Fuzzy Retrial Queues with Priority using DSW Algorithm
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- Patrick Nelson Carson
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1 ISSN e: Volume 6 Iue 9 Septeme 6 Intentonl Jounl of omputtonl Engneeng Reeh IJER Fuzzy Retl Queue wth Poty ung DSW lgothm S Shnmugunm Venkteh Deptment Of MthemtGovenment t ollege Slem-7 In Deptment Of MthemtSon ollege Of Tehnology Slem- In STRT In th ppe we tuy the poty queueng moel une fuzzy envonmentit optmze fuzzy poty queueng moel peemptve poty non-peemptve poty n whh vl te eve teetl te e fuzzy numeppomte metho of Etenon nmely DSW Dong Shh n Wong lgothm ue to efne memehp funton of the pefomne meue of poty queung ytem DSW lgothm e on the ut epeentton of fuzzy et n tn ntevl nly Numel emple lo llutte to hek the vlty of the moel Keywo: Fuzzy et theoy Retl queuepoty plne DSW lgothm Mthemt Sujet lton: 6K E7 I INTRODUTION Queueng theoy nh of pple polty theoy queue wtng lne of utome whh emn eve fom eve tton n t fome when eve not pove mmetely Queueng theoy w ntoue y K Elng The mn pupoe of the nly of queueng ytem to unetn the ehvo of the unelyng poee o tht nfome n ntellgent eon n e me n the ognzton Mot of the queueng moel wee tue wth queueng plne " Ft ome Ft Seve" Howeve tuton ommonly ou tht n vng utome my e tnguhe ong to ome meue of mpotne The plne ong to whh the eve elet the net unt n eve known poty plne When new ptent ve nto lge hoptl the evety of h polem onee ong to th evety he llowe nto poty queue lthough ley thee n uul queuethu poty queueng moel n eentl one n ptl lein poty plne hghe poty utome e elete fo eve he of thoe wth lowe poty egle of the vl nto the ytem If the eve fee t the tme of pmy vl the vng utome egn to e eve mmetely n utome leve the ytem fte the eve ompleton If the eve uy then the low poty utome goe to ot n eome oue of epete utome utome fom the ot wll ety to get eve fte ome nom tme If thee no hghe l utome n the queue then only the etl utome wll e eve y eve In poty plne thee e two e e: peemptve poty plne Non-peemptve poty plne In peemptve e the utome wth the hghet poty llowe to ente eve mmetely even nothe wth lowe poty ley peent n eve when the hghe utome ve to the ytemthe poty plne to e non-peemptve thee no nteupton n the hghet poty utome jut goe to the he of the queue to wt fo h tun n tlejo nlyze the ngle eve etl queue ujet to ekownretl queue wth ekown n ep w nvetgte y Kulkn hom/g// etl queueng ytem wth poty of pmy utome ue y ohov et l7 Dek n Woolfo tue peemptve poty queue wth lkng Retl queue n poty wee ue n etl y Flnn Templeton8Funmentl of queueng theoey w ee y Go n H Queueng ytem nlyze n moe epth y Leon Klenok 9 Nthn PShemn Jekey Khoufeh 6 hve tue etl queue wth unelle eve Shnthkumn n Shnmugunm ee etl Queue wth Feek on Non-Retl utome In ptlthe nput t uh vl te eve te n etl e unetnly known Unetnty eolve y ung fuzzy et theoyhene the ll queung moel wll hve moe pplton t epee ung fuzzy moelfuzzy Log w ntte n 96 y Zeh Fuzzy queung moel hve een ee y uh eehe lke L n Lee ukley 6 Neg n Lee e nlyze fuzzy queue ung Zeh etenon pnple Ko et l ontute the memehp funton of the ytem htet fo fuzzy queue ung pmet lne pogmmng wwwjeonlneom Open e Jounl Pge 8
2 Fuzzy Retl Queue Wth Poty Ung DSW lgothm pplton of fuzzy log w nlyze y Kl 7 The theoy of fuzzy uet ntoue y Kufmnn8 Zmmemnn9 evelope fuzzy et theoy n pplton Mult-eve fuzzy queue ung DSW lgothm w ue y ShnmugunmS n Venkteh Reently ot nly of poty queue nvetgte y Rth W n Llly Roet II DESRIPTION OF THE MODEL We one poty queueng ytem wth ngle eve nfnte llng populton wth vl te eve te n etl te The ojetve of tuyng queueng moel to eue the wtng tme of utome n queue n lo ot of the ytemhee ot of the ytem epeent long un vege ot pe unt tme uh ot of wtng pe onumpton ot of ytem flty ot of nune et To etlh the poty plne fuzzy queueng moel we mut ompe the vege totl ot of the ytem fo the thee e No poty plnepeemptve poty n non-peemptve poty plne whh e enote y n " epetvely III RISP RESULTS No Poty Retl Queueng Moel vege Totl ot Of The Sytem When Thee I No Poty Dplne Whee W W Peemptve Poty Retl Queueng Moel vege totl ot of the ytem when thee Peempton poty whee n T T T T Non-Peemptve Poty Retl Queueng Moel vege Totl ot Of Sytem When Thee I Non Peemptve Poty L L whee L n L ompon of the thee totl ot how whh of poty plne mnmze the vege totl ot funton of the ytem IV FUZZY RETRIL QUEUES WITH PRIORITY DISIPLINE Fuzzy etl queue wth poty plne e ee y fuzzy et theoy Th ppe evelop fuzzy etl queueng moel wth poty plne n whh the nput oue vl te eve te n etl te e unetn pmete ppomte metho of etenon e popgtng fuzzne fo ontnuou vlue mppng etemne the memehp funton fo the output vledsw lgothm one of the ppomte metho whh mke ue of ntevl t vou -ut level n efnng memehp funton It w the full -ut ntevl n tn ntevl nlyl The DSW lgothm getly mple mnpulton of the etenon pnple fo ontnuou vlue fuzzy vle uh fuzzy nume efne on the el lne V INTERVL NLYSIS RITHMETI Let I n I e two ntevl nume efne y oee p of el nume wth lowe n uppe oun Defne genel thmet popety wth the ymol * whee * ymollly the opeton I * I * epeent nothe ntevl The ntevl lulton epen on the mgntue n gn wwwjeonlneom Open e Jounl Pge 9
3 Fuzzy Retl Queue Wth Poty Ung DSW lgothm of the element n mn m whee e thmet pout n n e quotent VI DSW LGORITHM ny ontnuou memehp funton n e epeente y ontnuou weep of -ut ntem fom to It ue the full -ut ntevl n tn ntevl nly The DSW lgothm ont of the followng tep: Selet -ut vlue whee Fn the ntevl n the nput memehp funton tht oepon to th Ung tn ny ntevl opeton ompute the ntevl fo the output memehp funton fo the elete -ut level v Repet tep to fo feent vlue of to omplete -ut epeentton of the oluton VII SOLUTION PROEDURE Deon eltng the poty plne fo etl queueng ytem e mnly e on ot funton whee l n the unt ot of ytem fo unt n l n L the vege length n the ytem fo unt of Let u one etl queueng moel wth two unt le ve t of vl elong to one of the le n e n the othe l The vege vl te t the ytem follow Poon poe n ppomtely known n gven y the tpezol fuzzy nume The eve te fom ngle eve the me fo oth unt le follow n eponentl ptten n tute ong to the tpezol fuzzy nume n the etl of the low poty utome follow n eponentl ptten n gven y the tpezol fuzzy nume The memehp funton of vl te eve te n etl te e enote Then we hve the followng fuzzy et L { X } { } S epetvely { R} whee XYR e p unvel et of vl teeve teetl te epetvely The memehp funton of vl teeve teetl te e gven follow wwwjeonlneom Open e Jounl Pge
4 Fuzzy Retl Queue Wth Poty Ung DSW lgothm wwwjeonlneom Open e Jounl Pge The pole tuton of unt ot of the ytem fo unt n the me l etlhe y tpezol fuzzy nume wth memehp funton we hooe thee vlue of vz n Fo ntne when we otn ntevl follow Smlly when we otn ntevl n t enote y The vege totl ot of the ytem n thee tuton No poty plne Peemptve poty plne Nonpeemptve poty plne e lulte fo feent level vlue Intevl thmet ue fo omputtonl effeny vege totl ot of the ytem when thee no poty plne
5 Fuzzy Retl Queue Wth Poty Ung DSW lgothm vege totl ot of the ytem when thee peemptve plne ' ' ' ' ' ' VIII NUMERIL EXMPLE one telephone wthng ytem n whh ll ve n two le Wth utlzton of % n 8 % ll ve t th ytem n one wth poon poe the eve tme n etl tme follow n eponentl tuton The vl teeve te n etl te e tpezol fuzzy nume gven y 6 8 n 6 8 pe mnute epetvely The polty tuton of unt ot of ntvty of two le e tpezol fuzzy nume epetvely The ytem mnge The ytem mnge wnt to evlute the totl ot of the ytem when thee no poty plnepeemptve poty plne non-peemptve poty plne n the etl queue No Poty plne: : Peemptve Poty plne: 9 ' ' 8 ' Non-Peemptve Poty plne: ' ' ' 8 wwwjeonlneom Open e Jounl Pge
6 Fuzzy Retl Queue Wth Poty Ung DSW lgothm IX ONLUSION ompon of the thee totl ot how whh of the poty plne mnmze the vege totl ot funton of ytem Even though they e ovelppng fuzzy numeo mnmum vege totl ot of ytem heve wth the non peemptve poty plne The metho popoe enle eonle oluton fo eh ewth feent level of polty Th ppoh pove moe nfomton to help egn fuzzy poty plne queung ytem REFERENES K Elng The theoy of polte n telephone onevton Nyt Jnk mth -999 n tlejo JR on the ngle eve etl queue ujet to ekown Queueng Sytem KulknVG Dho Retl queue wth eve ujet to ekown n epqueueng Sytem Go D n H M Funmentl of Queung Theoy Wley New Yok998 S Dek n DG Woolfo peemptve poty queue wth lkng Euopen Jounl of Opetonl Reeh Nthn PShemnJekey PKhoufehn M/M/ etl queue wth unelle eve opeton Reeh Lette P P ohov I Pvlov n D Puzkovm M/G/l/ Retl Queueng Sytem wth Poty of Pmy utome Mthemtl n ompute Moellng Fln GI n Templeton JG "Retl Queue" hpmn Hll997 9 Leon Klenok Queueng ytem Volume John Wley on Snthkumn n ShnmugunmS Sngle Seve Retl Queue n enoull Sheule Wth Feek on Non-Retl utome Southet n ul-letn of Mthemt -7 L Jeh Fuzzy et Infomton n ontol L RJ n LeeES nly of fuzzy queue ompute n Mthemt wth pplton hng Ko hng-hung L hensp Pmet nonlne pogmmng to nly of fuzzy queue Fuzzy Set n Sytem Tmothy Roe Fuzzy Log n t pplton to engneeng Wley EtenTh Eton Neg DS n Lee ES nly n Smulton of Fuzzy Queue Fuzzy et n Sytem ukelyjj Elementy queueng theoy e on polty theoy Fuzzy n Sytem Geoge J Kl n o Yun Fuzzy Set n Fuzzy Log Theoy n pplton Pente Hll P T R uppe le ve New Jeey99 8 Kufmnn Intouton to the Theoy of Fuzzy Suet Vol I em PeNew Yok Zmmemnn HJ Fuzzy et theoy n t pplton n ekluwe-njhokoton99 ShnmugunmS Venkteh Mult Seve Fuzzy Queueng moel ung DSW lgothm Glol Jounl of Pue n pple Mthemt - Rth W n Llly Roet Fuzzy Queue wth Poty Dplnepple Mthemtl Sene 7-88 wwwjeonlneom Open e Jounl Pge
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