LNCS 5593 - Performance Analysis of Binary Negative ... - Springer Link
Performance Analysis of Binary Negative-Exponential Backoff Algorithm in IEEE 802.11a WLAN under Erroneous Channel Condition Bum-Gon Choi, Sueng Jae Bae, Tae-Jin Lee, and Min Young Chung School of Information and Communication Engineering Sungkyunkwan University 300, Chunchun-dong, Jangan-gu, Suwon, Kyunggi-do, 440-746, Korea
Abstract. IEEE 802.11 is the most famous protocol for implementation of wireless local area network (WLAN). To access the medium, IEEE 802.11 uses carrier sense multiple access with collision avoidance (CSMA/CA) mechanism, called distributed coordination function (DCF). Although DCF uses binary exponential backoff (BEB) algorithm to avoid frame collisions, wireless resources are wasted due to a lot of collisions under the condition that there are many contending stations. To solve this problem, a binary negative-exponential backoff (BNEB) algorithm has been proposed and its saturation throughput was evaluated under erroneous channel condition. As extention of our previous work, this paper evaluates performance of BNEB algorithm via mathematical analysis and simulations under saturation and erroneous channel condition in terms of the MAC delay and throughput. Also, we compare the performance of DCF with BEB to that with BNEB under normal traffic and erroneous channel condition by intensive simulations. From the results, BNEB yields better performance than BEB in general. Keywords: IEEE 802.11, WLAN, MAC, CSMA/CA, DCF, BNEB.
1
Introduction
The IEEE 802.11 WLAN employed DCF as a mandatory contention based channel access method [1]. DCF is a random access function, based on CSMA/CA protocol adopting BEB algorithm. Although IEEE 802.11 standard also introduces point coordination function (PCF) as a contention-free based channel access method, PCF is barely implemented in current products because PCF wastes some bandwidth due to polling overheads and null packets [2][3].
This research was supported by the MKE(Ministry of Knowledge Economy), Korea, under the ITRC(Information Technology Research Center) support program supervised by the IITA(Institute for Information Technology Advancement) (IITA-2009-C1090-0902-0005). Corresponding author.
O. Gervasi et al. (Eds.): ICCSA 2009, Part II, LNCS 5593, pp. 237–249, 2009. c Springer-Verlag Berlin Heidelberg 2009
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DCF operates with three parameters, backoff stage, backoff counter and contention window. In DCF, when a station has frame(s) to transmit, it sets backoff stage and randomly chooses backoff counter in the range [0, CW − 1], where CW is current contention window size. At the first transmission of a frame, a station sets backoff stage to 0 and contention window size to minimum contention window size (CWmin ). After a channel is sensed idle during DCF interframe space (DIFS), the station decreases backoff counter by one in every idle slot. When backoff counter of a station is equal to 0, the station transmits a frame at the beginning of slot time. If the station does not receive acknowledgement (ACK), it increases backoff stage by one and doubles their contention window size. If the station successfully transmits its frame, it resets backoff stage to 0 and contention window size to CWmin . However, in DCF, the more number of stations share the wireless resources, the more frames are collided. In order to solve this problem, much research on the IEEE 802.11 DCF is conducted. Bianchi presented an analytical model using bi-dimensional Markov chain model and showed that the proposed model is very accurate [4][5]. With simple modification of Bianchi’s model, Xiao showed the limits of throughput and delay of IEEE 802.11 DCF [6]. The performance of the DCF in the presence of transmission error was evaluated in [7][8]. In addition, they presented an analytical model to verify the performance of the DCF in presence of channel bit error rate. The gentle distributed coordination function (GDCF) was proposed by Wang et al. [9]. In GDCF, stations decrease their backoff stages by one whenever the number of consecutive successful frame transmissions reaches the maximum number of permitted consecutive successes. Since GDCF uses the fixed number of permitted consecutive successful transmissions for decreasing the backoff stage, its performance depends on the number of contending stations. The enhanced GDCF (EGDCF) uses a consecutive success counter to represent the number of consecutive successful transmissions at the same backoff stage [10][11]. If the number of consecutive successful transmissions reaches maximum-permitted value, stations decrease their backoff stages by one. Since the maximum permitted value of consecutive successful transmissions is assigned differently according to the backoff stage of stations, performance of EGDCF scarcely depends on the number of contending stations. A Binary Negative-Exponential Backoff (BNEB) algorithm has been proposed by Ki et al. [14]. The BNEB algorithm maintains the contention window to the maximum window size when stations experience a collision and reduces a contention window size by half when a frame is transmitted successfully without retransmission. Since BNEB introduces minus backoff stage to simply represent consecutive transmission successes. In [14] and [15], the results showed that the BNEB algorithm had better performance than conventional DCF in ideal and erroneous channel conditions. However, the performance was evaluated in saturation condition and the performance in terms of MAC delay was not evaluated. Based on our previous works [14][15], in this paper, we intensively evaluate performance of DCF with BNEB in terms of MAC delay and throughput under saturation and normal traffic conditions in erroneous channel. The rest of paper
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is organized as follows. Section 2 illustrates BNEB algorithm briefly. Section 3 derives an analytical model to evaluate the normalized throughput of BNEB under saturation and erroneous channel conditions. In Section 4, we verify our analytical model by simulations. Also, we compare the throughput and MAC delay of DCF with BNEB to that with BEB under saturation and normal traffic condition. Finally, we conclude in Section 5.
2
Binary Negative-Exponential Backoff Algorithm
The BNEB algorithm uses three parameters, backoff stage, backoff counter, and contention window. The roles of these parameters are similar to those in DCF with BEB. In DCF with BEB, contention window size becomes double whenever a station experiences a collision, until it reaches the maximum contention window size (CWmax ). However, in DCF with BNEB, contention window size initially sets to CWmax to reduce the probability that more than two stations select the same backoff counter value. When a frame successfully transmitted without retransmission, BNEB decreases the contention window size by half to reduce the delay related to backoff time. Since BNEB introduces minus backoff stage to simply represent consecutive transmission successes, it uses two counters, backoff stage and backoff counter. The contention window size Wi (CWmin ≤ Wi ≤ CWmax ) at backoff stage i is decided as follows. CWmax , 0 < i ≤ m, Wi = (1) max(2i (CWmax ), CWmin ), −L ≤ i ≤ 0, where m is the maximum retry limit and L is the natural number that plays a role in assistance number. CWmin and CWmax represent minimum contention window and maximum contention window, respectively. Stations having frame(s) randomly select their backoff counter values from [0, Wi − 1] and decrease their backoff counter values by one whenever a slot is idle. A station starts to transmit its frame if its backoff counter value reaches zero. For the frame to be transmitted, the backoff stage is decided by both the previous backoff stage used for the previous frame and the result of its transmission, success or collision. If the previous frame was successfully transmitted at the backoff stage i, the station sets its backoff stage to 0 for 0 < i ≤ m. The station sets its backoff stage to i − 1 for −L < i ≤ 0. And the station sets its backoff stage to −L if i = −L. If the transmission of the previous frame failed at the backoff stage i, the station sets its backoff stage to i + 1 if 0 ≤ i < m. The station sets its backoff stage to 1 for −L ≤ i < 0. And if the backoff stage is equal to m, the station drops its frame and then initializes its backoff stage to 0. Therefore, if a collision occurs, the station using BNEB algorithm can effectively resolve collision by using the maximum contention window size.
3
Analytical Model for BNEB
For the conventional DCF, Bianchi presented an analytical model using bidimensional Markov chain model and showed that the proposed model is very
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accurate [4][5]. Therefore, we expend Bianchi’s Markov chain model to evaluate the saturation throughput of BNEB in the presence of transmission error. In analytical model, we assume that there are n stations having frame(s) to transmit and each station has frame(s) after successful transmission. In addition, it is possible that a station fails to transmit a frame by a channel noise, not a collision. For a station, s(t) is defined as the random process representing the backoff stage and b(t) is defined as the random process representing the value of the backoff counter at time t. Then, BNEB algorithm can be modeled as a bi-dimensional discrete-time Markov chain (s(t), b(t)). Fig. 1 illustrates the state transition diagram of the Markov chain of the BNEB. Let lim P {s(t) = i, b(t) = j} = bi,j and p be the transmission failure probat→∞ bility that a station experiences a transmission failure due to collision or transmission error in a slot time. Then, we can make the following relations through chain regularities. bi,0 = (1 − p)−i b0,0 , Wi − j bi,j = b0,0 , Wi (1 − p)L b0,0 , b−L,0 = p bi,0 = pi−1 b0,0 , Wi − j bi,j = b0,0 , Wi From Equation (2) and
m W i −1
i ∈ [−L + 1, 0] , i ∈ [−L + 1, 0], j ∈ [0, Wi − 1], i = L, j = 0,
(2)
i ∈ [1, m] , i ∈ [1, m], j ∈ [0, Wi − 1]. bi,j = 1, we can derive b0,0
i=−L j=0
b0,0 =
1 m (W p+1)+ (1−p) [W ( 1−p 2 2 ) −1] p(1+p)
+
W +1 1−pL 2 ( 1−p )
.
(3)
Let τ be the probability that a station attempts to transmit a frame. Then we have m 1 1 − pm + τ= bi,0 = (4) b0,0 p 1−p i=−L
and p = 1 − (1 − τ )n−1 (1 − BER)l+H ,
(5)
where BER and l respectively represent the channel bit error rate and packet payload size. H(= P HYhdr + M AChdr ) represents the sum of packet header sizes, P HY header (P HYhdr ) and M AC header (M AChdr ). The transmission success probability Ps , the probability Pc that an occurred packet collides, and the probability Per that a packet received in error are calculated as nτ (1 − τ )n−1 Ps = (1 − P ER), (6) Ptr
Performance Analysis of BNEB Algorithm
Transmission Success Collision Occurance
L,0
L,1
L,2
L,WL-2
L,WL-1
j,Wj-2
j,Wj-1
2,W2-2
2,W2-1
1,W1-2
1,W1-1
p/Wmax
p/Wmax j,0
j,1
j,2 p/Wmax
p/Wmax 2,0
2,1
2,2 p/Wmax
1,0
1,1
1,2 p/Wmax
p/W0 (1-p)/W0 0,0
0,1
0,2
0,W0-2
0,W0-1
-1,W-1-2
-1,W-1-1
i,Wi-2
i,Wi-1
-m,W-m-2
-m,W-m-1
(1-p)/W-1 -1,0
-1,1
-1,2 (1-p)/W-2
(1-p)/Wi i,0
i,1
i,2
(1-p)/Wi-1
(1-p)/W-m -m,0
-m,1
-m,2 (1-p)/W-m
Fig. 1. Markov chain of BNEB
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nτ (1 − τ )n−1 , Ptr nτ (1 − τ )n−1 = P ER, Ptr
Pc = 1 − Per
(7) (8)
where Ptr is the probability that there are at least one transmission and P ER is packet error rate, Ptr = 1 − (1 − τ )n , P ER = 1 − (1 − BER)l+H .
(9) (10)
Let Ts be the mean time required for the successful transmission of a frame and Tc and Ter be the mean wasting time due to the collision and transmission error of a transmitted frame. Then, Ts , Tc and Ter are obtained as follows Ts = DIF S + H + E[P ] + 2δ + SIF S + ACK, Tc = DIF S + H + E[P ∗] + δ,
(11) (12)
Ter = DIF S + H + E[P ∗] + δ,
(13)
and where E[P ] and E[P ∗] are the mean transmission time of successfully transmitted packet and collided packet, respectively. SIFS represents a short interframe space and ACK denotes a transmission time of acknowledgement. The parameter δ denotes a propagation delay. Finally, we can obtain normalized saturation throughput of BNEB in presence of channel bit error rate as follows S=
Ptr Ps E[P ] , (1 − Ptr )σ + Ptr Ps Ts + Ptr Pc Tc + Ptr Per Ter
(14)
where σ is the duration of a backoff slot. To evaluate the saturation MAC delay of BNEB in the presence of transmission error, we define the mean sojourn time di at backoff stage i. Let Tb and Pb denote the mean freezing time due to the busy channel and the probability that channel is busy, respectively. Then, di is given by di = (1 − p)Ts + pTc + [(1 − Pb )σ + Pb Tb ]
Wi , 2
i ∈ [−L, m] .
(15)
Also, Pb and Tb are calculated as Pb = 1 − (1 − τ )n−1 , (n − 1)τ (1 − τ )n−2 (n − 1)τ (1 − τ )n−2 Tc . Tb = Ts + 1 − Pb Pb
(16) (17)
Therefore, when a previous frame was transmitted in stage i, Di is given by ⎧ −L ≤ i ≤ 0, ⎨ di + pD1 , 1 ≤ i ≤ m, (18) Di = di + pDi+1 , ⎩ di , i = m.
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The mean MAC delay D can be calculated as 0
D=
bi,0 Di
i=−L 0
.
(19)
bi,0
i=−L
4
Performance Evaluation
To evaluate the performance of DCF with BEB and BNEB, we consider L=5, m=7, and the MAC parameters are given in Table 1. In IEEE 802.11a, control packets such as ACK are transmitted with Control Rate(Ccon )[12][13]. 4.1
Performance Evaluation under Saturation Condition
In order to evaluate normalized throughput and MAC delay of BNEB under saturation condition, we assume that there are n stations having frame(s) to transmit and each station has frame(s) after successful transmission. When there is frame transmission error in wireless channel, normalized saturation throughputs of DCF with BEB and BNEB are shown in Fig. 2. For n = 5, the throughput of BNEB is sensitive to the BER. However, for n=25 and 50, the throughput of BNEB is not sensitive to the BER. From the results, for n=5, the saturation throughput of BNEB is less than that of DCF with BEB, however, the saturation throughput of BNEB is greater than that of DCF with BEB for n=25 and
Fig. 2. Saturation throughput of DCF with BEB and BNEB in IEEE 802.11a under varying BER (L=5, m=7)
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Fig. 3. Saturation MAC delay of DCF with BEB and BNEB in IEEE 802.11a under varying BER (L=5, m=7)
50. When BER ≥ 10−4 , the possibility of transmission failure by a transmission error is larger than that by a collision. Therefore, the throughputs of DCF with BEB and BNEB are closed to 0 as BER increases. Fig. 3 shows the saturation MAC delay of DCF with BEB and BNEB under varying BER. If frame transmission fails, BNEB stations increase contention window to CWmax , but BEB stations increase contention window by double. When the number of contending stations is small, transmission failure caused by transmission error is dominant. Therefore, the saturation MAC delay of BNEB is higher than that of DCF with BEB for n=5 and high BER because the CWmax Table 1. IEEE 802.11a MAC parameters PARAMETER Packet payload MAC header PHY header ACK length Control rate (Ccon ) Data rate (C) Propagation Delay SIFS DIFS Slot Time CWmin CWmax
VALUE 8184 bits 272 bits 128 bits 240 bits 24Mbps 54Mbps 1 µs 16 µs 34 µs 9 µs 16 1024
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Fig. 4. Saturation throughput of DCF with BEB and BNEB in IEEE 802.11a for BER and the number of stations (L=5, m=7)
causes long backoff time. For n=25 and 50, the saturation MAC delay of BNEB is less than that of DCF with BEB. The more the number of stations uses wireless resource, the more collision occurrences are possible than frame transmission error. Because BNEB can resolve the collision more effectively in case that there are many contending stations, the saturation MAC delay of BNEB is less than that of DCF with BEB for n=25 and 50. When BER is higher than 10−4 , difference of the MAC delay between DCF with BEB and BNEB decreases. Also, the saturation MAC delay sharply increases for BER ≥ 10−4 . Fig. 4 represents the normalized saturation throughput of DCF with BEB and BNEB as the number of contending stations increases when BER = 10−6 , 10−5 , and 10−4 . When there are many contending stations, the transmission failure related to the collision is more frequent than that related to transmission error. Therefore, BNEB which initially sets contention window to CWmax shows better performance than DCF with BEB. The waiting time due to the backoff slot time strongly affects the saturation throughput of DCF with BEB and BNEB when there are less contending stations. BNEB sets contention window to CWmax whenever a station experiences transmission failure. For this reason, as the transmission failure is increased by channel BER, the waiting time of BNEB is larger than that of DCF with BEB. Therefore, the performance of BNEB is less than that of DCF with BEB in the small number of contending stations and high BER. However, because the wireless devices operate in BER ≤ 10−5 in most cases, the performance of BNEB is better than that of DCF with BEB. The saturation MAC delay of DCF with BEB and BNEB is shown in Fig. 5. For BER = 10−6 and 10−5 , the saturation MAC delay of BNEB is less than that of DCF with BEB. However, for BER = 10−4 and n ≤ 35, the saturation MAC delay of BNEB is higher than that
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Fig. 5. Saturation MAC delay of DCF with BEB and BNEB in IEEE 802.11a for BER and the number of stations (L=5, m=7)
of DCF with BEB because transmission failure related to the transmission errors is more frequent than that related to the collision. 4.2
Performance Evaluation under Normal Traffic Condition
To evaluate performance of DCF with BEB and BNEB under normal traffic condition, we assume that packets arrive at devices as a Poisson process with a mean arrival rate λ. For BER = 10−6 , 10−5 , and 10−4 , the normalized throughput of DCF with BEB and BNEB varying packet arrival rates (λ) is shown in Fig. 6. The possibility that stations have frame(s) for transmission increases as λ increases until λ = λsat . If the packet arrival rate is larger than the specific value (λsat ), the probability that a station has frame(s) for transmission is close to 1. From the results, the throughput of DCF with BEB and BNEB linearly increases as λ increases until λ = λsat and maintains constant for λ ≥ λsat . The normalized throughput of BNEB is higher than that of DCF with BEB for BER = 10−6 and 10−5 . When BER > 10−5 , the possibility of transmission failure caused by a transmission error is larger than that of transmission failure caused by a collision. Therefore, the normalized throughput of BNEB is less than that of DCF with BEB for BER = 10−4 . Since the λsat of the BNEB is greater than DCF with BEB, the BNEB can serve more traffic than BEB. Fig. 7 shows the MAC delay of DCF with BEB and BNEB varying packet arrival rates (λ). As BER increases, the transmission failure due to the transmission error occurs more frequently than that due to collision. DCF stations set contention window size to CWmin when a station transmit a new frame and double their contention window size when DCF stations participate in the col-
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Fig. 6. Normalized throughput of the DCF and the BNEB varying packet alival rate for BER in IEEE 802.11a (L=5, m=7)
lision. However, to effectively resolve collisions, BNEB stations set contention window size to CWmin when a station transmit a frame. The possibility that a stations retransmits a frame is very small until λ = λsat . Also, the waiting time
Fig. 7. MAC delay of the DCF and the BNEB varying packet arrival rate for BER in IEEE802.11a (L=5, m=7)
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by the backoff strongly affects the MAC delay of DCF with BEB and BNEB when λ ≤ λsat . Therefore the MAC delay of BNEB is higher than DCF with BEB for λ ≤ λsat because BNEB stations use greater contention window size than that of DCF stations. However, when λ ≥ λsat , the MAC delay of BNEB is less than that of DCF with BEB for BER = 10−6 and 10−5 . For, BER = 10−4 , the MAC delay of BNEB is higher than that of DCF with BEB. However, because the wireless devices operate in BER ≤ 10−5 , in most cases, performance of BNEB is better than that of DCF with BEB.
5
Conclusion
In this paper, we briefly explained a binary-negative exponential backoff (BNEB) algorithm to enhance the performance of DCF with BEB. And we proposed a mathematical analysis model to evaluate the performance of BNEB in presence of channel bit error rate. Also, we verified our proposed algorithm via analytical model and simulations under saturation and erroneous channel condition. From the results, BNEB can resolve collision more effectively than DCF with BEB. We also evaluated the performance of BNEB algorithm in the presence of transmission error by simulations under normal traffic conditions. In low BER, performance of BNEB is better than that of DCF with BEB because of effective collision resolution. In high BER, throughput of BNEB is smaller than DCF due to ineffective management of backoff time. However, we expect that BNEB improves performance of DCF compared with BEB under erroneous channel condition.
References 1. IEEE standard for Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. ISO/IEC 8802-11 (1999(E)) (1999) 2. Kanjanavapasti, A., Landfeldt, B.: An analysis of a modified point coordination function in IEEE 802.11. In: Proc. of PIMRC 2003, vol. 2, pp. 1732–1736 (2003) 3. Xiao, Y.: Performance analysis of priority schemes for IEEE 802.11 and IEEE 802.11e wireless LANs. IEEE Trans. Wireless Commun. 4(4), 1506–1515 (2005) 4. Bianchi, G.: IEEE 802.11 saturation throughput analysis. IEEE Commun. Lett. 2(12), 318–320 (1998) 5. Bianchi, G.: Performance analysis of the IEEE 802.11 distributed coordination function. IEEE J. Sel. Areas Commun. 18(3), 535–547 (2000) 6. Xiao, Y., Rosdahl, J.: Throughput and delay limits of IEEE 802.11. IEEE Commun. Lett. 6(8), 355–357 (2002) 7. Chatzimisios, P., Boucouvalas, A.C., Vitsas, V.: Performance analysis of IEEE 802.11 DCF in presence of transmission errors. In: Proc. of IEEE International Conf. on Commun., vol. 7, pp. 3854–3858 (2004) 8. Chatzimisios, P., Boucouvalas, A.C., Vitsas, V.: Influence of channel BER on IEEE 802.11 DCF. Electronics Lett. 39(23), 1687–1689 (2003) 9. Wang, C., Li, B., Li, L.: A new collision resolution mechanism to enhance the performance of IEEE 802.11 DCF. IEEE Trans. Veh. Techno. 53(4), 1235–1243 (2004)
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10. Chung, M.Y., Kim, M.-S., Lee, T.-J., Lee, Y.: Performance evaluation of an enhanced GDCF for IEEE 802.11. IEICE Trans. Commun. E88-B(10), 4125–4128 (2005) 11. Kim, D.H., Choi, S.-H., Jung, M.-H., Chung, M.Y., Lee, T.-J., Lee, Y.: Performance evaluation of an enhanced GDCF under normal traffic condition. In: Proc. of IEEE TENCON, pp. 1560–1566 (2005) 12. Chatzimisios, P., Boucouvalas, A.C., Vitsas, V.: Effectiveness of RTS/CTS handshake in IEEE 802.11a wireless LANs. IEE Electronics Lett. 40(14), 915–916 (2004) 13. Raffaele, B., Marco, C.: IEEE 802.11 Optimal performances: RTS/CTS mechanism vs. basic access. In: Proc. of PIMRC, vol. 4, pp. 1747–1751 (2002) 14. Ki, H.J., Choi, S.-H., Chung, M.Y., Lee, T.-J.: Performance evaluation of Binary Negative-Exponential Backoff Algorithm in IEEE 802.11 WLAN. In: Cao, J., Stojmenovic, I., Jia, X., Das, S.K. (eds.) MSN 2006. LNCS, vol. 4325, pp. 294–303. Springer, Heidelberg (2006) 15. Choi, B.-G., Ki, H.J., Chung, M.Y., Lee, T.-J.: Performance evaluation of Binary Negative-Exponential Backoff Algorithm in presence of a channel bit error rate. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007. LNCS, vol. 4490, pp. 554–557. Springer, Heidelberg (2007)
Abstract. IEEE 802.11 is the most famous protocol for implementation of wireless local area network (WLAN). To access the medium, IEEE 802.11 uses carrier sense multiple access with collision avoidance (CSMA/CA) mechanism, called distributed coordination function (DCF). Although DCF uses binary exponential backoff (BEB) algorithm to avoid frame collisions, wireless resources are wasted due to a lot of collisions under the condition that there are many contending stations. To solve this problem, a binary negative-exponential backoff (BNEB) algorithm has been proposed and its saturation throughput was evaluated under erroneous channel condition. As extention of our previous work, this paper evaluates performance of BNEB algorithm via mathematical analysis and simulations under saturation and erroneous channel condition in terms of the MAC delay and throughput. Also, we compare the performance of DCF with BEB to that with BNEB under normal traffic and erroneous channel condition by intensive simulations. From the results, BNEB yields better performance than BEB in general. Keywords: IEEE 802.11, WLAN, MAC, CSMA/CA, DCF, BNEB.
1
Introduction
The IEEE 802.11 WLAN employed DCF as a mandatory contention based channel access method [1]. DCF is a random access function, based on CSMA/CA protocol adopting BEB algorithm. Although IEEE 802.11 standard also introduces point coordination function (PCF) as a contention-free based channel access method, PCF is barely implemented in current products because PCF wastes some bandwidth due to polling overheads and null packets [2][3].
This research was supported by the MKE(Ministry of Knowledge Economy), Korea, under the ITRC(Information Technology Research Center) support program supervised by the IITA(Institute for Information Technology Advancement) (IITA-2009-C1090-0902-0005). Corresponding author.
O. Gervasi et al. (Eds.): ICCSA 2009, Part II, LNCS 5593, pp. 237–249, 2009. c Springer-Verlag Berlin Heidelberg 2009
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DCF operates with three parameters, backoff stage, backoff counter and contention window. In DCF, when a station has frame(s) to transmit, it sets backoff stage and randomly chooses backoff counter in the range [0, CW − 1], where CW is current contention window size. At the first transmission of a frame, a station sets backoff stage to 0 and contention window size to minimum contention window size (CWmin ). After a channel is sensed idle during DCF interframe space (DIFS), the station decreases backoff counter by one in every idle slot. When backoff counter of a station is equal to 0, the station transmits a frame at the beginning of slot time. If the station does not receive acknowledgement (ACK), it increases backoff stage by one and doubles their contention window size. If the station successfully transmits its frame, it resets backoff stage to 0 and contention window size to CWmin . However, in DCF, the more number of stations share the wireless resources, the more frames are collided. In order to solve this problem, much research on the IEEE 802.11 DCF is conducted. Bianchi presented an analytical model using bi-dimensional Markov chain model and showed that the proposed model is very accurate [4][5]. With simple modification of Bianchi’s model, Xiao showed the limits of throughput and delay of IEEE 802.11 DCF [6]. The performance of the DCF in the presence of transmission error was evaluated in [7][8]. In addition, they presented an analytical model to verify the performance of the DCF in presence of channel bit error rate. The gentle distributed coordination function (GDCF) was proposed by Wang et al. [9]. In GDCF, stations decrease their backoff stages by one whenever the number of consecutive successful frame transmissions reaches the maximum number of permitted consecutive successes. Since GDCF uses the fixed number of permitted consecutive successful transmissions for decreasing the backoff stage, its performance depends on the number of contending stations. The enhanced GDCF (EGDCF) uses a consecutive success counter to represent the number of consecutive successful transmissions at the same backoff stage [10][11]. If the number of consecutive successful transmissions reaches maximum-permitted value, stations decrease their backoff stages by one. Since the maximum permitted value of consecutive successful transmissions is assigned differently according to the backoff stage of stations, performance of EGDCF scarcely depends on the number of contending stations. A Binary Negative-Exponential Backoff (BNEB) algorithm has been proposed by Ki et al. [14]. The BNEB algorithm maintains the contention window to the maximum window size when stations experience a collision and reduces a contention window size by half when a frame is transmitted successfully without retransmission. Since BNEB introduces minus backoff stage to simply represent consecutive transmission successes. In [14] and [15], the results showed that the BNEB algorithm had better performance than conventional DCF in ideal and erroneous channel conditions. However, the performance was evaluated in saturation condition and the performance in terms of MAC delay was not evaluated. Based on our previous works [14][15], in this paper, we intensively evaluate performance of DCF with BNEB in terms of MAC delay and throughput under saturation and normal traffic conditions in erroneous channel. The rest of paper
Performance Analysis of BNEB Algorithm
239
is organized as follows. Section 2 illustrates BNEB algorithm briefly. Section 3 derives an analytical model to evaluate the normalized throughput of BNEB under saturation and erroneous channel conditions. In Section 4, we verify our analytical model by simulations. Also, we compare the throughput and MAC delay of DCF with BNEB to that with BEB under saturation and normal traffic condition. Finally, we conclude in Section 5.
2
Binary Negative-Exponential Backoff Algorithm
The BNEB algorithm uses three parameters, backoff stage, backoff counter, and contention window. The roles of these parameters are similar to those in DCF with BEB. In DCF with BEB, contention window size becomes double whenever a station experiences a collision, until it reaches the maximum contention window size (CWmax ). However, in DCF with BNEB, contention window size initially sets to CWmax to reduce the probability that more than two stations select the same backoff counter value. When a frame successfully transmitted without retransmission, BNEB decreases the contention window size by half to reduce the delay related to backoff time. Since BNEB introduces minus backoff stage to simply represent consecutive transmission successes, it uses two counters, backoff stage and backoff counter. The contention window size Wi (CWmin ≤ Wi ≤ CWmax ) at backoff stage i is decided as follows. CWmax , 0 < i ≤ m, Wi = (1) max(2i (CWmax ), CWmin ), −L ≤ i ≤ 0, where m is the maximum retry limit and L is the natural number that plays a role in assistance number. CWmin and CWmax represent minimum contention window and maximum contention window, respectively. Stations having frame(s) randomly select their backoff counter values from [0, Wi − 1] and decrease their backoff counter values by one whenever a slot is idle. A station starts to transmit its frame if its backoff counter value reaches zero. For the frame to be transmitted, the backoff stage is decided by both the previous backoff stage used for the previous frame and the result of its transmission, success or collision. If the previous frame was successfully transmitted at the backoff stage i, the station sets its backoff stage to 0 for 0 < i ≤ m. The station sets its backoff stage to i − 1 for −L < i ≤ 0. And the station sets its backoff stage to −L if i = −L. If the transmission of the previous frame failed at the backoff stage i, the station sets its backoff stage to i + 1 if 0 ≤ i < m. The station sets its backoff stage to 1 for −L ≤ i < 0. And if the backoff stage is equal to m, the station drops its frame and then initializes its backoff stage to 0. Therefore, if a collision occurs, the station using BNEB algorithm can effectively resolve collision by using the maximum contention window size.
3
Analytical Model for BNEB
For the conventional DCF, Bianchi presented an analytical model using bidimensional Markov chain model and showed that the proposed model is very
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accurate [4][5]. Therefore, we expend Bianchi’s Markov chain model to evaluate the saturation throughput of BNEB in the presence of transmission error. In analytical model, we assume that there are n stations having frame(s) to transmit and each station has frame(s) after successful transmission. In addition, it is possible that a station fails to transmit a frame by a channel noise, not a collision. For a station, s(t) is defined as the random process representing the backoff stage and b(t) is defined as the random process representing the value of the backoff counter at time t. Then, BNEB algorithm can be modeled as a bi-dimensional discrete-time Markov chain (s(t), b(t)). Fig. 1 illustrates the state transition diagram of the Markov chain of the BNEB. Let lim P {s(t) = i, b(t) = j} = bi,j and p be the transmission failure probat→∞ bility that a station experiences a transmission failure due to collision or transmission error in a slot time. Then, we can make the following relations through chain regularities. bi,0 = (1 − p)−i b0,0 , Wi − j bi,j = b0,0 , Wi (1 − p)L b0,0 , b−L,0 = p bi,0 = pi−1 b0,0 , Wi − j bi,j = b0,0 , Wi From Equation (2) and
m W i −1
i ∈ [−L + 1, 0] , i ∈ [−L + 1, 0], j ∈ [0, Wi − 1], i = L, j = 0,
(2)
i ∈ [1, m] , i ∈ [1, m], j ∈ [0, Wi − 1]. bi,j = 1, we can derive b0,0
i=−L j=0
b0,0 =
1 m (W p+1)+ (1−p) [W ( 1−p 2 2 ) −1] p(1+p)
+
W +1 1−pL 2 ( 1−p )
.
(3)
Let τ be the probability that a station attempts to transmit a frame. Then we have m 1 1 − pm + τ= bi,0 = (4) b0,0 p 1−p i=−L
and p = 1 − (1 − τ )n−1 (1 − BER)l+H ,
(5)
where BER and l respectively represent the channel bit error rate and packet payload size. H(= P HYhdr + M AChdr ) represents the sum of packet header sizes, P HY header (P HYhdr ) and M AC header (M AChdr ). The transmission success probability Ps , the probability Pc that an occurred packet collides, and the probability Per that a packet received in error are calculated as nτ (1 − τ )n−1 Ps = (1 − P ER), (6) Ptr
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Transmission Success Collision Occurance
L,0
L,1
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j,Wj-2
j,Wj-1
2,W2-2
2,W2-1
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p/Wmax j,0
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j,2 p/Wmax
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-m,W-m-1
(1-p)/W-1 -1,0
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-1,2 (1-p)/W-2
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i,1
i,2
(1-p)/Wi-1
(1-p)/W-m -m,0
-m,1
-m,2 (1-p)/W-m
Fig. 1. Markov chain of BNEB
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nτ (1 − τ )n−1 , Ptr nτ (1 − τ )n−1 = P ER, Ptr
Pc = 1 − Per
(7) (8)
where Ptr is the probability that there are at least one transmission and P ER is packet error rate, Ptr = 1 − (1 − τ )n , P ER = 1 − (1 − BER)l+H .
(9) (10)
Let Ts be the mean time required for the successful transmission of a frame and Tc and Ter be the mean wasting time due to the collision and transmission error of a transmitted frame. Then, Ts , Tc and Ter are obtained as follows Ts = DIF S + H + E[P ] + 2δ + SIF S + ACK, Tc = DIF S + H + E[P ∗] + δ,
(11) (12)
Ter = DIF S + H + E[P ∗] + δ,
(13)
and where E[P ] and E[P ∗] are the mean transmission time of successfully transmitted packet and collided packet, respectively. SIFS represents a short interframe space and ACK denotes a transmission time of acknowledgement. The parameter δ denotes a propagation delay. Finally, we can obtain normalized saturation throughput of BNEB in presence of channel bit error rate as follows S=
Ptr Ps E[P ] , (1 − Ptr )σ + Ptr Ps Ts + Ptr Pc Tc + Ptr Per Ter
(14)
where σ is the duration of a backoff slot. To evaluate the saturation MAC delay of BNEB in the presence of transmission error, we define the mean sojourn time di at backoff stage i. Let Tb and Pb denote the mean freezing time due to the busy channel and the probability that channel is busy, respectively. Then, di is given by di = (1 − p)Ts + pTc + [(1 − Pb )σ + Pb Tb ]
Wi , 2
i ∈ [−L, m] .
(15)
Also, Pb and Tb are calculated as Pb = 1 − (1 − τ )n−1 , (n − 1)τ (1 − τ )n−2 (n − 1)τ (1 − τ )n−2 Tc . Tb = Ts + 1 − Pb Pb
(16) (17)
Therefore, when a previous frame was transmitted in stage i, Di is given by ⎧ −L ≤ i ≤ 0, ⎨ di + pD1 , 1 ≤ i ≤ m, (18) Di = di + pDi+1 , ⎩ di , i = m.
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The mean MAC delay D can be calculated as 0
D=
bi,0 Di
i=−L 0
.
(19)
bi,0
i=−L
4
Performance Evaluation
To evaluate the performance of DCF with BEB and BNEB, we consider L=5, m=7, and the MAC parameters are given in Table 1. In IEEE 802.11a, control packets such as ACK are transmitted with Control Rate(Ccon )[12][13]. 4.1
Performance Evaluation under Saturation Condition
In order to evaluate normalized throughput and MAC delay of BNEB under saturation condition, we assume that there are n stations having frame(s) to transmit and each station has frame(s) after successful transmission. When there is frame transmission error in wireless channel, normalized saturation throughputs of DCF with BEB and BNEB are shown in Fig. 2. For n = 5, the throughput of BNEB is sensitive to the BER. However, for n=25 and 50, the throughput of BNEB is not sensitive to the BER. From the results, for n=5, the saturation throughput of BNEB is less than that of DCF with BEB, however, the saturation throughput of BNEB is greater than that of DCF with BEB for n=25 and
Fig. 2. Saturation throughput of DCF with BEB and BNEB in IEEE 802.11a under varying BER (L=5, m=7)
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Fig. 3. Saturation MAC delay of DCF with BEB and BNEB in IEEE 802.11a under varying BER (L=5, m=7)
50. When BER ≥ 10−4 , the possibility of transmission failure by a transmission error is larger than that by a collision. Therefore, the throughputs of DCF with BEB and BNEB are closed to 0 as BER increases. Fig. 3 shows the saturation MAC delay of DCF with BEB and BNEB under varying BER. If frame transmission fails, BNEB stations increase contention window to CWmax , but BEB stations increase contention window by double. When the number of contending stations is small, transmission failure caused by transmission error is dominant. Therefore, the saturation MAC delay of BNEB is higher than that of DCF with BEB for n=5 and high BER because the CWmax Table 1. IEEE 802.11a MAC parameters PARAMETER Packet payload MAC header PHY header ACK length Control rate (Ccon ) Data rate (C) Propagation Delay SIFS DIFS Slot Time CWmin CWmax
VALUE 8184 bits 272 bits 128 bits 240 bits 24Mbps 54Mbps 1 µs 16 µs 34 µs 9 µs 16 1024
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Fig. 4. Saturation throughput of DCF with BEB and BNEB in IEEE 802.11a for BER and the number of stations (L=5, m=7)
causes long backoff time. For n=25 and 50, the saturation MAC delay of BNEB is less than that of DCF with BEB. The more the number of stations uses wireless resource, the more collision occurrences are possible than frame transmission error. Because BNEB can resolve the collision more effectively in case that there are many contending stations, the saturation MAC delay of BNEB is less than that of DCF with BEB for n=25 and 50. When BER is higher than 10−4 , difference of the MAC delay between DCF with BEB and BNEB decreases. Also, the saturation MAC delay sharply increases for BER ≥ 10−4 . Fig. 4 represents the normalized saturation throughput of DCF with BEB and BNEB as the number of contending stations increases when BER = 10−6 , 10−5 , and 10−4 . When there are many contending stations, the transmission failure related to the collision is more frequent than that related to transmission error. Therefore, BNEB which initially sets contention window to CWmax shows better performance than DCF with BEB. The waiting time due to the backoff slot time strongly affects the saturation throughput of DCF with BEB and BNEB when there are less contending stations. BNEB sets contention window to CWmax whenever a station experiences transmission failure. For this reason, as the transmission failure is increased by channel BER, the waiting time of BNEB is larger than that of DCF with BEB. Therefore, the performance of BNEB is less than that of DCF with BEB in the small number of contending stations and high BER. However, because the wireless devices operate in BER ≤ 10−5 in most cases, the performance of BNEB is better than that of DCF with BEB. The saturation MAC delay of DCF with BEB and BNEB is shown in Fig. 5. For BER = 10−6 and 10−5 , the saturation MAC delay of BNEB is less than that of DCF with BEB. However, for BER = 10−4 and n ≤ 35, the saturation MAC delay of BNEB is higher than that
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Fig. 5. Saturation MAC delay of DCF with BEB and BNEB in IEEE 802.11a for BER and the number of stations (L=5, m=7)
of DCF with BEB because transmission failure related to the transmission errors is more frequent than that related to the collision. 4.2
Performance Evaluation under Normal Traffic Condition
To evaluate performance of DCF with BEB and BNEB under normal traffic condition, we assume that packets arrive at devices as a Poisson process with a mean arrival rate λ. For BER = 10−6 , 10−5 , and 10−4 , the normalized throughput of DCF with BEB and BNEB varying packet arrival rates (λ) is shown in Fig. 6. The possibility that stations have frame(s) for transmission increases as λ increases until λ = λsat . If the packet arrival rate is larger than the specific value (λsat ), the probability that a station has frame(s) for transmission is close to 1. From the results, the throughput of DCF with BEB and BNEB linearly increases as λ increases until λ = λsat and maintains constant for λ ≥ λsat . The normalized throughput of BNEB is higher than that of DCF with BEB for BER = 10−6 and 10−5 . When BER > 10−5 , the possibility of transmission failure caused by a transmission error is larger than that of transmission failure caused by a collision. Therefore, the normalized throughput of BNEB is less than that of DCF with BEB for BER = 10−4 . Since the λsat of the BNEB is greater than DCF with BEB, the BNEB can serve more traffic than BEB. Fig. 7 shows the MAC delay of DCF with BEB and BNEB varying packet arrival rates (λ). As BER increases, the transmission failure due to the transmission error occurs more frequently than that due to collision. DCF stations set contention window size to CWmin when a station transmit a new frame and double their contention window size when DCF stations participate in the col-
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Fig. 6. Normalized throughput of the DCF and the BNEB varying packet alival rate for BER in IEEE 802.11a (L=5, m=7)
lision. However, to effectively resolve collisions, BNEB stations set contention window size to CWmin when a station transmit a frame. The possibility that a stations retransmits a frame is very small until λ = λsat . Also, the waiting time
Fig. 7. MAC delay of the DCF and the BNEB varying packet arrival rate for BER in IEEE802.11a (L=5, m=7)
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by the backoff strongly affects the MAC delay of DCF with BEB and BNEB when λ ≤ λsat . Therefore the MAC delay of BNEB is higher than DCF with BEB for λ ≤ λsat because BNEB stations use greater contention window size than that of DCF stations. However, when λ ≥ λsat , the MAC delay of BNEB is less than that of DCF with BEB for BER = 10−6 and 10−5 . For, BER = 10−4 , the MAC delay of BNEB is higher than that of DCF with BEB. However, because the wireless devices operate in BER ≤ 10−5 , in most cases, performance of BNEB is better than that of DCF with BEB.
5
Conclusion
In this paper, we briefly explained a binary-negative exponential backoff (BNEB) algorithm to enhance the performance of DCF with BEB. And we proposed a mathematical analysis model to evaluate the performance of BNEB in presence of channel bit error rate. Also, we verified our proposed algorithm via analytical model and simulations under saturation and erroneous channel condition. From the results, BNEB can resolve collision more effectively than DCF with BEB. We also evaluated the performance of BNEB algorithm in the presence of transmission error by simulations under normal traffic conditions. In low BER, performance of BNEB is better than that of DCF with BEB because of effective collision resolution. In high BER, throughput of BNEB is smaller than DCF due to ineffective management of backoff time. However, we expect that BNEB improves performance of DCF compared with BEB under erroneous channel condition.
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