Topology Analysis of Constructing Large-Cargo Transportation Network

Transcription

1 Topology Analyss of Consrucng Large-Cargo Transporaon Nework Rong ZENG *, Hanbn XIAO School of Logscs Engneerng, Wuhan Unversy of Technology, Wuhan , Chna Absrac A lo of research on large-cargo ransporaon manly focus on he selecon, opmzaon of ransporaon roue and desgn of ransporaon nework raher han consderng he essence of he enre nework from a macro pon of vew. Owng o ha, a large-cargo ransporaon nework model based on complex nework heory s proposed. Accordng o he characerscs of large-cargo ransporaon, can be dvded no wo caegores: physcal nework and servce nework. Ths paper sudes he evoluon model of servce nework and nroduces he evoluon algorhm of he nework, analyse he model of he degree of dsrbuon by usng mean-feld heory and propose an analyc formula for he degree of dsrbuon. The numercal smulaon resuls show ha he relaonshp beween he node degree of servce nework and cumulave node degree follows he power-law dsrbuon and has scale-free properes. The nework produced by he model ncarnaes he dynamc evoluonary process of ncrease and decrease of nodes and edges, whch agrees well wh he real suaon. Ths knd of nework can smulae he feaures of logscs servce nework obecvely. Keywords - consrucon logscs; opologcal srucure; complex nework; large-cargo ransporaon nework; degree dsrbuon I. INTRODUCTION Along wh he economc globalzaon, more and more nernaonal engneerng proecs are emergng, among whch are consrucon programs of elecrc power, perochemcal, ec. These programs are characerzed by complcaed logsc lnks, wde scope of servces, hgh echncal requremens ogeher wh consderable unceranes n he praccal operaon process. Therefore, proec logscs plays an essenal role n he successful compleon of he proec. Documen research makes clear ha he managemen n consrucon logscs no only can guaranee he successful compleon of he proec, bu also can save coss, especally n ransporaon. Consrucon logscs s ofen launched around a consrucon proec, whch s long n perod and complcaed n maerals requred (some common maerals lke fly ash, seel, cemen,ec and he urgenly needed maerals lke heavy and large cargoes), and here are many subecs nvolved n he proec (such as manufacurers, wholesaler, propreors, supervsng uns, supervsors, desgnng nsuons, general conracor, sub-conracors, supplers, ec.). In order o ensure he mplemenaon of he proec, schedule mus be srcly conrolled. Once he schedule delays, wll brng huge losses, so he maeral supply of he consrucon s very mporan. Only he maeral s suppled effecvely, mely and orderly, schedule of consrucon can be able o carred on smoohly. Dfferen from he general logscs proec, consrucon proec maerals usually are specal large equpmen (such as ulra-long, ulra-large, over-wegh cargoes, ec.), so he process of ranspor and handng s wh hgh dffculy and hgh rsk, herefore here s a poenal rsk of nducng all knds of accdens. And ulra-large, ulra-long and over-heavy ransporaon equpmen (such as ransformer, sheld machne, generaor ses, ec.) nvolved n hese large-scale consrucon proecs, whch are ofen he key equpmen of he naonal key consrucon proecs and naonal defense consrucon nvesed several hundreds of mllons Yuan or even ens of bllons Yuan, whch conans many resrcve facors, hgh rsks and grea dffcules n ransporaon. I s very mporan o ensure he safey and mely arrval of he cargoes for he whole consrucon proec. Many researches have been performed on he consrucon logscs ransporaon. Vdalaks C. [] assessed he performance and explores he relaonshp beween response capably and cos effcency of ransporaon based on a range of performance ndcaors. W., A. Ross uses rado frequency echnology o denfy and rack raffc consrucon and ransporaon maerals. Xu, Jupng [-4] formulaed a fuzzy, sochasc mulobecve b-level opmzaon model wh he hgher creron of mnmzng he oal ransporaon cos and me, and used adapve parcle swarm opmzaon algorhm o solve he model, seleced ranspor roues for ransporaon agences a a mnmum level of ravel coss. A he same me, a ravel me mahemacal model wh sof me wndows s bul by consrans of fully mprovng he sasfacon level of cusomers, and he model for s soluon s proposed by hm, and fnally he feasbly of he proposed model has been valdaed by means of nsances. L. Gan [5] focuses on how o avod sesmc rsk problems n he large-scale consrucon proecs and ransporaon sysems. The research of logscs ransporaon n Chna manly concenraes on he selecon of ransporaon modes, he opmzaon of ranspor plans, he research of ransporaon sysems and he rsk conrol durng ransporaon. I can be seen ha, DOI 0.503/ IJSSST.a ISSN: x onlne, prn

2 from ransporaon problems n heavy consrucons, many sudes focused he cos, me and vehcle roung problems n ranspor. Also, mos models have he characerscs of lmaon and specfcy whou akng accoun of ranspor nework from he perspecve of sysems, whle ranspor nework s exremely mporan for he proec. Ths paper s amed o sudy he opology characerscs of large-cargo ranspor nework by usng complex nework heores and focus on large-cargo ranspor problems from a sysem pon of vew. II. LARGE-CARGO TRANSPORTATION NETWORK Wh he ncreasng of large-cargo ransporaon, he complexy of s ranspor nework s more promnen. Dfference from general cargo ranspor, obecs of largecargo ranspor generally are exra heavy, exra long and exra large cargo, whch have hgher requremens for roads and pors durng ransporaon, such as he clear wdh of lnes, he mnmum urnng radus and he raed load srengh. The nodes of large-cargo ransporaon nework n consrucon logscs nclude no only he real road nersecon, bu he sorage facly and enerprse (such as producon enerprses, supplers, rans saons, warehouses, consrucon ses, ec.) n logscs acves, as well. The correspondng edges nclude he road edges and he delvery of goods and nformaon beween manufacurers and servce provders. So large-cargo ranspor nework n consrucon s a complex nework ha ncludes physcal nework and servce nework. A. Complex Nework The complex nework s a way o sudy complex sysem, focuses on opologcal srucure n whch facors n sysem work n conuncon wh each oher, and s he bass of undersandng he naure and funcon of a complex sysem. Was publshed a small- world nework model n Naure n 998 [6], Barabás and Alber [7] publshed a complex paper on scale-free nework n 999, snce hen he research on he srucure and properes of complex neworks has araced much more aenon n varous felds, such as formaon nework (World Wde Web, caons nework, compuer sharng nework), echnology nework (power nework, elephone nework), bologcal nework (food webs, neural nework, gene nework), socal nework (scenfc collaboraon neworks [8], move acor collaboraon nework) [9] and he ransporaon nework (roue nework, ralway nework, hghway nework, naural rver nework) and so on. WS and BA s he wo mos classcal nework models, oher common models nclude local-world evolvng model, mul-local-world evolvng model, generalzed scale-free dynamcal nework model, mxed preferenal model as well as he wreless sensor nework evolvng model and so on [0-5]. The consrucon of hese models provdes he necessary echnologcal means for he sudy of he relaed nework sysems. However, he research on he evoluon model of he ranspor servce nework s rarely nvolved. B. The Characerscs of Large-cargo Transporaon Nework Compared wh oher ransporaon neworks, he ransporaon nework of large-cargo n consrucon s a specal knd of raffc nework, whch s manly refleced n he followng four respecs: () The requremens of nework plannng are dfferen. For general cargo ranspor, he goal of road nework plannng s o reduce he cos of ranspor or o shoren he dsance beween he wo places. Due o he parculary of large-cargo n consrucon, he clear wdh of lnes, he mnmum urnng radus and he raed load srengh are requred, he passng ably of ranspor mus be fully mproved and he ransporaon rsk mus be reduced, so he basc prncple of large-cargo ranspor nework plannng s o fnd a praccable roue wh mnmum rsk, whch s dfferen from oher road ranspor nework. () The morphologcal srucure of nework s dfferen. The lnks and nodes of large-cargo ransporaon nework n general should ry o avod brdges, culvers or roads whch wh weak bearng capacy and n he secons of small urnng radus, whch hen lead o he morphologcal srucure s dfferen from ha of oher ransporaon nework. () The complexy of nework s varyng. The nodes and edges of large-cargo ransporaon nework are composed of he man roads and nersecons, whch s a par of he urban road nework, bu s dfferen from he urban road nework. I also ncludes he ranspor relaed servces organzaon, whch s a mullayer complex nework consss of he physcal nework and servce nework. (v) The ranspor mode of nework desgn s complex. For large-scale proecs, due o he long ranspor dsance, waerway, hghway and oher mulmodal ranspor modes are usually used when comes o nernaonal ransporaon. And he loadng and unloadng echncal of large-cargo requremens s hgh, he places of ranshpmen n he process of ransporaon should have he requred handlng echnque. All hese above facors consdered, large-cargo ransporaon nework n consrucon nevably presens dfferen opology propery from oher ransporaon neworks. The applcaon of he complex nework heory n he research abou he opology propery of large-cargo ransporaon nework s helpful o mprove he undersandng of he nework characerscs and o reduce he damage for he unknown rsk of he nework funcon, DOI 0.503/ IJSSST.a ISSN: x onlne, prn

3 and o ensure he smooh delvery of consrucon maerals n consrucon ses whou delayng he consrucon perod. III. TOPOLOGICAL STRUCTURE OF LARGE- CARGO TRANSPORTATION NETWORK In hs paper, he nework model s descrbed by analyzng he characerscs of he large-cargo ransporaon nework and he sascal characersc value of nework s calculaed, fnally numercal smulaon of he nework s performed. A. Nework Model Consrucon large-cargo ransporaon nework consss of wo maor layer neworks whch are physcal nework and servce nework. The nodes of physcal nework are he sarng pon, he endng pon and he ranson pon n he ransporaon process, he edges of ransporaon nework represen he pah beween he wo nodes. The specfc locaon of nodes and he roue algnmen are no consdered n he consrucon logscs ransporaon nework, bu he node degree and degree dsrbuon are manly consdered. Accordng o he mehod of graph heory, G ( V, E) can be used o represen he ransporaon nework of large-cargo n consrucon, where V s he node collecon of he nework G, represens he physcal locaon such as he sarng pon, he endng pon, he nersecon and he ranson pon, and so on n he ransporaon process. If here are M Mnodes n he nework, hen V { v, v,, v m }, E s a se of edges of consrucon logscs ransporaon nework, represens he se of he roads whch connecng he wo places, ncludng waerways, hghways and ralways, f here are N edges, hen E { ee,,, e n }, he dsances of large-cargo ranspor s long, he requremen for ranspor lnes s hgh, so he mode of ranspor s always mul-modal ranspor, nvolvng roads, waerways, ralways and oher dfferen ransporaon modes, here are many modes of ranspor can be seleced from V o V as shown n Fg.. Fg.. Large-cargo ransporaon physcal nework n consrucon The servce subec of large-cargo ransporaon servce nework n consrucon ncludes raw maeral producers, supplers, conracors, delvery ceners and carrers who are responsble for he sendng and recevng of he supply and demand nformaon, he selecon of ranspor mode and roue, and he ransporaon cos reducon under he premse of ensurng safey and whn he schedule. The obec s he consrucon large-cargo, G ( V, E) can also be used o represen he large-cargo servce nework, of whch V denoes he se of nodes n he large-cargo servce nework G and represens he raw maeral manufacurers, supplers, conracors, and organzaons lke delvery ceners and demand ceners durng ranspor. E s he se of nework edges and represens a demandng relaonshp or an nformaon exchange relaonshp beween he wo nodes. Ths paper manly focuses on he servce nework, whch means he nework nodes are he sorage ses of logscs acves or enerprses and edges are large-cargo ransporaon and nformaon exchange beween he sorage ses and enerprses. B. Consrucon of Topologcal Srucure In radonal consrucon large-cargo ransporaon, s usually consdered only from an ndvdual cusomer perspecve ha s enough o ranspor he large-cargo o he consrucon se safely and puncually, whou consderng how o effecvely negrae all he resources hroughou he ransporaon process o mee he needs of many cusomers from he vewpons of logscs servce provders. So hs arcle dscusses he large-cargo servce nework n consrucon wh he complex nework heory, whch s a complex nework composed of many OD for he formaon of cross-cung, whch reflecs he connecon beween dfferen nodes, and s a good ndcaon of he characerscs of he large-cargo ransporaon nework n consrucon. In order o esablsh a complex nework model of large-cargo ransporaon n consrucon, whch s based on adacen nodes, he basc defnons and assumpons abou nework opology have been made as follow: () The nodes of he nework are he raw maeral manufacurers, supplers, ransfer ceners, conracors, consrucon ses, ec. The edges of he nework are he dsrbuon roues and nformaon ransfer beween adacen nodes. () The nework s regarded as an un-weghed nework when he mes ha he ranspor vehcle passes hrough he sdes and he frequency of nformaon ransmsson are no consdered. () In order o save me n he process of reloadng. (v) The ransporaon nework n consrucon logscs s an undreced graphcal nework whou consderng he road drecons. (v) Suppler of maerals can fully mee he needs of he consrucon ses. DOI 0.503/ IJSSST.a ISSN: x onlne, prn

4 Therefore, he large-cargo servce nework model n consrucon has he followng characerscs: () The nework node s a par of he physcal nework, whch has an accurae geographcal locaon and space nformaon. () The srucure of he nework s subec o he physcal nework. () The node degree of nework s he mos obvous symbol of he servce nework, and he change of raffc assgnmen and raffc flow wll drecly affec he degree dsrbuon of he nework. (v)the pah capacy, rsk, cos and me need o be consdered n he pah choce of he nework dsrbuon, whch also drecly affec he characerscs of complex nework. C. Model Descrpon Accordng o he descrpon of he nework, drven by he benefs n large-cargo ranspor servce nework, new nodes such as new supplers, logscs servce provders and consrucon pares are emergng, as well exsng nodes are droppng ou for compeve reasons, smlarly here are new edges enry and ex beween nodes. For smulaon, we generaed a nework by he followng Algorhm: () Inal sae. There are m 0 nodes n he nework. () We add a new node whch have m edges o he nework wh he probably p(0 p ), he probably ha a new node wll be conneced o node depends on he degree k of node and aracon,such ha k ( k ) () k () We add m edges o he nework wh he probably q(0 q ), one end of he new edges s added o he nework wh random connecon, he oher end s added o nework wh he probably. (v) We remove he m 3 edges wh he probably r(0 r ), one end of he edges s chosen randomly, he oher end s seleced wh followng probably: k k () N (v) We randomly remove a node wh he probably s(0 s ), hen m 4 sdes of he node are also removed, where p qrs k k mp (3) k IV. A. Degree Dsrbuon ANALYSIS OF NETWORK CHARACTERISTICS We can oban he degree dsrbuon of he nework node based on mean feld heory. () New nodes are added wh he probably p(0 p ) : () m nodes are added wh he probably q : k k mq mq ( ) (4) N() N() k () m 3 nodes are removed wh he probably r : k mr 3 mr 3 ( ) ( k ) (5) 3 N () N () N () (v) A node s removed wh he probably s, hen: k sm 4 (6) 4 N () In sep, he sum of degree n he nework and he sum of nodes are: k k k mp mq mq( ) k N N k () () sm4 mr 3 mr 3 ( ) ( k) N () N () N () N () The nal condons are: kd ( ) m, we can ge B A k () ( ) A m A B Where mp mq A, ( pm qm rm sm ) p And 3 4 ( pm qm ) m q rm sm B ( pm qm rm sm ) p p s 3 4 The probably Pk () k han k can be gven: 3 4 ha he degree k () less m B A m B A Pk kp k B A m P S k B A Assume ha / a / A / / / 0 ( ) / P k Pk k, we can ge k DOI 0.503/ IJSSST.a ISSN: x onlne, prn

5 Where / A B B P k m k (7) A A / A. B. Cluserng Coeffcen In neworks, f he node s conneced o he node, he node s conneced o he node k, hen he node k s lkely o be conneced o he node. Ths phenomenon reflecs he naure of he dense connecons beween some of he nodes, whch can be shown by he cluserng coeffcen CC, n he undreced nework, cluserng coeffcen s defned as: E C ( ) (8) k ( k ) And he average cluser coeffcen s: C N N C (9) In he formula (9), E represens he number of edges among all he neghbors of he node. C. Average Pah Lengh degree dsrbuon Fg.3 s obaned by numercal smulaon. The resuls show ha he opologcal srucure of ransporaon servce nework n consrucon logscs whch s generaed by he mechansm proposed n hs paper has scale-free properes. Fgure.3 (a) shows he degree dsrbuon whle p = s =0, hen here are no changes n he amoun of he nework nodes, only changes n degree dsrbuon of neworks when edges ncreased or decreased, whch means ha here are no nodes such as new manufacurers and supplers, onng and exng n a ceran perod of large cargo ransporaon nework n consrucon, only flucuaon of ranspor servce and nformaon ransfer beween nodes. Fg.3 (b) shows he degree dsrbuon whle q = r =0, only akes no accoun of he node s flucuaon, no he parcular degree dsrbuon of neworks when edges have no changes. From he Fg.4 he relaons beween node degree dsrbuon and node numbers, we can see mos nodes have a smaller degree, only a few nodes have a hgher degree (hub pons), whch llusraes agan ha he consrucon logscs servce nework s a ypcal scalefree nework. The Fg.5 shows he regular paern of he cluserng coeffcen wh he varaon of he scale of he nework, when he nework sze s nfne, he cluserng coeffcen ends o zero, does no have he obvous characerscs of cluserng. The dsance d beween node and n he nework s defned as he edges connecng he wo nodes n he shores pah, hen he average pah lengh L n he nework s he average value of he dsance beween any wo nodes. The formula s: L d (0) N( N ) N For he consrucon servce nework, he average pah lengh manfess he ranspor dsance and he effcency of nformaon ransmsson, n order o mee cusomers needs and enhance her own compeveness, supplers, logscs provders, rans saons should accelerae he speed of ransmng nformaon, reduce he ransporaon me, and delver he maerals n me whou consrucon delay. Promp delvery of maerals and nformaon ransfer reacon of he ranspor servce nework has a small average pah, whch reflecs he characerscs of a small- world. Fg.. Degree dsrbuon. D. Numercal Smulaon and Analyss of Resuls To furher nvesgae he sascal characerscs of he model, we assume ha p = 0.4; q = 0.3; r = 0.; s = 0.; N = 000; m = 0; m = 0; m 3 = 0; = 0; DOI 0.503/ IJSSST.a ISSN: x onlne, prn

6 (a) p = s =0 Fg.5. The regular paern of cluserng coeffcen wh he varaon of he scale of he nework. V. CONCLUSION (b) q = r =0 Fg.3. he p(k) of smulaon resuls wh p = s =0 and wh q = r =0 (b). Fg.4. Degree dsrbuon of nodes (a); Accordng o characerscs of he large-cargo ransporaon nework, he paper descrbes he physcal nework and servce nework of large-cargo ransporaon, analyzes he characerscs of he servce ranspor nework n he growh process, and esablshes dynamc evoluon model wh he growh and deleon of edges afer synhecally consderng he growng and exng of he nework nodes. The paper derves node degree dsrbuon based on mean feld heory, hen analyzes he opologcal properes of large-cargo ranspor servce nework n consrucon by usng degree dsrbuon parameer. We selecs 000 nodes as he sample daa, he degree dsrbuon obeys power-law ndex dsrbuon P (k) k-γ by smulaon analyss, whch reveals s scalefree properes; hrough he analyss of cluserng coeffcen and average pah s changes wh he growh of nework sze, he resuls show agan ha he nework has scale-free and small-world characerscs. In he ranspor process of consrucon logscs, he ransporaon and servce asks are usually compleed by a few manufacurers, servce provders and oher companes. If he ranspor and servce of hese enerprses once blocked, he enre ranspor servce nework wll be desroyed. Thus, we should ry o share busness pressures of key enerprses on he premse of ensurng he smooh of hese crcal busness servces and ranspor, and make he nework show a ceran degree of modulary and herarchy so ha he nvulnerably of he enre nework n he face of unexpeced evens can be enhanced. DOI 0.503/ IJSSST.a ISSN: x onlne, prn

7 REFERENCES [] C. Vdalaks and J. Sommervlle, Transporaon responsveness and effcency whn he buldng supply chan, Buldng Research and Informaon, vol. 4, pp , 03. [] F. Yan, J. Xu and B. T. Han, Maeral ransporaon problems n consrucon proecs under an unceran envronmen, KSCE Journal of Cvl Engneerng, vol. 9, pp. 40-5, 05. [3] Y. Ma and J. Xu, Vehcle roung problem wh mulple decsonmakers for consrucon maeral ransporaon n a fuzzy random envronmen, Inernaonal Journal of Cvl Engneerng, vol., pp , 04. [4] J. Xu and J. Gang, Mul-obecve beleve consrucon maeral ransporaon schedulng n large-scale consrucon proecs under a fuzzy random envronmen, Transporaon Plannng and Technology, vol. 36, pp , 03. [5] L. Gan and J. Xu, Rerofng ransporaon nework usng a fuzzy random mul-obecve beleve model o hedge agans sesmc rsk, Absrac and Appled Analyss, vol., pp. -4, 04. [6] D. J, Was and S. H. Srogaz, Collecve dynamcs of 'smallworld' neworks, Naure, vol. 393, pp , 998. [7] A. L. Barabas and R. Alber, Emergence of scalng n random neworks, Scence, vol. 86, pp ,999. [8] M. L, H. Zou and S. Guan, A coevolvng model based on preferenal radc closure for socal meda neworks, Scenfc Repors, vol. 3, pp. 5-5, 03. [9] X. M. L, X. H. Xu and L. H. Meng, Flucuaons n arpor arrval and deparure raffc: A nework analyss, Chnese Physcs B, vol., , 0. [0] A. X. Cu, Y. Fu, M. S. Shan, The emergence of local srucure of complex neworks: he evoluon of he common neghbour drven nework, Journal of Physcs, vol. 60, pp , 0. [] J. Q. Fang, The developmen of nework scence, Journal of Guangx Normal Unversy: Naural Scence Edon, vol. 5, pp. -6,007. [] H. Jeong, S. P. Mason and A. L. Barabás, Lehaly and cenraly n proen neworks, Naure, vol. 4, pp. 4-, 00. [3] A. Scala, L. A. N. Amaral and M. Barhelemy, Small-world neworks and he conformaon space of a lace polymer chan, Epl-Europhys Le, vol. 55, pp , 000. [4] X. L, G. Chen, A local-world nework evolvng model, Physca Sascal Mechancs & Is Applcaons, vol. 38, pp , 003. [5] S. Tan, H. J. L, Y. Zhao, Analyss of a novel mul local world nework model, Compuer applcaon research, vol. 30, pp , 03. DOI 0.503/ IJSSST.a ISSN: x onlne, prn