of SS 2) Adaptive BW Increasing Rate: As analyzed in [8], the exponential increasing of BW is effective when there is a Fig. 7. Possibility of collision happens between the SSs with different retries. medium number of contending SS. When the number is small or large, it is time wasting. In WDIA, the BW increasing rate α is adapted to the intensity of contention. This is different B. Function Setting from the ﬁxed value chosen by binary exponential back-off. The setting of the deterministic and random functions is Under the overlap restricted BW, a big intensity of contention based on the analysis and adjusted through experiment. is indicated if an SS encountering a collision with relative bigger BO; thus a bigger rate is set. Otherwise, the rate is l T3 Wr (W T ) = W T (mod ). (9) set a smaller value to avoid unnecessary time waste caused Tf by a big BW. The estimation of the number of contending δ 8 if r = 0 SSs is based on probability of collissions happen at a SS with Wr = δ (10) i αWr−1 if r = 0 big BO. Pc,r (BO > k|n) is the probability of collissions of SS i when its BO value is bigger than k and the number of Through our simulation we get that setting a bigger increas- contending SSs is n. It is derived as: ing rate is effective when the BW is relatively small so we δ adapt the value of α in ﬁrst two transmission stages. To best T 3/Tf −k+Wr −2 n−1 i Tf · u m+1 m beneﬁt the contention performance we set α = 3 if the ﬁrst Pc,r (BO > k|n) = Cn−1 ( δ ) . back-off value is more than 8 or the second back-off value is u=1 m=1 T 3 · Wr (8) more than 16, otherwise α = 2. This equation gives the conﬁdence interval of n if SS i C. Simulation Results experienced a collission when its BO value is bigger than k. In Fig. 7, we show that the percent of collisions happens V. P ERFORMANCE E VALUATION between the SSs with different retries is below 7.11%. It proved that under this timeout triggered backoff mechanism, A. Simulation Model most collisions happens between the SSs in the same retry The scenario is constructed by one central BS and several stage. If we focus on the collision type with big probability in SS randomly located using QualNet version 4.0. The OFDMA the analysis model, the type with a much smaller probability PHY is supported and IR is processed using RNG-REQ can be omitted. Thus assumption (3) is reasonable. and RNG-RSP messages. To test the performance of initial In the following ﬁgures, solid lines depict metrics of WDIA ranging, the Poisson process (with parameter λ) is used for and dash lines for TBEB. modeling the arrival of new SS. In the simulation scenario, the In Fig. 8 solid line shows the percent of SSs that ﬁnish IR channel condition is ideal thus retransmission is only caused within one UCD interval with average user arrival rate below by collision and the RNG-RSP is received after successful 20/s. It proves that with the typical value of UCD interval transmission of RNG-REQ. The parameters of the simulation (5s, which is frame duration Tf 20ms), assumption (2) is are shown in Table I referring to [7], [9]. reasonable. The dash line shows that WDIA achieves bigger 5 700 Percent of successful rng−req 100 TBEB WDIA WDIA 600 TBEB 98 500 Delay(ms) 96 400 94 300 92 200 100 2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30 35 40 Arrival rate (/s) Number of SS Fig. 10. Initial ranging access delay of WDIA and TBEB. Fig. 8. Possibility of the arrived SSs ﬁnish IR in one UCD. 800 Number of RNG−REQ transmission 150 WDIA WDIA 600 TBEB TBEB Number of Frame UCD interval 100 400 200 50 0 5 10 15 20 25 30 35 40 0 Number of SS 5 10 15 20 25 30 35 40 Number of SS Fig. 11. TO required for initial ranging in one UCD Fig. 9. Total number of RNG-REQ transmissions of WDIA and TBEB. and resource utilization. value than TBEB so more SSs can be accepted to the network WDIA is efﬁcient for all types of contention-based uplink within one UCD interval. access, including initial ranging, periodic ranging, handoff Fig. 9 plots the total number of RNG-REQ transmitted by ranging and bandwidth request, under both light and heavy n SS to process network entry. It can be observed that the load conditions. In our future work, we aims to design a total retransmission is reduced using WDIA by 28.5% up to priority-based WDIA to achieve QoS guarantee for ertPS when 37.5%. This improvement is gained from the reduced overlap contention based bandwidth request is used. of BW and the adaptive BW increasing rate, which effectively R EFERENCES separates BW and dramatically reduces collisions. [1] J. Chi, Y. Wang, B. Xia, X. Gao, R. Lin, and X. 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