Performance enhancement of IEEE DCF using novel backoff algorithm

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1 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 RESEARCH Open Access Performnce enhncement of IEEE using novel ckoff lgorithm Cho-Yu Kuo 1, Yi-Hung Hung 2* nd Kun-Cheng Lin 3 Astrct In the IEEE distriuted coordintion function (), the inry eponentil ckoff lgorithm selects rndom ckoff numer from uniform proility distriution to void the prolem of pcket collision. In this rticle, we present novel ckoff lgorithm tht uses inominl distriution rther thn uniform distriution to determine the ckoff vlue. Simultion results show tht the proposed lgorithm outperforms the originl IEEE lgorithm. Keywords: Binry eponentil ckoff, IEEE 82.11, Crrier sense multiple ccess/collision voidnce (CSMA/CA) Introduction Advnces in wireless communiction technology hve incresed the demnd for wireless networks. The IEEE stndrd defines the specifictions for medium ccess control (MAC) nd the physicl lyers in wireless locl re network. The IEEE stndrd provides two mechnisms for the MAC protocol: the point coordintion function (PC) nd the distriuted coordintion function (). The PC utilizes sic ccess mechnism tht supports contention-free services. Therefore, the PC requires se sttion tht coordintes chnnel ccess mong nodes. On the other hnd, the utilizes n ccess mechnism tht supports contention-sed services. The ccess mechnism dicttes tht ll the nodes should rndomly ccess chnnels using the crrier sense multiple ccess/collision voidnce mechnism. This mechnism employs the cknowledgment (ACK) feture to detect trnsmission filures. In other words, if n ACK response is not received, it implies tht pcket trnsmission hs filed. Nodes will wit for n interfrme spce (IS), nd then, they will invoke the inry eponentil ckoff (BEB) lgorithm [1] tht uses n uniform rndom distriution clled contention window (cw) size to generte rndom ckoff vlue within the rnge of [, cw 1]. * Correspondence: ehhwng@mil.ntcu.edu.twl 2 Deprtment of Mthemtics Eduction, Ntionl Tichung University of Eduction, Tichung, Tiwn ull list of uthor informtion is ville t the end of the rticle In this study, the initil vlue of cw is set to cw min (the minimum contention window) nd the cw vlue will e douled when the pcket trnsmission fils. or node to otin ckoff vlue, it hs to first determine whether the chnnel is in use. If the chnnel is not usy, then the ckoff vlue will decrese y 1 in every time slot nd the node will trnsmit the dt when the ckoff vlue reches zero. However, if the chnnel is usy, the ckoff counter will freeze. When the chnnel is in n idle stte, it will wit for IS (DIS) time period, nd then, the ckoff vlue will egin decresing gin. If the pcket trnsmission continues to fil, the cw vlue will increse to cw m (the mimum contention window); when the node receives n ACK pcket, cw will e reset to cw min. If node receives n error pcket, it hs to wit for n etended IS (EIS) time. Then, the node determines whether the chnnel is in n idle stte gin. If it is, then fter DIS time period, the ckoff vlue will decrese y 1 fter ech idle slot. Recent studies hve reveled tht mny commercil network interfce crds re dopted with non-uniform distriution for generting ckoff vlues during contention periods in order to otin etter performnce [2,3].The p-persistent-sed model in [4] shows tht the ckoff vlue is smpled y using the p vlue in geometric distriution. In [4], it ws proved tht the nlyzed result ws slightly etter thn the simultion result (uniform distriution). In ddition, Li et l. [5] hve pointed out tht very little reserch hs een done on the proility distriution of slot selection. Even though 212 Kuo et l.; licensee Springer. This is n Open Access rticle distriuted under the terms of the Cretive Commons Attriution License ( which permits unrestricted use, distriution, nd reproduction in ny medium, provided the originl work is properly cited.

2 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 2 of 11 some improvements hve een proposed y Li et l. [5], however, they did not consider how to improve the performnce of throughput nd collision proility under the sme cw men vlue. All of these perspectives hve inspired us to eplore whether the throughput efficiency will remin the sme under different distriutions ut with the sme cw men vlue. Hence, in this rticle, we present novel ckoff lgorithm tht uses inominl distriution rther thn uniform distriution to minimize the degrding effect of rndom numer genertors. Simultion results demonstrte tht the proposed lgorithm outperforms the IEEE lgorithm. The reminder of this rticle is orgnized s follows. In the following section, the ckground nd the nlyticl model for the IEEE lgorithm re riefly reviewed. In Section The inominl ckoff lgorithm, the proposed inominl ckoff lgorithm is descried. In Section Simultions, the ccurcy of the proposed inominl ckoff lgorithm is verified vi simultion eperiments. inlly, the rticle ends with some conclusions. Bckground nd relted study In recent reserches, two types of contention window vlue djustments hve een presented to improve network performnce. The first type stticlly djusts the contention window size when continuous pcket collision is detected [1,5,6]. The other type dynmiclly djusts the contention window size on the sis of the type of network environment [4,7-9]. It is not esy to ccurtely estimte the contention window size in the second type of djustment ecuse network environments my chnge rpidly. Thus, this type is generlly not suitle for rel networks. Hence, in this study, we focus on the first type. Binchi nd Tinnirello [1] developed n nlyticl model to determine whether the men contention window size dopted y the BEB lgorithm for different distriutions is equl; if so, the network throughput will lso e equl. Thus, the performnce of ech modified BEB lgorithm could e emined y pplying it to the prolem of finding the men contention window size. Yun et l. [5] proposed rndom wlking ckoff (RWBO) lgorithm to enhnce the performnce of the IEEE In the RWBO lgorithm, the BEB lgorithm decreses the ckoff vlue y 1 with proility p d ( < p d < 1). Similrly, the performnce of the RWBO lgorithm cn e nlyzed y pplying it to different distriutions such s uniform nd geometric distriutions to determine network throughputs. Cli et l. [4] proposed n IEEE lgorithm tht uses geometric distriution to pproimte uniform distriution. Simultion results demonstrted tht the performnce of the geometric distriution ws slightly etter thn the uniform distriution under the sme men vlue for the contention window. This implied tht dopting different distriution function would likely e to influence network performnces. Although few studies hve ddressed the prolem of different proility distriution functions for the BEB lgorithm, the nlyticl model in [11] clerly eplins the effects of proility distriution functions when the sme men contention window size is used. Hu et l. [11] introduced the concept of post-usy slot, i.e., the slot fter usy slot. After node hs trnsmitted dt in usy slot, it my hve the opportunity to trnsmit dt in the post-usy slot (this phenomenon is clled short-term non-uniform ccess in [11]). urther, this phenomenon cnnot e nlyzed ccurtely using the model given in [1,12,13], ecuse the collision proility p is neither constnt nor independent, s ssumed for the nlyticl model given in [1,12,13]. In ccordnce with the specifictions, fter DIS time period, the ckoff counter t sttion will decrese the count y 1 only fter nother idle ckoff slot hs elpsed. Hence, only successful trnsmitting sttion my ccess the post-usy slot fter the DIS. However, ssumption 1 in ref. [12] implies tht the ccess proility of ech post-usy slot is identicl. Hence, the phenomenon of short-term non-uniform ccess cnnot e nlyzed using the p-persistent-sed model. Thus, Hu et l. proposed non-p-persistentsed model to nlyze this phenomenon. The min underlying concept for the non-p-persistent-sed model is descried s follows: The nodes tht contend for the post-usy slot cn e divided into two groups: one group comprises nodes tht hve trnsmitted dt in the previous usy slot, nd the other group comprises nodes tht hve not trnsmitted dt in the previous usy slot. In the BEB lgorithm, the nodes in the former group otin zero ckoff vlue from the distriution function nd the nodes in the ltter group otin non-zero ckoff vlue from the distriution function. In other words, the different proility distriutions dopted y the BEB lgorithm ffect the proility of node ccessing the post-usy slot. Therefore, it is necessry to nlyze the non-p-persistent-sed model for the effects of the different proility distriutions dopted y the BEB lgorithm. The inominl ckoff lgorithm In this study, we ssume tht (1) ech node is in sturted condition (i.e., it lwys hs pcket to trnsmit) nd (2) the chnnel is free from errors. Pcket loss occurs only ecuse of collisions during the pcket

3 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 3 of 11 trnsmission process, nd the hidden terminl prolem is not considered. Suppose X is the selected ckoff vlue for the BEB lgorithm. The proility tht X = is.5 on the stte spce {, W} (W = min {2 k cw min 1, cw m 1}, k =, 1,..., L, nd L is the retry limit), nd hence, the proility density function is given s follows: f X ðþ¼ :5 X 2 f ; W g X =2 f; Wg : ð1þ Thus, the proposed lgorithm is given s follows: Bckoff Time ¼ ðcmþ SlotTime: Here, (cw) = cw uniform distriution either over or 1 (5% ech), where cw is n integer within the rnge of vlues for the PHY chrcteristics, CWmin, nd CWm, nd CWmin cw CWm. SlotTime ¼ slot time: As the men contention window size for uniform distriution nd inominl distriution re equl, i.e., ((cw 1)/2), it is possile to differentite etween the effects of these two proility distriution functions on the network performnce using the non-p-persistentsed model. However, the ccess proility of the inomil lgorithm for ech slot is different, where oth the p-persistent-sed model nd the non-p-persistent-sed model cnnot e used for n nlysis. Therefore, we use the following emple to illustrte how the inomil lgorithm performs in the ckoff process. Due to the chrcteristic of inomil lgorithm, when the cw vlue is 31, the node cn only choose etween nd 31 s its ckoff vlue, wheres the proility of it choosing other vlues s ckoff vlue is. At this time, we my regrd ech slot s 31 independent chnnels, where collision will only hppen when the different nodes enter n identicl chnnel. On the contrry, when different nodes enter different chnnels, collision will not e possile. As shown in igure 1, if two nodes wnt to trnsmit dt simultneously. In the eginning, oth the nodes will set their cw vlue to 31, if nodes 1 nd 2 oth choose the ckoff vlue of t the sme time, then nodes 1 nd 2 will collide (oth nodes hve to doule their ckoff vlues, which mens tht the cw vlue will e set to 63). If node 1 chooses s its ckoff vlue nd node 2 chooses 63 s its ckoff vlue, then oth these nodes will e in different chnnels. When the ckoff vlue of node 1 is, node 2 will not e le to decrese its ckoff vlue progressively. At this time, the ckoff vlue of node 2 will e frozen; the node will hve to wit until node 1 complete its dt trnsmission nd then compete gin in the net round. When node 1 reselects its ckoff vlue s 31 (the ckoff vlue of node 1 is then 31, nd the ckoff vlue of node 2 is 63), node 1 will trnsmit its dt successfully fter processing 31 empty slots; then, the ckoff vlue of node 2 will ecome = 32. If node 1 gin chooses 31 s its ckoff vlue, node 1 will gin trnsmit its dt successfully fter processing those 31 empty slots; consequently, the ckoff vlue of node 2 will ecome = 1. If node 1 yet gin chooses 31 s its ckoff vlue, it will process 1 empty slot nd the ckoff vlue of node 2 will ecome. Then, node 2 will strt its dt trnsmission, nd the ckoff vlue of node 1 will ecome 31 1 = 3. By oserving the repetition of such process, we otin the following results: When the ckoff vlue of node 1 is nd the ckoff vlue of node 2 is 1, the dt trnsmission of node 1 will succeed. And in the net round, when node 1 chooses 31 s its ckoff vlue nd now the ckoff vlue of node 2 is 1. After one slot, then the ckoff vlue of node 2 is nd the ckoff vlue of node 1 is 3, the dt trnsmission of node 2 will succeed. When the ckoff vlue of node 2 is 31 nd the ckoff vlue of node 1 is 3, then oth the nodes will trnsmit dt in different chnnels without ny collision Node 1 Node (Bckoff vlue) (Bckoff vlue) Successful dt trnsmission iled dt trnsmission reeze node s reduction on ckoff vlue igure 1 Emples of two nodes.

4 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 4 of 11 etween the nodes. Therefore, fter the initil collision process nd different nodes choosing different ckoff vlues in the inomil lgorithm, ech node would enter into different chnnels to reduce the proility of collision. We then use igure 2 to illustrte the ckoff phenomenon of the inomil lgorithm. When cw is set to 31, the nodes will hve 1% proility of remining in the sme chnnel (if the ckoff vlue is or 31, then mod 31 = nd 31 mod 31 = ). When cw is set to 63, the nodes will hve 5% proility of remining in the sme chnnel (ckoff vlue is ) nd 5% chnce of switching to the net chnnel (if the ckoff vlue is 63, then 63 mod 31 = 1). When cw is set to 127, the nodes will hve 5% proility of remining in the sme chnnel (ckoff vlue is ) nd 5% chnce of switching to the net three chnnels (if the ckoff vlue is 127, then 127 mod 31 = 3); When cw is set to 255, the nodes will hve 5% proility of remining in the sme chnnel (the ckoff vlue is ) nd 5% chnce of switching to the net seven chnnels (if the ckoff vlue is 255, then 255 mod 31 = 7). When cw is set to 511, the nodes will hve 5% proility of remining in the sme chnnel (the ckoff vlue is ) nd 5% chnce of switching to the net 15 chnnels (if the ckoff vlue is 511, then 511 mod 31 = 15). When cw is set to 123, the nodes will hve 1% proility of remining in the sme chnnel (if the ckoff vlue is or 123, then mod 31 = nd 123 mod 31 = ). Therefore, the trnsition digrm of the stte cn e drwn s given in igure 2. The stte vlue of, in igure 2, illustrtes tht the node will hve 5% proility of remining in the sme chnnel nd 5% proility of switching to net chnnel(s) (31 chnnels form circultion chnnel, nd the chnnel is clculted y using the modulo method). Simultions Environmentl settings In the simultions, we use two performnce indices throughput nd conditionl collision proility with different node to ssess the performnce of ech lgorithm [12]. We define the throughput s follows [1-12]: P s pylod throughput¼ ; P i t slot þp s t success þp c t col ð2þ where P i is the proility tht slot is idle, P s is the proility tht slot trnsmits dt successfully, P c is the proility tht slot is in collision stte, pylod is the time spent to trnsmit dt, t slot is n idle slot time (SlotTime), nd t success is the time spent to trnsmit pcket successfully. Notly, t success = DATA + SIS + ACK + DIS when the lgorithm does not utilize the RTS/CTS method. urther, t col is the time spent during pcket collision. Notly, t col =DATA m + DIS when the lgorithm does not utilize the RTS/CTS method. DATA m is the mimum witing time when pcket collision occurs. The normlized throughput performnce indictor used in this study is the sme s the throughput defined y the formul shown in Eqution (2). The conditionl collision proility with different nodes, P cc, is defined s the collision proility tht node ttempts to trnsmit dt. A high P cc vlue does not men tht P c is high. or instnce, if four nodes re trnsmitting dt simultneously in the sme slot, the numer of colliding nodes with P cc is 4; however, the numer of collisions with P c is 1. In igure 3, ssume tht there re 15 slots, with the numer in slot representing the trnsmitting dt in tht slot. Thus, there re eight ville empty slots, three slots where dt re trnsmitted successfully nd four slots with dt collisions. Therefore, P s = 3/15, P c = 4/15, P i = 8/15, nd P cc =( )/( ) = 11/14. Moreover, conditionl collision proility with different node is used insted of the collision proility when node is trnsmitting dt to show the effect of pcket collision. In generl, it is difficult to detect the stte (idle, dt trnsmission, collision) of slot. This is ecuse, in wireless environment, the informtion of ech node S,,+1,+3,+7,+15, S S: Successful dt trnsmission : iled dt trnsmission igure 2 Trnsition digrm of the stte in the proposed lgorithm.

5 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 5 of 11 igure 3 Stte of virtul slot. needs to e collected nd compiled to determine whether the slot is in the idle, collision, or dt trnsmission stte nd clculte the P i, P s, nd P c vlues. However, in some cses, inconsistent informtion will pper for some nodes. or emple, node tht receives n error pcket hs to enter n EIS time, nd then, DIS time efore entering the ckoff stge. If the slot is in the usy stte when entering the ckoff stge, the node will not e le to distinguish whether this slot hs entered the EIS time. Therefore, the slot sttus of this node could e different from other nodes nd result in informtion inconsistencies etween these nodes. Becuse this phenomenon mkes it difficult to clculte the P i, P s, nd P c vlues, we cn only use the P cc vlue to represent the collision stte. We use NS2 [14] ( network simultor) s our simultion tool nd use the network environment prmeters presented in Tle 1 s simultion prmeters. Eperiments re repeted 1 times using different seeds, nd the results of these 1 runs re verged to otin the simultion results. Eperiment I: fied contention window size We fi the contention window size cw t 32 to compre the performnce of the proposed scheme with uniform distriution, s shown in igure 4 d. igure 4 represents of igure 4, nd igure 4d represents of igure 4c. igure 4 shows tht the performnce of the proposed inominl lgorithm is worse thn the uniform distriution when the is Tle 1 Simultion prmeters Dt rte 11 Mps PCLP dt rte 1 Mps Bsic rte 1 Mps Slot time 2 μs SIS 1 μs DIS 5 μs EIS SIS + DIS + (ACK length)/sic rte PHY heder 192 MAC heder 224 ACK length PHY heder CW min 32 CW m 124 Pcket size 5 B + PHY heder + MAC heder less thn 54. The proposed inomil lgorithm in igure 4 d performed poorer thn the uniform distriution due to the fied cw size. This result cn e epected ecuse the proposed inominl lgorithm hs only one chnnel. Therefore, the proposed inominl lgorithm will hve higher collision proility nd stndrd devition thn the uniform distriution. As for igure 4, the proposed inominl lgorithm will only chieve higher throughput thn the uniform distriution when the re higher thn 54. This result is cused y the effect of EIS (equivlent to 18 slots (EIS = = 364 μs) [12]), which increses the proility of incresing the numer of chnnels. Once node enters into EIS nd there re no nodes trnsmitting during this time period, the node tht entered into EIS will hve the opportunity to switch to different chnnels. Therefore, when the numer of nodes increses, the proility of nodes switching to different chnnel lso increses. Hence, the proposed inomil lgorithm chieves higher throughput thn the uniform distriution when the numer of nodes re higher thn 54. Eperiment II: comprison etween different distriutions This section compres the normlized throughput nd the conditionl collision proility for the RWBO + BEB, uniform, geometric, nd inominl distriutions for the sme men cw. The men cw for ech distriution (Tle 2) is computed in ccordnce with the RWBO + BEB(.25) [5]. igure 5 shows tht the normlized throughput nd conditionl collision proility with different nodes of the inominl ckoff lgorithm re pprently etter thn other distriutions. In prticulr, the conditionl collision proility of the inominl ckoff lgorithm is 24% smller thn other distriutions. urther, the throughput of the inominl ckoff lgorithm is 6% etter thn other distriutions. This result shows the impct of different distriutions on the network performnce. igure 5 represents of igure 5, nd igure 5d represents of igure 5c. As we cn see from igure 5,d, the smpling chnges in the proposed lgorithm is lrger thn other methods. This is ecuse the node tht uses inomil ckoff lgorithm must serch for chnnels first. As result, in the proposed lgorithm is lrger thn other methods. However, igure 5 shows tht the mimum stndrd devition for inominl is only

6 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 6 of 11 normlized throughput c.35 d.3.8 the conditionl collision proility igure 4 Normlized throughput nd conditionl collision proility with different node. () cw=cw min =cw m = 32: normlized throughput with different node. () cw=cw min =cw m = 32: stndrd devition (normlized throughput). (c) cw=cw min =cw m = 32: conditionl collision proility with different node. (d) cw=cw min =cw m = 32: stndrd devition (conditionl collision proility)..34 nd igure 5d shows tht the mimum stndrd devition for inominl is only.128. The reson for this is ecuse the inominl collision proility is lredy smll, so the chnges in smpling dt will e reltively lrger. Results presented in igure 6 re derived from igure 5. However, we re unle to eperiment with lrge mount of nodes in our simultions due to NS2 nd hrdwre (i.e., CPU, memory) constrints. Therefore, the results presented in igure 6 re produced y self-written simultion progrm. Clcultions used in this simultion progrm re sed on slot. Tht is, we ssume tht node is in success or collision stte only uses one slot time. Hence, we simply investigte the percentge of slots tht is in idle, success, or collision sttes. Ech simultion is repeted 1 times with 1,, slots, nd verge proility is clculted for ech sttes. In ddition, from the result oserved from igure 5, we cn see tht the simultion results for ll distriutions re similr ecept for the inomil distriution. Therefore, simultion conducted in Tle 2 Men of RWBO + BEB(.25) set for vrious distriutions Retrnsmitting pcket numer Men of RWBO + BEB (.25) 124 (248) (1/125) (248) (54) (1/253) (54) 2 58 (116) (1/59) (116) 3 12 (24) (1/121) (24) (488) (1/245) (488) (8184) (1/493) (8184)

7 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 7 of 11 RWBO+BEB(.25).3.3 normlized throughput RWBO+BEB(.25) c d RWBO+BEB(.25) the conditionl collision proility RWBO+BEB(.25) igure 5 Comprison of normlized throughput nd conditionl collision proility with different nodes for different distriutions. () Normlized throughput with different nodes. () Stndrd devition (normlized throughput). (c) Conditionl collision proility with different nodes. (d) Stndrd devition (conditionl collision proility). igure 6 only compres etween the inominl distriution nd the uniform distriution. igure 6 shows tht when the reches 1, in the uniform distriution, the proility of idle, success, or collision stte seems likely to tend to fied vlue of their respective. As for igure 6, when the numer of nodes reches 14 in the inominl distriution, sme phenomenon ppers to hppen erlier thn the 1 (idle) (success) (collision) 1 (idle) (success) (collision) proility proility igure 6 Comprison of the proility for different in idle, success, nd collision sttes with different distriutions. () Proility of nodes in idle, success, nd collision sttes (uniform). () Proility of nodes in idle, success, nd collision sttes (inominl).

8 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 8 of 11 Tle 3 Ech node uses CBR Trffic to set its time for sending dt, = 2, 4, 6,...,16 Node numer Strt time (s) End time (s) uniform distriution. Therefore, from igure 6 nd Eqution (2) we cn infer tht when the reches 14 in igure 5, the result of the inominl distriution my lso rrive t flt horizontl line grdully. urthermore, y compring oth igure 6,, when the reches 144 in the uniform distriution, the proility of success stte in the uniform distriution is only slightly higher thn the proility of success stte in the inominl distriution out.23. When the numer of nodes reches 6 in the uniform distriution, the proility of collision stte in the uniform distriution is only slightly higher thn the proility of collision stte in the inominl distriution out.3. Therefore, from Eqution (2), we cn infer tht when the increses, the normlized throughput in the inominl distriution will chieve etter result thn the uniform distriution. Eperiment III: chnging in simultion process with different distriutions In this eperiment, the performnce of the proposed lgorithm is evluted y chnging the in the simultions. We ssume tht the nodes trnsfer dt to ech other using CBR trffic (11 Mps). Tle 3 shows the trnsfer time for ech node. The simultion time is 7 s. When we use the prmeters for ech distriution given in Tle 2 nd the network prmeters given in Tle 3, the performnce of the proposed lgorithm is etter thn the other methods in chnging network environment (igure 7). In prticulr, the conditionl collision proility of the inominl ckoff lgorithm is 3 19% smller thn the other distriutions. In ddition, the throughput of the inominl ckoff lgorithm is slightly normlized throughput RWBO+BEB(.25) RWBO+BEB(.25) c.2 d the conditionl collision proility RWBO+BEB(.25) RWBO+BEB(.25) igure 7 Comprison of normlized throughputs nd conditionl collision proility with different nodes for different distriutions in dynmic environment. () Normlized throughput with different nodes. () Stndrd devition (normlized throughput). (c) Conditionl collision proility with different node. (d) Stndrd devition (conditionl collision proility).

9 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 9 of 11 etter ( 5%) thn the other methods. As the men cw is lrge, the performnce of the inominl ckoff lgorithm is improved slightly. This result shows the impct of different distriutions on the network performnce. igure 7 represents of igure 7, nd igure 7d represents of igure 7c. As we cn see from igure 7,d, the smpling chnges in the proposed lgorithm re similr to other methods. igure 7 shows tht the mimum stndrd devition for inominl is only.53 nd igure 7d shows tht the mimum stndrd devition for inominl is only.78. This is ecuse the numer of chnnel is 248, which is wy lrger thn the numer of node used in the eperiment. As result, the stndrd devition will e reltively low. Eperiment IV: comprison with We set the contention window size cw within the rnge cw = [cw min = 32, cw m = 124] to compre the performnce of the proposed scheme with, s shown in igure 8,c. igure 8c shows tht the proposed inominl lgorithm cn decrese the conditionl collision proility (6 39%), nd igure 8 shows tht it hs etter throughput (2 14%) thn the IEEE Thus, the inominl lgorithm cn decrese the conditionl collision proility nd gives etter throughput thn the IEEE igure 8 represents of igure 8, nd igure 8d represents of igure 8c. As we cn see from igure 8,d, the smpling chnges in the proposed lgorithm re lrger thn method. This is ecuse the node tht uses inomil ckoff lgorithm must serch for chnnels first nd the numer of chnnel is 32 where the numer of node is etween 2 nd 1. As result, in the proposed lgorithm is lrger thn method. However, igure 8 shows tht the mimum stndrd devition for inominl is only.118 nd igure 8d shows tht the mimum stndrd devition for inominl is only.365. In igure 9, the -is represents the nd the y-is represents the E[cw] vlue mesured in the normlized throughput c.4.35 d the conditionl collision proility igure 8 Normlized throughput nd conditionl collision proility. () Normlized throughput with different nodes. () Stndrd devition (normlized throughput). (c) Conditionl collision proility with different nodes. (d) Stndrd devition (conditionl collision proility).

10 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 1 of 11 igure 9 E[cw] for nd inominl method. simultion eperiment relted to the results shown in igure 8. The inominl (idel) curve represents the idel inominl results. In igure 9, the inominl (idel) curve only shows the ovious vlue chnges in E[cw] t the point where the is 32. This is ecuse cw min = 32, when there re only 31 chnnels, nd only when the is ove 32, there will e 2 or more nodes contending for one chnnel; then, only this normlized throughput c.6 d.4.5 the conditionl collision proility igure 1 Comprison of normlized throughputs nd conditionl collision proility with different nodes in dynmic environment. () Normlized throughput with different nodes. () Stndrd devition (normlized throughput). (c) Conditionl collision proility with different nodes. (d) Stndrd devition (conditionl collision proility).

11 Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 Pge 11 of 11 sitution will cuse the vlue of E[cw] to increse. rom the comprison result etween the inominl curve nd the inominl (idel) curve shown in igure 9, due to shorter eperiment time for the inominl curve, the collision tht hppens t the eginning when the nodes re serching for chnnels hs lrger influence on the incrementtion of inominl curve E[cw] vlue. Moreover, s epected, the inominl curve will ecome closer nd closer to the inominl (idel) curve s the simultion time increses. This phenomenon will lso slightly improve the performnce of the inominl method relted to the results shown in igure 8. Eperiment V: comprison with for chnging in the simultion process In this eperiment, the performnce of the proposed lgorithm is evluted y chnging the in the simultions. We ssume tht the nodes trnsfer dt to ech other using CBR trffic (11 Mps). Tle 3 lists the trnsfer time for ech node. The simultion time is 7 s. When we use the network prmeters given in Tle 3, the performnce of the proposed lgorithm is found to e etter thn the IEEE for chnging network environment (igure 1). In prticulr, the conditionl collision proility of the inominl ckoff lgorithm is 16 4% smller thn the IEEE In ddition, the throughput of the inominl ckoff lgorithm is slightly etter (4 11%) thn the IEEE Since the men cw is lrge, the performnce of the inominl ckoff lgorithm is slightly improved. Thus, the inominl lgorithm cn decrese the conditionl collision proility nd it gives etter throughput thn the IEEE igure 1 represents of igure 1, nd igure 1d represents of igure 1c. As we cn see from igure 1,d, the smpling chnges in the proposed lgorithm is lrger thn method. This is ecuse the node tht uses inomil ckoff lgorithm must serch for chnnels first nd the numer of chnnel is 32 where the numer of node is etween 8 nd 64. As result, in the proposed lgorithm is lrger thn method. However, igure 1 shows tht the mimum stndrd devition for inominl is only.13 nd igure 1d shows tht the mimum stndrd devition for inominl is only.55. The reson for this is ecuse the inominl collision proility is lredy smll, so the chnges in smpling dt will e reltively lrger. Conclusions In this rticle, we proposed novel ckoff lgorithm tht uses inominl distriution, insted of uniform distriution, to select the ckoff vlue. After the initil collision process nd fter different nodes hve chosen different ckoff vlues in the inomil lgorithm, ech node enters different chnnels to reduce the proility of collision. Simultion results showed tht the proposed lgorithm performs etter thn the IEEE lgorithm for conditionl collision proility nd normlized throughput. We pln to study the ehvior of the inomil ckoff lgorithm further s our future study nd lso pln to propose mthemticl model to nlyze the performnce of this type of lgorithm. Competing interests The uthors declre tht they hve no competing interests. Author detils 1 Deprtment of Computer Science nd Engineering, Ntionl Chung Hsing University, Tichung, Tiwn. 2 Deprtment of Mthemtics Eduction, Ntionl Tichung University of Eduction, Tichung, Tiwn. 3 Deprtment of Mngement Informtion Systems, Ntionl Chung Hsing University, Tichung, Tiwn. Received: 18 June 211 Accepted: 8 August 212 Pulished: 23 August 212 References 1. IEEE Computer Society, IEEE Stndrd 82.11: Wireless LAN Medium Access Control (MAC) nd Physicl Lyer (PHY) Specifictions (IEEE Press, New York, 1999) 2. G. Binchi, A. Di Stefno, C. Giconi, A. Scglione, L. Scli, G. Terrzzino, I. Tinnirello, Eperimentl ssessment of the ckoff ehvior of commercil IEEE network crds, in Proceedings of the Annul Joint Conference of the IEEE Computer nd Communictions Societies (INOCOM), Anchorge, Alsk, USA, My 27, pp Bich, M. Comisso, A. 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