Study on Improved Truncated Binary Exponential Back-off Collision Resolution Algorithm

Transcription

1 IJCSNS Inernaional Journal of Couer Siene and Nework Seuriy, VOL. 6 No.11, Noveber 6 97 Sudy on Iroved Trunaed Binary Exonenial Bak-off Collision Resoluion Algorih Yongfa Ling and Deyu Meng Fauly of Siene, Xi an Jiaoong Universiy, Xi an 7149, China Absra: The runaed binary exonenial bak-off algorih has been widely alied in he ollision resoluion roess of rando uliaess hannel. Based on he analysis of is basi ehanis, one iroved algorih o se iniial window dynaially, and he oher o se iniial and end window dynaially, were roosed. The exerienal resuls indiaed ha hese iroved algorihs were sable and effeive, and had higher resoluion effiieny and beer hroughu urve han he basi algorih. Key words: rando uli-aess hannel; binary exonenial bak-off algorih; ollision resoluion; ie slo Muli-aess is an aess onrol roool of oon hannel ha is shared by uli-user. Is logi oology shows as figure Syse 1 3 Shared Channel Shared Channel User1 User User N Fig. 1 Muli-aess Syse 1. I has been widely alied in various o- Fig. Disree Tie Channels * The auhors wish o hank anonyous reviews for useful oens. This work was suored by he Naional Siene Foundaion ( No ) of China. * Ling Yongfa (1973-), ale, naive of Shangyou of Jiangxi Provine, osdoor, oriened in Nework Algorih and Nework Conrol -uniaion syses [1],suh as saellie ouniaion syse, obile ouniaion syse, loal area nework(lan) and eroolian area nework(man). Muli-aess hiefly follows he hree ouniaion roool odels: fixed alloaion, alloaion aording o needs, rando onenion. Seially, he rando onenion odel has been widely alied due o is effeive hannel resoure uilizaion and reduing swih delay under erain ondiion [-3]. ALOHA [4] and sloed ALOHA [5] whih were roosed by N. Abrasona and L.. Robers in 197 and 197 reseively are a kind of yial rando onenion syse odel. In he sloed ALOHA syse, oon hannel is divided ino disree fixed-lengh ie slies alled slo, see figure. Every slo has hree ossible saes: idle (no ake ouies his slo), suess (jus one ake ouies his slo), ollision (wo or ore akes aly for his slo). A user erinal an ransi akes only a he beginning of a slo ( i ) and only one ake is eried in one slo. The users in he syse randoly ouy he hannel resoure, and ollision ours when wo or ore user erinals aly for a slo o send akes siulaneously. The users involved in ollision need o reransi he akes in he subsequen slos aording o a seifi ollision resoluion rule unil all he onfli users suessfully send heir akes. The sloed ALOHA syse is ousanding due o is no need of enralized onrol, easily adding or reduing user erinal, sily oeraion and sall ransission delay, e. When lighly loaded, he onfli robabiliy of daa akes is sall,hene every user erinal an effeively uilize he hannel resoure aording o needs. Wih he syse load grows, ollision will inrease whih resuls in aess delay growing, hroughu dereases, evenly akes losing or syse breakdown. So i is riial o roerly hoose aess odel and ollision resoluion algorih in order o irove he erforane of rando onenion uli-aess syse. 1 Trunaed Binary Exonenial Bak-off Algorih (TBEB) The binary exonenial bak-off algorih is an algorih odel ha he reransission delay and reransission ie of a onfli erinal onsis a binary exonenial relaionshi. Wih he reransission ies grow, he san of he bak-off delay inreases aording o -exonenial. I has been widely used in LAN and HFC nework [6]. The algorih an be desribed as follows: When ollision ours, he onfli erinal randoly hooses a value fro he slo window san rovided by he algorih eah ie, and his rando value is he slo nuber ha he erinal us give u before reransi he akes. Assue ha he wo erinals T 1 and T onfli, he algorih ses he soe of iniial slo window 1~16, and he ollision resoluion rogress randoly alloaes 5 slos and 1 slos for erinal T 1 and erinal T reseively, his eans ha he erinal T 1 and erinal T an only reransi inforaion afer 5 slos and 1 slos reseively. Le ζ denoe he bak-off delay of he erinal, he algorih an be desribed as follows: ζ = ζ = ζ τ rando[1, n ] Where, τ is a syse-relaed ie onsan. Afer a onfli resoluion is finished, judge wheher ollision resoluion over eah erinal sueeds. If he ollision resoluion fails, he onfli erinal us ener he nex resoluion. Then he algorih adds he bak-off slo window size aording o -exonenial (bu sill saller han he bigges bak-off slo window), eah onfli er-

2 98 IJCSNS Inernaional Journal of Couer Siene and Nework Seuriy, VOL. 6 No.11, Noveber 6 inal sohasially seles a value again in he new slo window, and reeas he above delay roess unil he ollision resoluion sueeds. In order o guaranee he ie delay erforane of he syse, he reeiion roess anno be unliied, and he algorih seifies he axiu value of he binary index 1 and he ax nuber of reeiion 16. When he resoluion ie exeeds 16, he resoluion fails and akes of he onfli erinals lose. Aording o he rule above, suose here are N erinals onflis in he syse. The ollision resoluion roess based on he fundaenal runaed binary exonenial bak-off algorih an be desribed as follows: Firsly, he syse eners he firs 1 ollision resoluion eriods, suose he window size of he h ollision resoluion is, n ]: [ Le, 1 = + 1 [1,1 ] n = n 1 + n denoe he iniu and axiu of he window of he h ollision resoluion reseively. When =1, and n reresen he iniial values equal o. For exale, in he 1 s onfli resoluion( =1), he algorih rovides 1 slo values in [+,+ 1 ](here are 1 and ), hen eah erinal randoly hoose a slo value in he above soe and judges wheher he resoluion sueeds, naely, oare he N slo values alloaed o he N onfli erinals o find wheher here are values idenial. All he erinals ha have differen slo values reain heir values searaely whih eans ha he ollision resoluions over hese erinals sueeds; he oher erinals (N 1,N 1 N) ha have he sae slo values sill onfli and ollision resoluion oninues, hus he nd resoluion( =) ours. In he nd 1 + ] (here are 3, 4, 5 and 6) and he above roess will reea unil suessfully resolved. If he resoluion is ye unsuessful unil =1, hen ener he laer 6 ollision resoluion eriods. Unlike he firs 1 ollision resoluions, in he laer 6 ollision resoluion, he slo window size reains 1 (1,4). The slo window size of he h resoluion is [, n ] resoluion, he algorih rovides slo values in [ + 1, Table 1 Window Size of Collision Resoluion (Uni: ie slo) The rior 1 resoluion window size The laer 6 resoluion window size Ties () Iniial value ( ) End value (n ) Ties () Iniial value ( ) End value (n ) [1,6 1 = ] 1 n = n Where and n reresen he iniu and he axiu of he window of he h ollision resoluion reseively. When =1, and n reresen he iniial value, reseively equal o 13 and 46. In he laer 6 onfli resoluion eriods, he ehod of randoly alloaing slos o eah erinal and judging wheher he resoluion is suessful is sae as he ehod in he firs 1 onfli resoluions. The size soes of slo window in he 16 ollision resoluions are given in able 1. If ollision sill exiss afer 16 ies resoluion, hen he enire ollision resoluion fails and all he inforaion o be sen of he onfli erinals is disarded. Assue he nuber of onfli erinals (N) is 6, he ollision resoluion roess shows in Figure 3. In he figure, a, b,, d, e and f wih arrow reresen six onfli erinals reseively. The resuls indiae ha he ollision of he six onfli erinals is suessfully resolved a =3, hus don ener he laer 6 ollision resoluions eriods. The reques inforaion of a, b,, d, e and f will be sen suessfully afer waiing 8, 14, 1, 3, 6 and 9 slos reseively. 14 slos are used in he enire resoluion roess. a d f b e =1 No onfli resoluion sueed over all erinals 1 slo d a f b e = Resoluions sueed over erinals d and e slo =3 a f slo b Resoluion sueed over all erinals Fig. 3 Collision Resoluion Proess over 6 Confli Terinals

3 IJCSNS Inernaional Journal of Couer Siene and Nework Seuriy, VOL. 6 No.11, Noveber 6 99 TBEB Algorih wih Dynaially Seing Iniial Window In TBEB algorih, when he nuber of onfli erinals N 4, he ollision resoluion sars sill fro exonenial =1 ( rovides slo window soe [1, ]), and as a resul, he robabiliy of invalid resoluion (naely in eah ie rak does no have suessful sae) aears o be very large. Therefore, if we an se he iniial window aording o he nuber of onfli erinals dynaially, he ollision resoluion effiieny will be iroved grealy. The ioran differene beween he iroved algorih wih seing iniial window dynaially and he basi algorih lies in: Unlike basi algorih ha ses he iniial window size as [1,] wihou onsideraion of he nuber of onfli erinals, when alying iroved algorih, we se he iniial window size dynaially. Aording o he referene [7], a heory ha dynaially ses he iniial window size based on he iniial onfli erinal nuber is roosed. Table shows he resuls. Table Seing Iniial Window Based on Confli Terinals Nuber of Confli erinal 4~1 11~ 1~5 51~1 11~ Iniial window (W) b d e f a = slo e Resoluions sueed over erinal a, b, d and f = slo Resoluions sueed over all erinals Fig. 4 Collision Figure Resoluion 4 Collision Resoluion Proess Proess over over 6 Confli 6 Terinals(Se Iniial Iniial Window) window) Noe ha he iniial window size inludes he value of he rior windows ie slos. For exale, suose he nuber of onfli erinals N=, =3 (in basi algorih =1), hen he iniial window size should be [1,14], no [1,8], as he size inludes he ie slos soe [1, 6] rovided by he riori window =1 and = and hen adds on ie slos [7,14] rovided by =3, see Table 1. Oher han seing he iniial window size aording o he syse load, he ollision resoluion roesses in he iroved algorih reains onsisen wih he basi algorih. Siilarly, suose he nuber of onfli erinals N=6, he ollision resoluion roesses of he iniial window (his ie =) are showed in figure4. The resuls indiae ha he 6 onfli erinals suessfully resolve he ollision when =3; oared wih he basi algorih, he iroved algorih only arries on wo ollision resoluion, and he ollision resoluion has no enered he laer 6 onfli resoluion yles. The reques inforaion of onflis erinals a, b,, d, e and f will be suessfully ransied afer waiing 6, 1, 1,, 9 and 4 slos reseively. Alogeher, he ollision resoluion roess has used 14 ie slos. 3 TBEB Algorih wih Dynaially Seing Iniial Window and End Window The iroved algorih wih seing he iniial window and he end window us dynaially se he size of he window on whih he las ollision resoluion is arried. Aording o he regulaion of he runaed binary exonenial bak-off algorih ollision resoluion algorih, he bak-off of he window size hanges by -exonenial, bu i differs fro he firs wo algorihs, in he ollision resoluion roess, when only a erain erinals onfli in a ie slo in a seifi ollision resoluion, he algorih eners he las he ollision resoluion roess. The window size of he las he ollision resoluion will be dynaially se aording o he nuber of onfli erinals (no bak off by -exenenial, bu he las onfli nuber). Provided ha here sill exis onfli afer he las ollision resoluion, hen he enire ollision resoluion fails. For insane, suose he onfli erinal nuber N=, when =4 (assue here are only 3 erinals onfli in he 18h ie slo), hen eners he las he ollision resoluion roess, rovides a ie slo window suh as [31,38] for he 3 onfli erinals (Noaion: when =4, he rior window rovides he ie slo size [1,3]) and ener he las he ollision bu no rovides ie slo window [31, 6] aording o -exenenial bak-off anner. Suose he onfli erinals nuber N=6,and he ollision resoluion roess of he iniial window (=) and he end window (=4, naely [7,1]) show in figure 5. The resul indiaed ha he 6 onfli erinals ener he las ollision resoluion when =, and he algorih also only arried on wo ollision resoluion, ore, only 1 ie slos (14 ie slos were used in rior iroved algorih) are used, he ollision resoluion has no enered he las 6 onfli resoluion eriods. The reques inforaion of onfli erinals a, b,, d, e and f will be suessfully ransied afer waiing 6, 1, 9,, 8 and 4 slos reseively.

4 1 IJCSNS Inernaional Journal of Couer Siene and Nework Seuriy, VOL. 6 No.11, Noveber 6 b d e f a = slo e w= slo Resoluions sueed over a, b, d and f and ener he las resoluion. Resoluions sueed over all erinals; w reresens window size Figure 5 Collision Resoluion roess over 6 onfli erinals(se iniial and end window) Fig. 5 Collision Resoluion Proess over 6 Confli Terinals(Se Iniial and End Windows) Table 3 Siulaion Resuls of Basi and Iroved Algorihs (Uni:ie slo) N Basi algorih Iniial window Iniial and end window algorih Basi algorih Iniial window Iniial and end window algo- algorihs N algorih rih Maxslo Maxslo Maxslo Maxslo Maxslo Maxslo Resuls Analysis 1 siulaions are arried ou on he ouer. Le N denoe he nuber of onfli erinals and Maxslo reresen he average axiu slos value needed in he 1 siulaions of he N onfli erinals. The forula is given by: Maxslos = ( 1 i= 1 j= 1 j ) /1 Where is he ax bak-off exonenial in a erain suessful ollision resoluion, and he siulaion resuls of he hree algorihs are shown in Table 3, and oun is he resoluion ies of a suessful onfli resoluion. Under differen arrival rae (),he hroughu (S) an S Fig. 6 Throughu Curves of Binary Exonenial Bak-off Algorih be desribed as [8] Iniial and end (o) Iniial (iddle) Basi(low) S = + e N k k! k= 1 E( L ) Where N is he nuber of onfli erinals, and E (L k ) is he average nuber of slos. Figure 5 shows he hroughu erforane urves of he hree algorihs. (1) The siulaion resuls indiae ha under he eried ax reea ies, he ax nuber of onfli erinals ha he basi algorih an resolve is abou 5, he seing iniial window algorih is abou 37 and he seing iniial and end window algorih is abou 44. Thus grealy iroves he onfli resoluion effiieny. () A onlusion an be ade fro able 3 ha if he onfli erinal nuber is sae, he wo iroved algorihs redue he ollision resoluion ies and save he slo sae oared o he basi algorih. (3) A onlusion an be ade fro able 3 ha he average needed slos inreases linearly wih he growing of he nuber of onfli erinals; Fro figure 5, we onlude ha he syse hroughu is in he rend o be sable wih he load () grows (he sable hroughu value of he basi algorih, iniial window algorih and iniial and end window algorih ends o be aroxiaely.18,.1 and.3 reseively). This indiaes ha he binary exonenial bak-off onfli resoluion algorih is sable and valid. (4) Fro he hroughu forula, we an see ha he ax hroughu of he iniial and end window algorih is Sax=.3944 (=1.6), he ax hroughu of he iniial window algorih is Sax=.3941 (=1.), and he ax hroughu of he basi algorih is Sax=.393 (=.9). A onlusion an be ade fro figure 5 ha he erforane of he wo iroved algorihs is beer han he basi algorih. The i- k

5 IJCSNS Inernaional Journal of Couer Siene and Nework Seuriy, VOL. 6 No.11, Noveber 6 11 roved algorihs have higher syse hroughu and an ake he syse work under higher hroughu. (5) The iroved binary exonenial bak-off ollision resoluion algorihs roosed in he aer are helful o enhane he erforane of all kinds of binary exonenial bak-off algorihs. Referenes [1] Shen Lansun, Tian Dong. The Develoen of Wireless Video Transission Tehnology [J]. Eleroni Tehnology Aliaion, 1, (1): 6-9. [] ROM R. SIDI M. Mulile aess roools [J]. New York Berlin Heidelberg, 1989, (6): 5-3. [3] Vanik V. Tree-Based uli-aess roools where ollision uliliiies are known [J]. IEEE Trans Coun, 1985, (33): 999. [4] N. Abrason. The ALOHA syse-anoher alernaive for ouer ouniaions [J]. Pro 197 Fall Join Couer onf, 197, (37): [5] L.. Robers, ALOHA ake syse wih and wih and wihou slos and aure [J], ACM SICOMM Coue. Coon. Rev., 1975, (5): 8-4. [6] Dolor, Sala. Conunion resoluion algorih he Chaer 6 of he Ph.D[J]. eorgia Insiue of Tehnology, 1998, (3): [7] Xu Tian, Ye Jiajun. Collision Resoluion Algorih Aliable o HFC Nework [J]. Television Tehnology,, (1): 18-. [8] J. L. Massey. Collision-Resoluion Algorihs in and Rando- Aess Couniaions [J]. Muli-User Couniaions CISM Course and Leure Series, 1981, (65): Yongfa Ling, reeived he B.S. and M.S. degree fro Yunnan Minzu Universiy. Now he is he Posdooral sudens in Xi an Jiaoong Universiy. His sienifi ineress are in he fields of nework algorih and nework onrol. Deyu Meng, reeived he B.E. degree in Inforaion Siene in 1 and M.E. degree in alied aheais in 4 fro he Xi'an Jiaoong Universiy. He is urrenly a dooral suden a Shool of Eleroni and Inforaion Engineering in Xi'an Jiaoong Universiy. His sienifi ineress are in he fields of ahine learning and daa ining.