Departure Scheduling in a Multi-airport System

Transcription

1 Eghth USA/Europe Ar Trffc Mngement Reserch nd Development Semnr (ATM2009) Deprture Schedulng n Mult-rport System Ynun Wng, Mnghu Hu, Dong Su, Yong Tn Insttute of Ar Trffc Flow Mngement Nnng Unversty of Aeronutcs nd Astronutcs Nnng, Chn wngy@nu.edu.cn; mnghuhu@263.net; dong_su@nu.edu.cn; @263.net; Abstrct In ths pper, we consder schedulng problem for mult-rport deprture flghts. A mthemtcl model s presented for sequencng deprture flghts n dfferent rports wthn one termnl re. Due to the trffc nfluences between rports, both rport runwys nd deprture routes re consdered n the model. Moreover, prctcl ssues tht ffect the mplementton of the schedule re lso crred out by the Constrnt Poston Shftng (CPS). Then tbu serch lgorthm s developed nd mplemented to obtn resonble solutons wthn cceptble computton tmes. Fnlly, we pply the proposed model nd lgorthm to rel cse study of Shngh Termnl Are wth deprture flghts from Shngh HongQo Interntonl Arport nd Shngh PuDong Interntonl Arport. The computtonl results vldte the proposed model nd show the dvntge of the lgorthm. Effcent schedulng flghts for tkeoff cn fully utlze crtcl resources nd reduce the mpct of trffc ntercton between rports. Keywords- Ar Trffc Flow Mngement, Multrport System, Deprture Schedulng, Tbu Serch Algorthm. I. INTRODUCTION Tremendous growth n r trnsportton demnd s chllengng the exstng Ar Trffc Mngement (ATM) system. When ATM cpcty cn not meet the trffc demnd, rspce congeston nd flght delys occur. Gret efforts hve been mde to ensure the sfety nd effcency of the ATM system. Sgnfcnt mprovements hve lredy been cheved n ncresng rport cpcty, such s constructon of new rport nd expnson of runwy system. New opertonl methods nd tools re ppled n r trffc flow mngement (ATFM) feld. The mportnt spects of ATFM re the mngement of deprture flow nd rrvl flow n termnl re, whch re known s deprture mngement nd rrvl mngement. There s consderble mount of lterture on rrvl schedulng problem (ASP). The erlest work n ths feld could be found n [1], where Der studed the rcrft schedulng problem wth poston shft constrnt. In [2] nd [3], where Psrfts nd Bnco showed tht the ASP s equvlent to the cumultve symmetrc trvelng slesmn problem. They used dynmc progrmmng formulton to ttn lower bounds for the problem nd then heurstc lgorthms were ppled to get solutons. Another welth of nformton cn be found n [4], n whch n extensve Jnmng Zhn Ar Trffc Mngement Dvson Ar Trffc Mngement Bureu of Centrl South Chn Gungzhou, Chn mzhn@tmb.org lterture overvew on the rrvl problem ws mde. Then Besley et l. gve mxed nteger progrmmng model for rrvl sequencng problem. In the model, termnl re ws treted s sngle resource; dfferent constrnts (such s lndng tmes or tme wndows) nd dfferent obectve functons were dopted. However, these studes dd not provde munch ttenton to the rspce restrcton. In [5] nd [6] Erzberger nd Glbo demonstrted tht congeston mght pper not only n the runwy but lso n the fxes. Ppers relevnt to rrvl problems wth rspce constrned were publshed n [7-10], Arcrft mneuver, few rspce segments of fnl pproch nd holdng ptterns were consdered n ther work respectvely. Mny reserchers hve recently turned to the deprture schedulng problem (DSP). Bolender n [11] studed two mor problems reltng to the deprture mngement. The frst one s the schedulng of rcrft for deprture nd the second s mergng deprture flghts onto ther fled routes n congested rspce envronment. Greedy serch lgorthms nd genetc lgorthms were desgned to mnmze the totl tme to deprt set of rcrft. A bref summry of some of relevnt work n deprture schedulng s presented n [12], where Atkn et l. ppled hybrd metheurstcs to d runwy schedulng t London Hethrow Arport. They developed model bsed on the specfc holdng pont structure nd rspce envronment n Hethrow, nd proposed hybrd metheurstc system to enhnce the throughput of runwy. In [13], Blkrshnn et l. presented n effcent lgorthm bsed on dynmc progrmmng, to determne deprture schedules tht stsfy vrous upstrem nd downstrem constrnts. Furthermore, decson support tools (DST) re developed nd utlzed to help termnl re controller del wth deprture nd rrvl trffc. Arrvl DSTs re Trffc Mngement Advsor (TMA), the Descent Advsor (DA) nd the Fnl Approch Spcng Tool (FAST), Arrvl Mnger (AMAN) etc. Deprture mngement tools could ssst controller to enhnce the deprture performnce by modfcton the deprture sequence. Deprture mnger (DMAN) s the tctcl controller ssstnce system, optmzng the r trffc flow form the gte to the deprture runwy. The Mnte Deprture Sequencer (MADS) s plnnng decson support tools for tower controller whch ws developed by the Ntonl Aerospce Lbortory NLR.

2 MADS cn ssst controller n the estblshment of optml deprture sequences nd the plnnng of ntl clmb phses nd s such optmzes the use of runwys[14]. However, the prevous studes mnly focused on sngle rport rrvl schedulng (SAASP) or sngle rport deprture schedulng (SADSP). To the best of our knowledge, none of ttempt hs been gven to schedulng rrvl or deprture flghts n mult-rports wthn termnl re. A study presented by Bonnefoy et l. showed tht the trnston from sngle-rport to mult-rport systems s nd wll remn key mechnsm by whch the r trnsportton system scles nd wll meet growng demnd n the future [15]. A geogrphcl dstrbuton of mult-rport systems s llustrted n Fgure 1. sequence one needs to stsfy the followng constrnts tht re mposed on the termnl re system. A. Mnmum Tkeoff Seprton A mnmum tkeoff seprton between rcrfts from the sme rport must be enforced for the consderton of deprture sfety. The requred tme seprton S for two consecutve rcrft nd s determned by the wke types of two rcrft nd the Stndrd Instrument Deprture (SID) routes whch they re usng. Arcrft re dvded nto there types (Hevy, Medum, nd Lght) ccordng to the mxmum tkeoff weght cpcty. A wke vortex seprton w s requred for rcrft to prevent wke-vortex cused by the former rcrft. Prllel runwys my be used for ndependent nstrument deprtures f the runwy centre lnes re spced by the dstnce specfed n Annex 14, Volume I nd the deprture trcks dverge by t lest 15 degrees mmedtely fter tkeoff. Otherwse segregted operton mode my be used. Addtonlly, to ensure tht rcrft wll not cuse rspce congeston, the route spcng requrement r for rcrft usng dfferent SIDs s defned. Ths depends on the SID group nd rcrft speed group. Here mnmum tkeoff seprton S = mx( w, r ) s cheved. Fgure 1. Geogrphcl dstrbuton of mult-rport systems worldwde (cte from [15]) In ths reserch, the defnton of mult-rport system s gven s: set of sgnfcnt rports tht serve commercl trnsport n metropoltn regon, wthout regrd to ownershp or poltcl control of the ndvdul rport [16]. In ths pper, we develop new model nd n effcent lgorthm for computng n optml deprture sequence n mult-rport tht wthn termnl re. The structure of the pper s s follows. Secton II descrbes the mult-rport deprture schedulng problem (MADSP) n detl. In secton III we present mxed nteger progrm model of MADSP. A hybrd serch lgorthm to obtn resonble soluton s desgned n secton IV. The mplementton of ths pproch to relstc scenros drw from dt of deprture flow from Shngh Termnl Are s gven n secton V. The pper ends wth some concluson n secton VI. II. MULTI-AIRPORT DEPPARTURE SCHEDULING PROBLEM A smplfed opertonl scheme of termnl re wth mult-rport system nd the deprture process t ech rport nd fxes s shown n Fgure 2. The purpose of deprture schedulng n mult-rport s to determne n optml sequence nd tkeoff tmes under dfferent obectves. These obectves nclude mxmzng the runwy throughput, mnmzng the totl dely, nd ensurng rlnes or rports equtes n the deprture sequence. To optmze the deprture Fgure 2. Scheme of deprture n termnl re wth mult-rport B. Deprture Tme Wndow A deprture tme wndow wll be ssgned to prtculr rcrft, to whch the rcrft must dhere. It s possbly becuse of downstrem trffc flow mngement to vod congeston en route nd t busy destnton rports. These tme wndows mpose n erlest nd ltest deprture tme for n rcrft. If ny rcrft mssed ts tme wndow, t wll be delyed for nother chnce of lloctng tme wndow. Ths usully hppens n U.S. rports or Europen rports. In Chn we mpose mnmum tkeoff seprton between two consecutve rcrft whch hve the sme destnton nsted of deprture tme wndow. For exmple, rcrft from Gungzhou to Beng must meet mnmum of 10 mnutes tkeoff seprton requrement. The erlest tkeoff tme of the lter rcrft s 10 mnutes lte fter the former rcrft

3 deprture. No ltest tme s specfed for the lter rcrft. C. Poston Shft Constrnts The most common wy to sequencng deprture flghts hs been to mntn the Frst-Come-Frst-Served (FCFS) order. A FCFS schedule s esy to mplement, nd t lso mntns sense of frness. Obvously drwbck of the FCFS schedule s tht t my lmt the throughput of runwy due to lrge spcng requrement. As dscussed prevously, the requred tkeoff seprton s bsed on the types of rcrft nd the SIDs group. Hevy rcrft usully cuse lrge seprton whle lght rcrft hve smller one. One cn obtn deprture queue wth the smllest mkespn by groupng hevy rcrft nd plcng them fter lght rcrft. However, such prctce should be gven up becuse t my rse the dspprovl of frness mong rlners. The Constrned Poston Shftng (CPS) concept ws frst ddressed n[1] by Der (1976). In the CPS frmework, there hs certn degree of flexblty to shft n rcrft n the FCFS sequence by smll number of postons. The Mxmum Poston Shftng (MPS) s n mportnt prmeter s ntroduced to specfy the mxmum number of postons n rcrft cn shft from ts FCFS order. Consequently CPS my ncrese runwy throughput whle ensurng some degree of frness. D. Mult-runwy Operton For the rport wth multple runwys used for deprture, the reltve mgntude of the delys experenced t ech runwy cn drectly ffect the cpcty nd effcency. Due to the nture of deprture demnd, rcrft tx restrcton, nd controller ctons, runwy mblnces my occur. Although the globl obectve s to reduce deprture dely, we don t expect the stuton tht there s long queue exstng t one runwy whle nother runwy s dle. The prmry sources of deprture runwy mblnces re the homogenety n drecton of flght durng deprture push nd the procedures for runwy ssgnments[17]. Assgn rcrft to the runwy ner ts pron s common strtegy used by tower controller whch cn reduce ddtonl tx tme. Runwy blncng s complcte nd dffcult. Schedulng n mult-runwy opertonl envronment s very dffcult problem. Bolender et l. conducted study to evlute schedulng strteges for multple runwys[18]. However, schedulng methods for mult-runwy s out of the scope of ths study. In ths pper we dscuss the deprture schedulng problem tht ech rport hs only one runwy used for deprture. E. Trffc Intercton between Arports The sgnfcnt dfference between SADSP nd MADSP s the rule of usng the shred nd crtcl deprture resources, such s deprture fxes nd SID segments. In mult-rport termnl re, deprture routes of ech rport re stcked n the lmted rspce. They my ntersect t fx (ncludng deprture fx) or even hve sme route segment. Controller wll keep sfe seprton for rcrft flyng over ntersecton pont. Therefore deprture trffc from one rport my hve mpct on flghts from other rports. Wth ntersecton lmtton, deprture schedulng must tke the whole flow nto consderton; otherwse t wll cuse rspce congeston nd ncrese controller worklod. III. MODEL OF MULTI-AIRPORT DEPARTURE SCHEDULING In ths secton we present schedulng model for mult-rport to determne deprture sequence nd deprture tmes for gven set of flghts, complyng wth seprton rules. Let AD = {1, 2,..., A} be the set of rports ndces, where A s the number of rports under consderton. Let PT = {0,1, 2,..., P} be the set of ntersecton ponts ndces, where P s the number of the ponts. Let FL = {1, 2,..., N} be the set of deprture flghts ndces, where N s the totl number of flghts under consderton. Let AD be the rport tht flght deprts from. Let p PT to represent the ntersecton pont n the route of flght. Prtculrly, p = 0 stnds for there s no ntersecton pont of flght. Other vrbles re defned s follows: e : Erlest tke off tme of flght o : Poston of flght n the FCFS schedule of rport k : A predetermned number of MPS b : Erlest tme of Deprture Tme Wndow for flght l : Ltest tme of Deprture Tme Wndow for flght c F : Set of flghts wth deprture tme wndow, F : Set of deprture flghts from rport, N : Number of flghts n the set F F c F FL FL p t : Flyng tme of flght between ts orgn rport nd route pont p p τ : Requred tme seprton mposed on two consecutve flghts tht pss route pont p Here we hve decson vrbles: c : An nteger tht represents the poston of flght n the deprture order of rport, F d : The clculted tke off tme of flght When schedulng flghts n mult-rport, the sequences of flghts pssng ntersecton ponts hve gret mpct on the entre termnl opertng effectvely nd effcently. If we swp the postons of two flghts nd tht deprt from dfferent rports n the sequence, ll the flghts n the rport tht tke off fter flght my be delyed. Ths s one of the mor constrnts n the mult-rport deprture schedulng. So we ntroduce nother decson vrble to determne the deprture sequence of entre termnl re: c : An nteger tht represents the poston of flght n the deprture order of entre termnl re, FL The deprture flght wll request to strtup when t s redy. No punshment wll be ssgned to flght for t tkes off before ts scheduled deprture tme. Whle n n rrvl schedulng problem, n ddtonl cost wll be produced for flght lndng before ts preference tme. Snce no flght cn

4 tke off before t s redy. We hve: d e for ll FL. (1) In ths model, the frst flght s ssumed to tke off t ts erlest tke off tme: d = e f c = 1, FL. (2) To llevte the controllers worklod, reschedulng flghts n n rport should stsfy the CPS constrnt: c o k for ll F, AD. (3) Flghts wth deprture tme wndow hve to tke off wthn the ssgned slot or t wll be delyed, b d l F c. (4) Most mportnt spect of schedulng deprture flghts s tht ll flghts must comply wth the requred seprton rules. Flghts from the sme rport should fulfll the mnmum tkeoff seprton requrement. Flghts overflyng sme route pont should mntn predefned seprton. Here we hve: nd d mx ( d + S ) (5) FL c < c, = p p p ( d + t ) ( d + t ) τ (6), FL, p PT c > c, p = p = p The terms from (1) to (6) mke up the bsc constrnts of mult-rport deprture schedulng model. The mor obectve of deprture schedulng s to reduce rcrft dely. Here we use the verge dely of totl flghts n the termnl re s the obectve functon of Model I : ( d t ) I FL J ( d ) = N (7) In the model, the verge dely suffered by rport s computed s: D = F ( d t ) N We m to mnmze the verge dely of termnl re whle tkng ech rport s verge dely under consderton. The obectve functon of Model II s ntroduced s followng: (8) IV. TABU SEARCH APPROACH Tbu serch (TS) lgorthm n [19, 20] s metheurstc pproch desgned to fnd ner-optml soluton of combntorl optmzton problem. The bsc de of TS s to explore the serch spce of ll fesble schedulng soluton by sequence of moves. Vessens showed tht TS methods re superor over other pproches (n specfc ob schedulng cses) such s smulted nnelng, genetc lgorthms, nd neurl networks[21]. The lgorthm cn be sketched s follows: TS strts wth n ntl fesble soluton x 0, nd replce x 0 by the best neghbor soluton x ' whch s determned by mens of the mesurng functon nd tbu lst. In ech terton step, tbu lst s used to remember the locl optml soluton nd the recent moves n order to prevent repetng these processes n next few steps. If the neghborhood set s connected, then the globl optml soluton wll be found by usng the TS lgorthm. There re totl fve key essentls of TS lgorthm: (1) Intl soluton; (2) Neghborhood serchng; (3) Tbu lst; (4) Mesurng functon; (5) Stop condton. (1) Intl Soluton In order to be ppled, the TS lgorthm requres n ntl soluton. FCFS polcy my be used to get the ntl soluton. For ll flghts under consderton, sequence x 0 n order of scendng ETD wth severl dustments wll be the strtng pont for TS. The prncple of dustments s tht try to sctter the rcrft tht usng the sme route ponts n the sequence whle under the CPS constrnt. For exmple, the orgn deprture sequence s shown n the Fgure 3. Flght 3 from rport 1 nd flght 11 from rport 2 use the sme route pont 3. Although swp the posons of flght 3 nd 4 n the sequence of rport 1 cn cuse bgger wke seprton, t wll vod the route pont conflct whch could evoke the huge trffc dely. The ntl deprture sequence for TS lgorthm fter dustment s shown n Fgure 4. Fgure 3. Orgn deprture sequences of flghts n termnl re I ( d ) = ( ) ( ) + D J d α (9) II I J J d AD The coeffcent α works s the weght of rport. It llows us to cheve dfferent obectve by dustngα under dfferent stuton. Fgure 4. Intl deprture sequence of flghts for TS lgorthm

5 (2) Neghborhood Serchng Our neghborhood N( x) s defned s constrned 2-opt. A neghbor s generted by swppng the postons of two rcrft n x whle complyng wth the CPS. It must be noted tht the CPS constrnt s mposed on the deprture sequence of ech rport. Smply swp two postons of rcrft n the termnl sequence wth predefned MPS wll reduce the soluton-spce. We use the followng wy to generte the neghborhood. Frst, rndomly select two rcrft n the termnl sequence nd swp ther poston wthout consderton of CPS constrnt. Second, vldte the new sequence by checkng whether every deprture sequence of ech rport s stsfyng the CPS constrnt. If ths neghbor s n effectve move, then dd the neghbor n the N( x) ; otherwse bndon the sequence nd generte next neghbor. A cnddte setv( x) s used to llevte the computtonl burden. If nnx ( ( )) > 100, we rndomly generte 100 new neghbors to mke up V( x) ; else we select the whole neghborhood N( x ) s cnddte set V( x). (3) Tbu Lst A tbu lst s bult up from the hstory of moves used to explore serch spce untl the old soluton re s left behnd. The lst 20 moves of ech rcrft re stored n the tbu lst. Any moves tht plce the rcrft bck to ts ntl poston remembered n the lst s reected. Two sprton crter wll be used n the process of terton. One crter s tht when ll solutons n cnddte set re forbdden, then the soluton wth mnml obectve vlue s chosen to unbnd. The other s tht lthough one soluton s forbdden but ts mesurng functon vlue s better thn the vlue of the current best soluton, then ths soluton cn be unbound nd return to the cnddte set. (4) Mesurng Functon A new strtng pont wll be selected from cnddte set through the mesurng functon. Here we tke the obectve II functon J ( d ) s the mesurng functon. (5) Stop Condton As heurstc lgorthm, the TS lgorthm s desgned to fnd stsfctory soluton of the problem wthn n cceptble tme-spn. The TS lgorthm stops fter t hs run for predetermned number of tertve steps MAX_ITER. Another condton tht lgorthm termnted s when the obectve vlue does not decrese n lmted steps MAX_OPT. In our mplementton, MAX_ITER=1000, MAX_OPT=200. (6) The lgorthm procedure Step 1. Get n ntl soluton x now s descrbed n (1). Let the terton number N ter =0, the number of optml * now soluton occurs N opt =1, the current optml soluton x = x, nd set tbu lstt =Φ. (b) Else rndomly select 100 new solutons n N( x now ) or the whole N( x now ) to form the cnddte set V( x now ). These solutons re not forbdden or unbound formed under sprton crter. Step 3. For ll solutons n V( x now ), get the optml one next now next nd denote t by x, nd let x = x, N =N +1. * Step 4. () If F( x now ) < F( x ), let x * = x now, N opt =1; (b) Else let N =N +1. opt opt Step 5.Updte T, then goes to step 2 V. CASE STUDY A. Scenro In ths secton, we pply our model nd lgorthm to ssess the potentl benefts. Here we use deprture dt on 11th December 2006 n Shngh Termnl Are bsed on the flght dt from Opertons Mngement Centre of Ar Trffc Mngement Bureu, CAAC. Shngh Termnl Are s one of the busest termnl res n Chn whch covers two hub rports, nmely Shngh HongQo Interntonl Arport (ZSSS) nd Shngh PuDong Interntonl Arport (ZSPD). A smplfed termnl rspce s shown n Fgure 5. There re totl of 567 flghts tht re scheduled to deprt from Shngh Termnl Are (252 from ZSSS nd 315 from ZSPD) durng tht dy. The deprture demnd t the rports dstrbuted for ech hour s shown n Fgure 6. We select the flghts from 15:00 to 16:00 s the nput n our experment. Tble 1 shows the sttstcs result of deprture flghts for ech rport through dfferent fxes durng the perod. Fgure 5. Stndrd Instrument Deprture of Shngh Termnl Are (From AIP) ter ter Step 2. () If N ter =MAX_ITER,or N opt =MAX_OPT, termnte the lgorthm nd output the optmzed soluton.

6 Number of Deprture Flghts ZSPD ZSSS Tme Perod Fgure 6. Hstogrm of deprture rtes t Shngh termnl re on Dec.11, 2006 Tble 1. Sttstcs result on number of deprture flghts from 15:00 to 16:00 Fx HSN LAMEN ODULO PIKAS SX Totl Arport ZSPD ZSSS Totl In ths experment, the mnmum runwy seprton s 2 mnutes s ll rcrft types n experment re ether hevy or medum. The requred tme seprtons t dfferent fxes ccordng to flght destnton re lsted n tble 2. Bsed on the model nd lgorthm descrbed n prevous sectons, we developed prototype system to schedule deprture flghts n mult-rport wth Mcrosoft Vsul C The computng tme s n order of 1 2 mnutes run on PC wth 1.4 GHz processor speed. Below we present the computtonl results usng bove dt under three dfferent cses. Cse A s tht ZSPD s open whle ZSSS s closed. Cse B s tht ZSSS s open whle ZSPD s closed. Cse C s tht both ZSPD nd ZSSS re open durng the perod. Fx HSN PIKAS SX ODULO LAMEN Tble 2. Mnute-In-Trl requrement t deprture fxes Mnute-In-Trl Seprton Flghts to Hong Kong nd Mco requre n 8 mnutes dstnce; others 5 mnutes 7 mnutes Flghts whch deprt from the sme rport requre 7 mnutes dstnce;otherwse 3 mnutes 8 mnutes 5 mnutes ll the flghts from ZSSS nd 25% of the flghts from ZSPD. Therefore, concluson my be mde tht the ntercton of trffc through the PIKAS nd SX hs gret mpct on the whole deprture flow. Hence, smoothng the trffc through PIKAS nd SX s the key element to reduce the verge dely. Tble 3. Comprtve results on rcrft dely under dfferent cses nd polces (n mnute per rcrft) Cse A Cse B Cse C Fx/Arport FCFS Model I. FCFS Model I. FCFS Model I. HSN LAMEN ODULO PIKAS SX ZSPD ZSSS Termnl Tble 4 shows the sttstcs result of seprton between every two consecutve flghts t dfferent fxes. We note tht the verge deprture seprton of ech rport under Cse C s greter thn they open seprtely. Ths result clerly ndctes tht the runwy cpcty s no longer the prmry cuse of flght dely. At the sme tme, n n optml polcy, the seprton t PIKAS nd SX drops to the lowest, 7.09 mnutes (7 mnutes s the lower bound) nd 5.82 mnutes respectvely (see Tble 5.). The cpctes of these two fxes re fully utlzed. Ths s n ccordnce wth the concluson dscussed prevously nd supports tht mkng best use of shred nd crtcl deprture resources s of sgnfcnce n schedulng rcrft deprture t rports. Tble 4. Averge tme ntervls between rcrft t fxes (n mnute) Cse A Cse B Cse C Fx/Arport FCFS Model I. FCFS Model I. FCFS Model I. HSN LAMEN ODULO PIKAS SX ZSPD ZSSS B. FCFS Schedule nd Model I Schedule To llustrte the trffc ntercton between rports, deprture dely result under dfferent cses s summrzed n tble 3. As expected, the verge dely t ech fx (even HSN, LAMEN, nd ODULO) nd rport under Cse C s much hgher thn tht of Cse A or Cse B, no mtter n FCFS polcy or n n optml polcy. It must be ponted out tht the mount of flghts deprtng through PIKAS nd SX exceeds the totl flghts of entre termnl re by 60%, whch ncludes Tble 5. Tme ntervls between rcrft t PIKAS nd SX, Cse C (n mnute) PIKAS SX FCFS Model I FCFS Model I

7 Averge Fgure 7 depcts the deprture sequence nd deprture tme of ech flght. As cn be seen, the deprture tme wth optml sequence re much better dstrbuted thn FCFS sequence n the entre tme-spn. In the optml sequence, flghts from ZSSS nd ZSPD tke off lterntely, nd the verge dely reduces from mnute per rcrft to mnute per rcrft. Deprture Tme (s) Flght Deprt from ZSPD, FCFS Flght Deprt from ZSSS, FCFS Flght Deprt from ZSPD, Model I Flght Deprt from ZSSS, Model I Deprture Sequence Fgure 7. Deprture tme nd sequence for flghts under dfferent polces C. Comprson of Model I nd Model II A comprson of Model I nd Model II ws crred under Fgure 8. Computtonl results on verge dely of Model I nd Model II

8 Cse C to show the nfluence between rports. The grphcl representton of the termnl dely nd rport delys s shown n Fgure 8. As expected, there s lttle fluctuton of termnl dely durng the 100 computtonl tests both n Model I nd Model II (see Fg. 8() nd Fg. 8(b)). Ths could be explned by the nture of the TS lgorthm. As one knd of heurstc lgorthm, TS lgorthm could not gurntee fnd the globl optml soluton. However t provdes you stsfctory soluton wthn n cceptble tme horzon. Attenton should be pd to tht there lwys exst bout 10 mnute dfferences of verge dely between ZSSS nd ZSPD n Model I. Ths s probbly due to the obectve of Model I, whch s to mnmze the verge dely of termnl re rther thn mnmze verge dely of every sngle rport. Although the entre termnl dely of Model II s 2 mnutes hgher thn tht of Model I (see Fg. 8(c)), the dfferences of delys between the two rports decresed to 1 mnute by settng coeffcent α1 = α2 = 2 (see Fg. 8(d)). All of flghts deprt from ZSSS use only two deprture fxes, whch re PIKAS nd SX. Wthout the competton of ZSPD, the lower bound of ZSSS dely s bout 9 mnute per rcrft (see Tble 3.). Tht s the mn reson ZSSS lwys hs hgher dely thn ZSPD. VI. CONCLUSION In ths pper, we proposed new model for solvng deprture schedulng problem n mult-rport system. In the model, both runwys nd deprture fxes were consdered s the crtcl resources of termnl re. The frness mong rlners ws gurnteed by the CPS. Addtonlly, tbu serch lgorthm hs been bult nd relzed n order to get globl optml soluton of the problem. The presented model nd lgorthm were vldted through the opertonl flght dt of Shngh Termnl Are. From the bove dscusson, t seems tht the lmted cpcty of deprture fxes s the mn fctor confnng the growth of deprture flow n mult-rport system. Optmze utlzng the shred deprture fxes wll result n n enhncement of termnl cpcty. Deprture trffc ntercton between rports cn brng the unfrness mong rports. Fortuntely ths cn be elmnted by resonble deprture control strtegy. Some mprovement to the deprture schedulng my be ncludng the rlners preferences n the model. Integrl schedulng deprture nd rrvl flow n termnl re wll be nother chllengng spect n ATFM feld. ACKNOWLEDGMENT The uthors re grteful to Zhen Hung (ssstnt engneer n Ar Trffc Mngement Bureu of Est Chn) for hs comments on n erler verson of ths pper. AUTHOR BIOGRAPHY Ynun Wng receved the B.S. degree n Ar Trffc Control nd the M.S. degree n trnsportton engneerng from Nnng Unversty of Aeronutcs nd Astronutcs, Nnng, Chn n 2004 nd 2007 respectvely. He s currently workng towrd the Ph.D. degree n trnsportton engneerng t the Nnng Unversty of Aeronutcs nd Astronutcs. He hs prtcpted n mny dfferent proects n r trffc mngement system, such s modelng nd nlyss the cpcty of rports nd termnl res, desgnng nd relzng the Ar Trffc Flow Mngement System of Gungzhou Opertng Centre, CAAC. Hs reserch nterests nclude modelng, schedulng, nd optmzng of r trffc system. Mnghu Hu receved the M.S. degree n 1987 from Nnng Unversty of Aeronutcs nd Astronutcs, Nnng, Chn. He s currently Professor wth College of Cvl Avton nd the drector of the Ar Trffc Flow Mngement Insttute, Nnng Unversty of Aeronutcs nd Astronutcs. He s lso the ntonl r trffc flow mngement expert. He s nterested n mny res, ncludng r trffc flow mngement, rport nd rspce cpcty evluton, nd trnsportton plnnng nd mngement. Dong Su receved the Ph.D. degree n 2007 from Southest Unversty, Nnng, Chn. He s currently n ssstnce professor wth College of Cvl Avton nd the drector of the Deprtment of r trffc mngement. Hs reserch res ncludes vton sfety, rspce mngement, controller worklod ssessment. Yong Tn receved the Ph.D. degree n 2009 from Nnng Unversty of Aeronutcs nd Astronutcs, Nnng, Chn. He s currently lecturer t College of Cvl Avton, Nnng Unversty of Aeronutcs nd Astronutcs. Hs reserch nterests nclude ntellgent trffc, rport nd rspce cpcty evluton. Jnmng Zhn receved the B.S. degree n Ar Trffc Control nd the M.S. degree n trnsportton engneerng from Nnng Unversty of Aeronutcs nd Astronutcs, Nnng, Chn n 1994 nd 2003 respectvely. He s currently n r trffc control engneer t Ar Trffc Mngement Bureu of Centrl South Chn. References [1] P. G. Der, The dynmc schedulng of rcrft n the ner termnl re, R76-9, Flght Trnsportton Lbortory, M.I.T, Cmbrdge, USA, [2] H. N. Psrfts, A dynmc progrmmng pproch to the rcrft sequencng problem, FTL R78-4, Flght Trnsportton Lbortory, Cmbrdge, USA, [3] L. Bnco, G. Rnld, S. Rccrdell et l., Schedulng tsks wth sequence-dependent processng tmes, Nvl Reserch Logstcs, vol. 30, pp , [4] J. E. Besley, M. Krshnmoorthy, Y. M. Shrh et l., Schedulng rcrft lndngs The sttc cse, Trnsportton Scence, vol. 34, no. 2, pp , [5] H. Erzberger, Desgn prncples nd lgorthms for utomted r trffc mngement, AGARD Lecture Seres, vol. n. 200, [6] E. P. 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