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2 Cmputer Cmmuicatis 33 (21) Ctets lists available at ScieceDirect Cmputer Cmmuicatis jural hmepage: wwwelseviercm/lcate/cmcm Badwidth allcati with a particle swarm meta-heuristic fr etheret passive ptical etwrks U Gi J a, Alice E Smith b, * a Departmet f Idustrial ad Maagemet Egieerig, Su M Uiversity, Asa, Chugam , Republic f Krea b Departmet f Idustrial ad Systems Egieerig, Aubur Uiversity, Aubur, AL , USA article if abstract Article histry: Received 25 July 27 Received i revised frm 23 Octber 29 Accepted 27 Octber 29 Available lie 1 vember 29 Keywrds: Etheret Passive Optical etwrk Badwidth allcati Thrughput Weighted fairess Particle Swarm Optimizati (PSO) This paper csiders the badwidth allcati prblem fr a Etheret Passive Optical etwrk (EPO) A EPO is e f the best ptis fr high-speed access etwrks This paper frmulates the ptimal badwidth allcati prblem with a aalytical mdel t maximize thrughput ad weighted fairess simultaeusly First, the ptimal sluti uder certai cditis is characterized The, tw heuristic algrithms are devised which ptimize the allcati prblem uder geeral cditis Oe heuristic is a straightfrward cstructive e while the e use the Particle Swarm Optimizati (PSO) meta-heuristic, the first kw applicati f PSO t the EPO badwidth allcati prblem The heuristics are tested ad cmpared with previusly published results The cmputatial experiece shws that ur algrithms are bth effective ad efficiet i allcatig badwidth a EPO Ó 29 Elsevier BV All rights reserved 1 Itrducti This paper csiders the badwidth allcati prblem a Etheret Passive Optical etwrk (EPO), where there is e cmm fiber cectig several access pits which share the badwidth f the fiber T prvide service, tw types f passive cmpets are used Oe is the Optical Lie Termial (OLT) ad the ther is the Optical etwrk Uit (OU) The OLT prvides cecti betwee the backbe ad access etwrks at a cetral ffice, ad the OLT allcates the cmm badwidth accrdig t requested demads frm the cected access pits The requests fr badwidth ccur frm OUs lcated the access side f the etwrk The OU has buffer memry fr icmig traffic frm custmers ad fr utgig traffic t the OLT, ad csiders the trasmissi pririty f the packets waitig i the buffers T trasmit the traffic frm OLT t OU, OLT bradcasts the traffic ad the each OU receives the packets Hwever, chaels must be classified fr trasmissi f the packets frm OUs t a OLT sice there are may OUs ad there are cflicts whe OUs try t trasmit packets simultaeusly EPO uses the Time Divisi Multiple Access (TDMA) methd t reslve cflicts The badwidth allcati prblem is t fid a mechaism fr sharig the cmm badwidth withut cflict * Crrespdig authr Tel: addresses: ugj@sumackr (UG J), smithae@auburedu (AE Smith) May studies have bee published hw t allcate the cmm badwidth t the OUs Fr example, Kramer et al [1] ad Bai et al [2] develped badwidth allcati algrithms f iterleaved pllig with adaptive cycle time (IPACT), ad Kramer et al [3] develped a tw-stage buffer mechaism t reduce the light-pealty prblem f IPACT Assi et al [4] suggested a Ehaced Dyamic Badwidth Allcati (EDBA) algrithm A et al [5] develped a Hybrid Slt-Size/Rate (HSSR) algrithm, ad Yag et al [6] preseted a burst pllig algrithm fr badwidth allcati A gd survey these methds is give by Zheg ad Muftah [7] These papers all address fidig gd heuristic slutis with respect t sme specific measure such as thrughput, fairess r delay time Fr example, Bai et al [2] develped a weighted-based badwidth algrithm (W-DBA) t imprve fairess, delay time ad lik utilizati W-DBA assigs the excess badwidth t each OU prprtially t each relative weight The authrs shwed that W-DBA is superir t ather published algrithm (M-DBA) fr radmly geerated asymmetric traffic Our paper frmulates the allcati prblem as a liear mathematical e ad develps badwidth allcati algrithms which maximize thrughput ad weighted fairess simultaeusly Characterizig the ptimal allcati uder certai cditis is e gal f this paper The ther gal is t develp a effective ptimizer t the prblem uder geeral cditis This paper is structured as fllws: Secti 2 describes ad frmulates the badwidth allcati prblem The badwidth allcati prblem is characterized, ad tw heuristic algrithms are develped i /$ - see frt matter Ó 29 Elsevier BV All rights reserved di:1116/jcmcm29119

3 UG J, AE Smith / Cmputer Cmmuicatis 33 (21) Secti 3 These algrithms guaratee a ptimal sluti uder a specific cditi derived i Secti 3 Secti 4 carries ut a umber f umerical tests t evaluate the prpsed algrithms by csiderig thrughput, fairess, ad cmputati time Fially, Secti 5 ctais ccludig remarks 2 Prblem descripti This secti defies the badwidth allcati prblem i detail Let us defie sme tati fr the frmulati : umber f custmers (OUs) r i : demad f OU i measured i bits per secd, i ¼ 1; 2; ; w i : weight f OU i fr the fairess metric C: capacity f fiber (bits per secd) X i : prprti f allcated badwidth t demad f custmer i, 6 X i 6 1 fr all i Accrdig t the Multi-Pit Ctrl Prtcl (MPCP) f EPO [8], the OLT allcates badwidth ad determies time f trasmissi t OUs accrdig t their requests fr i g The allcati is perfrmed peridically durig each cycle time, ad each OU trasmits the packets waitig i its buffer frward t the OLT as a predetermied amut ad time f trasmissi alg the cmm lik T trasmit packets, setup is required betwee each trasmissi fr laser /ff ad guardig ifrmati, but this is idepedet f the OU type ad size f trasmissi ad ca be igred The time durati t trasmit a uit packet als depeds the distace betwee the OLT ad the OU Hwever, we ca set the uit time t 1 fr all OUs fr simplicity withut lss f geerality Due t the capacity restricti C the cmm lik, ly sme waitig packets i each buffer will be serviced at the curret cycle The remaiig will be serviced durig succeedig cycles Each OU has e chace t trasmit its packets at each cycle Therefre, we ca mdel the prblem by csiderig just e cycle There are several classes f service (CS) packets i a OU Each OU i has a weight w i t represet its CS accrdig t the Service Level Agreemet (SLA) EPO is required t utilize its capacity as much as pssible ad t prvide fair service Our paper csiders the badwidth allcati prblem t maximize utilizati (thrughput) ad weighted fairess simultaeusly The badwidth allcati prblem is frmulated as fllwig:!,! 2," # max X X r i X i X i w i X ðx i =w i Þ 2 ð1þ s:t: X r i X i 6 C 6 X i 6 1; i ¼ 1; 2; ; ð3þ Our aim is t fid the ptimal fx i g which maximizes the bjective fucti value f Eq (1) subject t Eqs (2) ad (3) The first term f Eq (1) represets thrughput, ad the remaiig terms represet fairess, where the fairess is a weighted variat f Jai s equalweight versi [9] T maximize thrughput, P r ix i, we eed t icrease the value f X i as much as pssible If we set the value f X i =w i as evely as pssible, the the fairess term P i X w i 2 h P ðx i=w i Þ 2 ð2þ i becmes clse t its maximum value f 1 Eq (2) implies that the ttal amut f assiged badwidth cat be larger tha the capacity C The decisi variable X i represets the prprti f demad allcated by OLT We ca btai the allcated badwidth r i X i fr OU i by slvig the badwidth allcati prblem 3 Badwidth allcati algrithms This secti frmulates the ptimal allcati t maximize thrughput ad fairess We first csider the prblem characterizati uder certai situatis 31 Prblem characterizati First, as a special case, if all weights f OUs are idetical, the ptimal allcati is determied as defied i Prpsiti 1 Prpsiti 1 If w i ¼ w fr all i, the ptimal allcati is X i ¼ mi C P r i; 1 fr all i ad its ptimal bjective value is mi P r i; C Prf If w i ¼ w fr all i, thrughput is maximized whe X i ¼ 1 fr all i ad fairess is maximized whe X i ¼ X fr all i, where X detesa cstat We ca easily shw the ptimal value f X is mi C P r i; 1 ad its bjective value is mi P r i; C This cmpletes the prf h If the weights f all OUs are idetical, we ca easily btai the ptimal sluti such that the bjective value is C whe X i ¼ C P r i fr all i if P r i P C, ad is P r i whe X i ¼ 1 fr all i therwise Hwever, if the weights are t idetical, it is t straightfrward t fid the ptimal sluti Fr the remaider f the paper, we will csider ly the geeral weight prblem Fr the geeral prblem, let Y ¼ mi C P w ir i ; P r P i w ir i be the ttal amut f required badwidth divided by the ttal weighted amut f required badwidth, where Y is determied by the requested badwidth fr i g The relatiship amg Y ; P r i ad C is derived as fllws Lemma 1 If Y 6 mi 16i6 f1=w i g, the P r i P C h Prf It is ticed that Y P ½mi 16i6 f1=w i gš mi C P i r i; 1 Therefre, if Y 6 mi 16i6 f1=w i g, the C P r i 6 1 This cmpletes the prf h P Accrdig t Lemma 1, it is true that if r i < C the Y > mi 16i6 f1=w i g Hwever, the iverse f Lemma 1 is t true Fr example, csider a EPO system with lik capacity f C Suppse that there are tw OUs with demad f ðr 1 ; r 2 Þ¼ð1; 6Þ Assume that their weights are ðw 1 ; w 2 Þ¼ð1; 2Þ The, Y ¼ C=22 > mi 16i6 f1=w i g¼:5 ad P r i ¼ 16 P C if the capacity C has a value f 11 6 C 6 16 Therefre, we use the relatiship Y 6 mi 16i6 f1=w i g istead f P r i P C fr frmulatis f the ptimal sluti Prpsiti 2 If Y 6 mi 16i6 f1=w i g, the ptimal allcati is btaied as X i ¼ w i Y ad has the ptimal bjective value f C Prf By Lemma 1, if Y 6 mi 16i6 f1=w i g the P r i P C Therefre, the thrughput term f Eq (1) has maximal value C at P X i r ix i ¼ C ad the remaiig terms f Eq (1) have the maximal value f 1 whe X i =w i ¼ Y 1 fr all i, where Y 1 is a cstat Fr the sluti f P r ix i ¼ C, let us substitute w i Y 1 fr X i ad simplify the equati; the we btai the result f Y 1 ¼ C P w ir i which equals Y by Lemma 1 The sluti fx i g als satisfies Eq (3) sice Y 6 mi 16i6 f1=w i g Fr the sluti f X i ¼ w i Y, the bjective value becmes C sice P r i P C by Lemma 1 This cmpletes the prf h

4 528 UG J, AE Smith / Cmputer Cmmuicatis 33 (21) OLT X1=2/61 X2=4/61 X3=6/61 Fr example, csider a EPO system with C ¼ 2 (Fig 1) Suppse that there are three OUs with demad f ðr 1 ; r 2 ; r 3 Þ¼ð1; 6; 16Þ at the begiig f a cycle Assume that their weights are ðw 1 ; w 2 ; w 3 Þ¼ð1; 2; 3Þ The, Y ¼ mi C P w ir i ; P r P i w i r i g¼mif2=61;23=61g¼ 2= 61 < mi 16i6 f1=w i g¼1=3 ad thus P r i ¼ 23 > C ¼ 2 Therefre, the ptimal allcati is btaied as X 1 ¼ w 1 Y ¼ 2=61; X 2 ¼ w 1 Y ¼ sð2þð2=61þ¼4=61, ad X 3 ¼ 6=61 by Prpsiti 2 Hwever, if Y > mi 16i6 f1=w i g, a glbal search mechaism is required t slve the prblem Fr example, csider a EPO system with C = 2 Suppse that there are three OUs with demad f ðr 1 ; r 2 ; r 3 Þ¼ð1; 6; 8Þ s that P r i ¼ 24 > C Assume that their weights are ðw 1 ; w 2 ; w 3 Þ¼ð1; 2; 3Þ The, Y ¼ mi C P w ir i ; P r P i w ir i ¼ mif2=46; 24=46g ¼ 2=46 > mi 16i6 f1=w i g¼1=3 I this case, the result f Prpsiti 2 such that X 3 ¼ 6=46 des t guaratee feasibility 32 Sluti algrithms C= Eq (1) is t ccave with respect t decisi variable X i Therefre, we eed a apprach which ca accmmdate this This secti develps tw heuristic algrithms First, we develp a heuristic algrithm based up the frmulati f the ptimal sluti Csiderig each bjective idividually, there are tw feasible slutis with maximum thrughput r maximum fairess, deted as S1 ad S2: Sluti S1: X i ¼ w i mi Y ; mif1=w i g ð4þ 16i6 (, ) X Sluti S2: X i ¼ mi C r i ; 1 fr all i OU 1 OU 3 OU 2 (w1=1) r1=1 (w2=2) r2=6 (w3=3) r3=16 traffic flw directi Fig 1 Example EPO system Sice slutis S1 ad S2 are feasible as shw by Prpsiti 3, the better e is a lwer bud t ur prblem We w devise a heuristic algrithm called H1 Heuristic algrithm H1: Select the sluti with the higher bjective value betwee S1 ad S2 Prpsiti 3 Algrithm H1 guaratees a ptimal sluti fr the badwidth allcati prblem satisfyig the relatiship f Y 6 mi 16i6 f1=w i g Prf T shw the feasibility f S1, we ca classify the prblem it tw classes f Y 6 mi 16i6 f1=w i g ad Y > mi 16i6 f1=w i g First, if Y 6 mi 16i6 f1=w i g, S1 has the value f X i ¼ w i Y The sluti X i satisfies 6 X i 6 1 fr all i ad P r ix i 6 C sice Y ¼ mi C P w ir i ; P r P i w ir i by defiiti Secd, if Y > mi 16i6 f1=w i g, the the resultig sluti f S1 becmes ð5þ X i ¼ w i ðmi 16i6 f1=w i gþ which satisfies the relatiship f 6 X i 6 1 fr all i, ad P r ix i ¼ mi 16i6 f1=w i g P w ir i < Y P w ir i ¼ mi C; P r i 6 C Similarly, we ca shw the feasibility f S2 by classifyig the prblem it tw cases f C P r i 6 1 ad C P r i > 1 If C P r i 6 1, the sluti becmes X i ¼ C P r i fr all i which has the relatiship f 6 X i 6 1 fr all i, ad P r ix i ¼ C Otherwise, X i ¼ 1 fr all i, ad the sluti leads t the relatiship f P r ix i ¼ P r i 6 C by the precditi f this case T csider ptimality, te that H1 always selects S1 as its sluti sice sluti S1 has the bjective value f mi P r i; C whe Y 6 mi 16i6 f1=w i gify 6 mi 16i6 f1=w i g, the sluti S1 f X i ¼ w i Y is the ptimal sluti by Prpsiti 2 This cmpletes the prf h Hwever, as a example fr H1, csider tw OUs with ðr 1 ; r 2 Þ¼ð1; 6Þ ad ðw 1 ; w 2 Þ¼ð1; 2Þ a lik with capacity C=15 The, Y ¼ mif15=22; 16=22g > mi 16i6 f1=w i g¼ :5, ad sluti S1 is X i ¼ w i ðmi fy ; mi 16i6 f1=w i ggþ; ðx 1 ; X 2 Þ¼ð:5; 1Þ with its bjective fucti value 11, ad sluti S2 is X i ¼ mi C P r i; 1 ¼ 15=16 fr all i ad has bjective value f 1395 Therefre, the sluti f H1 is S2, which has the larger bjective fucti value But we cat guaratee ptimality f sluti S2 sice the prblem des t satisfy the cditi Y 6 mi 16i6 f1=w i g f Prpsiti 3, ad there are ther better slutis such as ðx 1 ; X 2 Þ¼ð:9; 1Þ which has the bjective fucti value f T address the shrtcmigs f H1, we develp ather heuristic algrithm usig slutis S1 ad S2 This paper uses Particle Swarm Optimizati (PSO) fr the secd heuristic algrithm sice PSO is a effective ad cmputatially speedy glbal ptimizati techique fr multi-mdal ptimizati prblems i the real umber dmai [1,11] The PSO is a glbal ptimizati heuristic ispired by ature, i this case by bird flckig ad fishig schlig The uique aspect f this heuristic is that it balaces idividual (particle) kwledge with grup (swarm) kwledge The PSO use a ppulati called a swarm which is cmpsed f multiple particles The PSO cducts search by mvig the particles accrdig t a velcity vectr which establishes the search gradiet fr each particle This vectr is set by idividual kwledge (where the particle s best lcati has bee) ad grup kwledge (where the swarm s best lcati has bee) usig the cgiti ad scial cefficiets, respectively The best sluti fud by the swarm at the ed f the search iteratis is retured as the ptimal sluti This paper uses M particles X 1 ; X 2 ; ; X j ; ; X M, where each particle X j is cmpsed f variables X j ¼ X j 1 ; Xj 2 ; ; Xj; ; i Xj ; j ¼ 1; 2; ; M Fr ur prblem, X j i detes the allcated prprti f badwidth fr the jth particle f OU i Heuristic algrithm H2 Step 1 Set iitial values f the parameters icludig particle swarm size, iertia weight (w), cgiti ad scial weights ðc1; C2Þ, ad maximum iteratis ði max Þ f the PSO Read the prblem data f the badwidth requiremet r i ad weight w i fr each OU i; i ¼ 1; 2; ; Radmly geerate M particles fx j g as a iitial ppulati, j ¼ 1; 2; ; M where each particle j has terms Let k ¼ 1 Step 2 Fr each particle j, calculate its fitess F j usig Eq (7) ad fid the persal best particle fr each, pbest j i ; i ¼ 1; 2; ; ; j ¼ 1; 2; ; M, that is, the best

5 UG J, AE Smith / Cmputer Cmmuicatis 33 (21) sluti that a give particle has idetified ver the search Fr the first iterati, the persal best is the iitial sluti f particle j Step 3 Fid glbal best particle, gbest i ; i ¼ 1; 2; ; ver all M persal best particles Step 4 Update the allcated prprti X j i f each particle such that X j ¼ i Xj þ V j ; i i i ¼ 1; 2; ; ; j ¼ 1; 2; ; M where V j ¼ w V j þ i i C1ðR1Þ pbestj i Xj i þ C2ðR2Þ gbest i X j i fr give parameters w; C1 ad C2, ad radm umbers R1 ad R2 geerated frm the uifrm distributi dmai [,1] Let the velcity V j i have V mi 6 V j 6 V i max by settig V j ¼ V i mi if V j < V i mi, ad V j ¼ V i max if V j > V i max Additially, let X j ¼ X i mi if X j < X i mi, ad X j ¼ X i max if X j > X i max Step 5 Repeat Steps 2 4 by lettig k ¼ k þ 1 util k > I max Step 6 Fid the best feasible sluti (satisfyig Eqs (2) ad (3)) If the sluti f Step 3 is feasible, the select it as the best sluti Otherwise, take the last gbest i which is feasible Fr Step 1, this paper uses the values i Table 1 fr the parameters Dg et al [12] recmmeded usig 2 4 particles fr cmpsiti a swarm Our test results shw that the value f Eq (1) is ly slightly affected by the swarm size s we use 2 particles t reduce cmputatial time We select slutis S1 ad S2 f Eqs (4) ad (5) as tw particles f the iitial swarm (termed seedig the swarm) Sice algrithm H2 uses S1 ad S2 as particles, H2 als guaratees a ptimal allcati whe Y 6 mi 16i6 f1=w i g by Prpsiti 3 This paper uses C1=C2 = 2 fr Step 4 The iertia weight w is kw t have a rle i the perfrmace f PSO Elbeltagi et al [1] used a liear decreasig fucti the dmai f [4,12] which we use als: w ¼ W max ðw max W mi ÞðITERÞ=I max Table 1 Parameters fr the cmputatial experimets Parameter Value umber f particles (M) 2 (icludig S1 ad S2) C1, C2 2 Iertia weight (w) W max ðw max W mi ÞðITERÞ=I max W mi ; W max W mi ¼ :4; W max ¼ 1:2 umber f iteratis ði maxþ 5 V mi ; V max V mi ¼ 1; V max ¼ 1 X mi ; X max X mi ¼ ; X max ¼ 1 umber f OUs () 16, 32, 64 Lik capacity (C) 1 Mbps Badwidth requiremet f each (mea, 19 2 ) OU ðr i Þ Offered lad 1 1% (symmetric lad) i icremets f 1% 6 1% (asymmetric lad) i icremets f 5% Weight f each OU ðw i Þ U [1,6] umber f prblems 2 ð6þ where W max ¼ 1:2; W mi ¼ :4, ad ITER represets the umber f iteratis perfrmed The maximum umber f iteratis deted as I max is 5 accrdig t the result f [12] althugh ur results shw that the value f I max has ly a slight effect Eq (1) Sme slutis f Step 1 may t be feasible We remedy this by the fllwig three steps First, we let X j i ¼ X mi if X j i < X mi ad X j i ¼ X max if X j i > X max at Step 4, where X mi ¼ ad X max ¼ 1 sice the decisi variables fx i g must satisfy Eq (3) Secd, we let V j i ¼ V mi if V j i < V mi, ad V j i ¼ V max if V j i > V max at Step 4, where we set V mi ¼ 1 ad V max ¼ 1 Third, we let the fitess fucti F j f Step 2 have a pealty term fr ifeasible slutis as fllws:!! 2," # F j ¼ X X r i X j i X j i,w i X 2 X j =w i i ( ) max ; X r i X j C i ð7þ Yiqig et al [13] ted that the perfrmace f a pealty fucti methd was satisfactry whe a ptimizati prblem is t highly cstraied, which is true here Hwever, eve thugh these steps are used t fid a feasible sluti, the resultat slutis may t be feasible S, Step 6 is added t select a best feasible sluti as the fial PSO sluti The verall prcedure f H2 is give i Fig 2 4 Cmputatial experiece Start Read C,, r i, w i, i=1,2,, Calculate S1 ad S2 usig Eq(4) ad Eq(5) Calculate S1 ad S2 usig Eq(1) ad use the larger as the sluti f H1 Read w, C1, C2, M, I max Geerate radm M-2 particles ad add S1 ad S2 t make M iitial particles Set k=1 Calculate fitess usig Eq(7) ad fid pbest j ad gbest, j=1,2,, M Update particles usig Step 4 f H2 ad set k= k+1 k>i max Yes Select gbest as the sluti f H2 Stp Fig 2 Flwchart f H2 Fr the evaluati f H1 ad H2, we csider a EPO system with 32 OUs usig a cmm fiber f 1 Mbps speed as described i the lwer part f Table 1 This prblem is take frm Bai et al [2] T csider differet umbers f OUs, we the develped prblems with = 16 ad 64 We assume that the icmig traffic the EPO system is cmpsed f 2% f Expedited Frwardig (EF), 4% f Assured Frwardig (AF), ad 4% f Best Effrt (BE) traffic, where the size f the EF traffic is 7 bytes, ad each size f the AF ad BE traffic is uifrm bytes [2] If we suppse that the size f a packet is distributed accrdig t a uifrm distributi ad there are may packets, we ca use the rmal distributi with a stadard deviati 19 Mbps as a apprximate distributi f iput traffic We csider bth symmetric ad asymmetric traffic Symmetric traffic csists f geeratig balaced traffic i each OU fr a ffered lad f 1 1% Asymmetric traffic is balaced except fr e OU, where that OU makes a ffered lad f 6 1% ad the ther -1 OUs maitai traffic f 6% lad Each OU has its class f service accrdig t a SLA This paper csiders six classes f service [14] The classes are radmly geerated frm a discrete uifrm (DU) distributi the dmai f [1,6] Fr each cmbiati f parameters, we devised 2 radmly geerated prblems havig Y > mi 16i6 f1=w i g ad slved them with H1, H2 ad the methd f Bai et al [2] usig cde i Micrsft vi-

6 53 UG J, AE Smith / Cmputer Cmmuicatis 33 (21) sual studi C++ a PC (Itel Petium 14 GHz) Bai et al [2] csidered ly asymmetric traffic with their algrithm W-DBA ad use a weight w i fr each OU isice W-DBA is a superir perfrmig methd, we use it fr cmputatial cmparis We select mea deviati as the perfrmace measure where mea deviati is the prprti f imprvemet i the bjective fucti value equati (1) ver the H1 sluti Sice H2 tries t imprve the result f H1, a larger mea deviati implies a mre imprved sluti Hwever, the mea deviati will be zer if the prblem istace beig csidered satisfies the relatiship Y 6 mi 16i6 f1=w i g sice bth H1 ad H2 guaratee a ptimal sluti i this case The test results are give i Figs 3 6, where Figs 3 ad 4 shw the mea deviati f H2 ad W-DBA frm H1 The figures shw the deviati the y-axis ad the percet ffered lad the x- axis Fig 4 shws that the mea deviati f H2 des t decrease with the ffered lad ad H2 imprves the result f H1 up t abut 4% Fr asymmetric traffic, the imprvemet becmes larger as the ffered lad icreases Therefre, the PSO f H2 is effective i allcatig badwidth ad imprves up the sigle bjective H1 Whe we csider the results frm [2], H1 is much better tha that f Bai et al s W-DBA fr all data sets except fr symmetric traffic with 1% ffered lad (3125 Mbps) This ca be verified i Figs 5 ad 6, where we calculated the thrughput ad fairess value part f Eq (1) fr varyig percetages f maximum ffered lad Each pit i Figs 5 ad 6 display a pair f fairess ad thrughput values fr a give ffered lad The pit fr each ptimizati methd clsest t the x-axis (that is, the smallest y value) is fr the lwest ffered lad Sice ur bjective is t maximize bth fairess ad thrughput, the ideal pit f these graphs lies at the upper right crer (maximum fairess ad maximum thrughput) Fr asymmetric traffic, H2 dmiates W-DBA Fr symmetric traffic, this is true except fr the maximum ffered lad W-DBA tries t imprve fairess by assigig the excess badwidth t verladed OUs as fairly as pssible, thus the algrithm des well asymmetric traffic with a small umber f extrardiary (verladed) OUs Hwever, ur heuristics assig badwidth fairly fr all OUs icludig uder laded es Furthermre, fr symmetric traffic W-DBA leads t mre verladed OUs because W-DBA ca assig badwidth t a OU exceedig its requiremet while ur heuristics d t assig mre badwidth tha a OU requires Thus, the fairess f W-DBA decreases as the ffered lad icreases sice the umber f verladed OUs icreases Hwever, after a pit, the fairess icreases agai with lad because the amut f excess badwidth is much smaller The iflexi pit at 5% (15625 Mbps) ffered lad i Figs 4 ad 6 shws the pheme f W-DBA fr symmetric traffic (which was t studied i the rigial paper [2]) As expected i bth graphs, H2 has less fairess tha H1 (which maximizes fairess) hwever, H2 s thrughput is higher mea deviati (%) ffered lad (%) Fig 4 Mea deviati fr symmetric traffic H2 W-DBA Fig 5 Mea thrughput ad fairess fr asymmetric traffic at differet ffered lad amuts where the pit clsest t the x-axis fr each series is the lwest ffered lad 2 mea deviati (%) H2 W-DBA ffered lad (%) Fig 3 Mea deviati fr asymmetric traffic Fig 6 Mea thrughput ad fairess fr symmetric traffic at differet ffered lad amuts where the pit clsest t the x-axis fr each series is the lwest ffered lad We ext csidered the effect f umber f OU s Figs 7 ad 8 shw the perfrmace f H2 relative t H1 accrdig t the umber f OUs, = 16,32,64 I all cases H2 imprved ver H1 ad the imprvemets were especially sigificat as the ffered lad icreased fr asymmetric traffic Fr cmputatial effrt, it is difficult t make a defiitive assessmet Certaily, H2, a iterative meta-heuristic, takes mre CPU time tha either H1 r the W-DBA algrithm H2 raged frm 119 CPU secds t 126 CPU secds fr each prblem with

7 UG J, AE Smith / Cmputer Cmmuicatis 33 (21) Mea relative deviati (%) = 32 a Itel Petium 14 GHz PC S, H2 is very fast ad wuld be viable i the ear real time wrld f EPO badwidth allcati 5 Cclusis =16 =32 = Offered lad (%) Fig 7 Mea relative deviati f H2 cmpared with H1 asymmetric traffic where the pit clsest t the x-axis fr each series is the lwest ffered lad Mea relative deviati (%) Offered lad (%) =16 =32 =64 Fig 8 Mea relative deviati f H2 cmpared with H1 symmetric traffic where the pit clsest t the x-axis fr each series is the lwest ffered lad This paper csiders a EPO system which uses a fiber fr each directi f traffic A efficiet badwidth allcati methd is required t use the cmm fiber This paper frmulates the badwidth allcati prblem t maximize thrughput ad weighted fairess simultaeusly The ptimal allcati is characterized, ad tw heuristic algrithms are desiged based up the characterizati The first algrithm is a very fast heuristic e, which is ptimal uder certai restricted cditis, ad the secd e is a PSO meta-heuristic This is the first kw applicati f PSO t the EPO badwidth allcati prblem We test bth heuristics ad cmpare t recet results frm the literature The results shw that the heuristic algrithms perfrm well ver a rage f prblem istaces ad types (symmetric versus asymmetric ad differet lad values ad varyig umbers f OU s) The PSO early dmiates a stadard methd frm the literature (W-DBA frm [2]) Eve thugh this paper csiders the multiplicative bjective fucti frm f thrughput ad fairess, ther frms such as thrughput plus fairess culd be als slved with ur algrithms by mdifyig Eq (7) f the PSO As ather aveue f research, fr a give amut f allcated badwidth t each OU, the sequecig rule f Weighted Shrtest Prcessig Time (WSPT) culd be used t reduce delay time But, badwidth allcati ad schedulig f packets eed t be csidered simultaeusly, which is cmplicated Refereces [1] G Kramer, BG Mukherjee, G Pesavet, IPACT: a dyamic prtcl fr a Etheret PO (E-PO), IEEE Cmmuicatis Magazie (22) 74 8 [2] X Bai, A Shami, C Assi, O the fairess f dyamic badwidth allcati schemes i Etheret passive ptical etwrks, Cmputer Cmmuicatis 29 (26) [3] G Kramer, B Mukherjee, S Dixit, Y Ye, R Hirth, Supprtig differetiated classes f service i Etheret passive ptical etwrks, Jural f Optical etwrkig 1 (22) [4] CM Assi, Y Ye, S Dixit, MA Ali, Dyamic badwidth allcati fr quality-fservice ver Etheret POs, IEEE Jural Selected Areas i Cmmuicatis 21 (23) [5] F-T A, H Bae, Y-L Hsueh, KS Kim, MS Rgge, LG Kazvsky, A ew media access ctrl prtcl guarateeig fairess amg users i Etheret-based passive ptical etwrks, IEEE Optical Fiber Cmmuicatis 11 (23) [6] Y-M Yag, J-M h, P Mahalik, K Kim, B-H Ah, A traffic-class burstpllig based delta DBA scheme fr QS i distributed EPOs, Cmputer Stadards & Iterfaces 28 (26) [7] J Zheg, HT Muftah, Media access ctrl fr Etheret passive ptical etwrks: a verview, IEEE Cmmuicatis Magazie (25) [8] G Kramer, Etheret Passive Optical etwrks, McGraw-Hill, ew Yrk, 25 [9] R Jai, A Durresi, G Babic, Thrughput fairess idex: a explaati, i: ATM Frum, 1999 Available frm: <http//wwwcsehi-stateedu/~jai/atmf/a99-45html> [1] E Elbeltagi, T Hegazy, D Griers, Cmparis amg five evlutiary-based ptimizati algrithms, Advaced Egieerig Ifrmatics 19 (25) [11] F va de Bergh, AP Egelbrecht, A study f particle swarm ptimizati particle trajectries, Ifrmati Sciece 17 (26) [12] Y Dg, J Tag, B Xu, D Wag, A applicati f swarm ptimizati t liear prgrammig, Cmputers ad Mathematics with Applicatis 49 (25) [13] L Yiqig, Y Xigag, L Ygjia, A Imprved PSO Algrithm fr Slvig cvex LP/MILP Prblems with Equality Cstraits, Cmputers ad Chemical Egieerig, 26 Available frm: < [14] ITU-T Y1541, etwrk Perfrmace Objectives fr IP-based Services, Iteratial Telecmmuicatis Ui, 22