Airport Apron Capacity Estimation Model Enhancement

Transcription

1 Avalable onlne at Proceda Socal and Behavoral Scences 0 (011) th EWGT & 6 th MEC & 1 st RH Arport Apron Capacty Estmaton Model Enhancement Bojana Mrkovc a,* a Unversty of Belgrade, Faculty of Transport and Traffc Engneerng, Vojvode Stepe 305, Belgrade 11000, Serba Abstract Ths paper dscusses analytcal models for apron capacty estmaton. Two exstng analytcal apron models are descrbed and smple extenson of the models s suggested. Instead of expressng apron capacty by one number, apron capacty envelope s proposed to llustrate capacty changes, or apron capablty to accept dfferent demand, n respect to mx of domnant users n demand. Smlarly to runway capacty envelope that contans nformaton on capacty for one runway system confguraton and gven fleet mx, for dfferent arrval/departure shares, apron capacty envelope provdes nformaton on capacty for one apron confguraton (n respect to stand sze and polcy of usage) and gven fleet mx, for dfferent shares of domnant users n demand. Dependng on the polcy of stand assgnment users can be arlnes/allances and/or dfferent combnatons of orgn/destnaton of flght and level of securty requred (e.g. Schengen/non-Schengen). 011 Publshed by Elsever Ltd. Open access under CC BY-C-D lcense. Selecton and/or peer-revew under responsblty of the Organzng Commttee. Keywords: Arport Apron, Analytcal Modelng, Capacty Estmaton, Apron Capacty Envelope 1. Introducton In the long hstory of arfeld modellng many models (of dfferent level of detal, methodology and scope) have been developed. The great majorty of them were focused on runway system that s consdered to be the major arport capacty constranng factor. Regardng taxway and apron modelng, not much was done n the feld of macroscopc modelng, ether because they were not consdered as a serous capacty constrant, or they were too specfc to be represented generally. Although apron capacty s affected by almost the same factors as runway system capacty (desgn, demand characterstcs, operatonal constrants, and local condtons), the operatonal constrants and relatons to other arfeld elements are very locally specfc and very dffcult to be generalzed, whch s not the case wth runways. Therefore, aprons (together wth taxway system) are usually observed, modeled and resolved on a case-to-case bass and they exst as part of ntegrated hgh level of detal smulaton models. There are few generc apron models that can be found n the lterature. They calculate dynamc apron capacty based on apron layout (number of stands), use strategy (by arcraft sze or user) and weghted average stand occupancy tme of arcraft mx demandng servce. Exstng models are dscussed n Secton 1, and a smple model * Tel.: ; fax: E-mal address: b.mrkovc@sf.bg.ac.rs Publshed by Elsever Ltd. Open access under CC BY-C-D lcense. Selecton and/or peer-revew under responsblty of the Organzng Commttee do: /j.sbspro

2 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) extenson of s proposed. The results from extended model are compared to results obtaned through FAA graphcal gate capacty estmaton approach. In the Secton apron capacty envelope s suggested to llustrate results from the macroscopc apron capacty models. The common way to represent maxmum throughput capacty of the runway system s runway capacty envelope. A runway capacty envelope shows maxmum throughput capacty for one runway confguraton and gven demand structure (fleet mx), but for dfferent arrval/departure shares. Smlar representaton can be used to show maxmum throughput capacty of the arport apron. Proposed apron capacty envelope wll gve range of capacty for one apron confguraton and gven fleet mx, for dfferent shares of domnant users n demand. Concluson and drectons of the future work are gven n Secton 3.. Models for Apron Capacty Estmaton Exstng analytcal apron models calculate dynamc apron capacty based on number of stands and weghted average stand occupancy tme of arcraft mx demandng servce, takng n account restrctons on stand use. Two dfferent models can be found n the lterature. The smpler one assumes that all arcraft can use all the stands avalable at an arport. The other assumes restrcton on stand use t s assumed that arcraft of a certan sze can use the stands that are desgned for that or any larger arcraft. Runway capacty models calculate, so called, maxmum throughput capacty or saturaton capacty. Maxmum throughput capacty ndcates the average number of movements that can be performed on the runway system n 1h n the presence of contnuous demand, whle adherng to all the separaton requrements mposed by the ATM system (De eufvlle and Odon, 003). Smlarly to that, maxmum throughput capacty of the apron (further n the text apron capacty) can be defned as the average number of arcraft that can be served at the apron area (fxed number of stands) n 1h, n the presence of contnuous demand (defned by fleet mx and user mx), whle adherng to all restrctons on stand use. Unrestrcted stand use strategy When there are no restrctons on the stands use, all arcraft can use all the stands, the capacty of the apron can be expressed as: C (1) t total number of avalable stands t weghted average stand occupancy tme of all arcraft demandng servce t p T () p proporton of arcraft class n the populaton of arcraft demandng servce T average stand occupancy tme of the arcraft of class Apron capacty model wth no restrcton for stand use (and numercal examples) can be found n all relevant lterature: Horonjeff (1975), Horonjeff and McKelvey (1994), Ashford (199), De eufvlle and Odon (003), Horonjef et al. (010). Restrcted stand use strategy Second model assumes restrcton n stand use, by the stand sze. It s defned by Horonjeff (1975), reformulated n later edtons (Horonjef, McKelvey, 1994; Horonjef, et al., 010). For restrcted stand use, t s necessary to defne group of stands that can accommodate each arcraft class (classfcaton s based on arcraft sze). It s assumed that a stand can accommodate arcraft class they are desgned for and all smaller-sze arcraft. Apron capacty lmted by each group of stands s calculated from number of stands n the group and weghted average stand occupancy tme of arcraft usng that group of stands. Mnmum of the capactes set by each group of stands s total apron capacty: C mn( C ) (3)

3 1110 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) C s derved from the condton that stand tme suppled has to be larger or equal to stand tme demanded for each user (n ths case s sze of the arcraft grouped nto classes; = 1 s the smallest, = n s the largest arcraft): t C (4) - stand utlzaton factor of the group of stands that can be used by arcraft class - number of stands that may be used by arcraft of class (stands desgned for arcraft class and for arcraft larger than ):... (5) 1 n t - expected stand occupancy tme demanded by all arcraft whch can use stands from th group: t j p T j j p proporton of arcraft class j n the populaton of arcraft demandng servce j T average stand occupancy tme of the arcraft of class j j C - apron capacty lmted by the group of stands avalable for arcraft class If we assume that capacty utlzaton factor s 1 (stands are fully, 100%, utlzed), then we have: C (7) t The condton (4) (gate tme suppled gate tme demanded ) s fulflled for each group of stands, only f we declare the mnmum of the capactes set by each group of stands for total apron capacty (3). Ashford and Wrte (199) explan apron capacty model for restrcted use (by arcraft sze), but under dfferent assumpton. They assume that each stand can be used only for the arcraft they are desgned for (small for small, mddle for mddle, large for large). It s not taken n account that each stand can also accommodate smaller arcraft. So, apron capacty n ther, so called exclusve use apron capacty model, s: C mn( C ) (8) Where apron capacty lmted by the group of stands desgned for arcraft class s: C (9) p T - number of stands desgned for arcraft class (only) p proporton of arcraft class n the populaton of arcraft demandng servce T average stand occupancy tme of the arcraft class Ths apron capacty model for exclusve use s not sutable for apron capacty estmaton wth restrcton by stand sze, snce the man assumpton s not sutable for ths case. But, such approach can be appled for capacty estmaton of apron wth exclusve use of stands by dfferent arlnes (typcal for U.S. arports), or by dfferent users based on other crtera lke securty level requred (e.g. Schengen/non-Schengen separaton, typcal for European arports). When we have apron wth separate areas exclusvely used by one user each, one can (ncorrectly) conclude that total capacty of the apron s sum of the capactes of these separate areas: C (10) T But, that s not the case. To what extent each apron area s utlzed depends on share of users n demand ( p ). The most restrctng apron area restrcts total apron capacty: C mn( C ). At the same tme other areas are underutlzed. To clarfy ths, let s observe an apron wth two separate apron areas, one for arlne X and one for arlne Y. And let s take, for example, extreme demand case - n an hour we have all flghts operated by arlne X (no flghts of arlne Y). Under such demand structure, total capacty of the apron s equal to (restrcted by) capacty of apron area X, whle at the same tme apron area Y s completely unutlzed. (6)

4 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) Apron capacty model extenson Based on prevously dscussed models an extenson s here proposed, that combnes sze and user restrctons. Mnmum of the capactes set by each j group of stands s apron capacty ( user, j arcraft sze): j C mn C mn (11) j j j t j - number of stands that may be used by user class and arcraft of class j (stands desgnated for user, j desgned for arcraft class j and stands desgned for arcraft larger than j) t - expected stand occupancy tme demanded by all arcraft whch can use stands from ths group j C - apron capacty lmted by the group of stands avalable for user class, arcraft class j j In ths model users can be dfferent arlnes (typcal U.S. stand usage strategy - exclusve, preferental, jont), and/or dfferent type of flghts n respect to destnaton/securty level requred (typcal for European arports - Schengen, non-schengen, nternatonal, domestc, specal countres requrements). Example 1: An apron conssts of two areas. One s area for Schengen flghts (comng from and gong to Schengen countres) and second area for Other flghts. (Other flghts, further n the text, non-schengen/non- Schengen and mxed Schengen/non-Schengen rotatons). Schengen area has stands for arcraft class 1 and stands for arcraft class. Area for other flghts s conssted of 1 stand for arcraft class 1, stands for arcraft class and 3 stands for arcraft class 3. Demand structure and average stand occupancy tmes are gven n the Table 1: Table 1. Demand structure and average stand occupancy tmes, example 1 number of stands user arcrfat class share n populaton (%) avg. stand occupancy tme (mn) Schengen Other flghts In ths example we have 5 groups of stands: 1. group of stands for Schengen flghts, arcraft class 1 ( 11 4). group of stands for Schengen flghts, arcraft class ( 1 ) 3. group of stands for Other flghts, arcraft class 1 ( ) 4. group of stands for Other flghts, arcraft class ( 3 5) 5. group of stands for Other flghts, arcraft class 3 ( 3) Expected stand occupancy tme demanded by all arcraft whch can use stands from these groups s: 1. t 11 0,3 30 0, ,5 mn. t 1 0,1 45 4,5 mn 3. t 1 0,1 30 0,3 45 0, 80 3,5 mn 4. t 0,3 45 0, 80 9,5 mn 5. t 3 0, 80 16,5 mn 3 Apron capacty under gven demand structure s: C mn C, C1, C1, C, C3 mn 17,8;6,7;11,1;10,;11,3 10, 11 arcraft/h Comparson to FAA graphcal method For quck estmaton of apron capacty there s also FAA s graphcal method (Advsory Crcular 150/5060, Arport Capacty and Delay, 1983). An example from AC 150/5060 s used and the results from graphcal approach are compared to results from analytcal model prevously explaned. Example (from AC 150/5060): An apron has 10 stands allocated to three arlnes, X, Y and Z. Apron X has 4 stands for small (narrow-body) arcraft and 1 stand for large (wde-body) arcraft, apron Y has stands for small and 1 for large arcraft and apron Z - stands for small arcraft. Durng an hour arlne X schedules 13 small arcraft

5 111 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) wth an average stand occupancy tme (SOT) of 45mn, and large arcraft wth an average stand occupancy tme of 55mn. Arlne Y schedules 8 small (SOT=40mn) and arlne Z 4 small arcraft (SOT=35mn). If we express numbers of flghts as shares n total demand (Table, column 4) we can estmate apron capacty usng extended apron capacty model. Table. Demand structure and average stand occupancy tmes, example number of stands user user share n populaton (%) avg. stand occupancy tme (mn) arlne X arlne Y arlne Z Apron capacty s lmted by the frst (of 4) group of stands: C mn C11, C1, C1, C31 mn 60, 60, 60, 60 0, , , ,3 40 0,1535 C mn 11,8;15,6;15;,8 11, arcraft/h 8 Graphcal approach proposed by FAA, Fgure 1, calculates hourly apron capacty expressed n movements/h as: G * S, where: G* s hourly gate capacty base, S s gate sze factor and s number of gates. Fgure 1. FAA s graphcal method to calculate hourly gate capacty

6 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) For the gven example, t s calculated (Table 3) that apron hourly capacty s: 13 movements/h for apron area X, 9 movements/h for apron area Y and 7 movements/h for apron area Z. They calculate total capacty of the termnal (ncorrectly) as a sum of these three whch makes 9 movements/h. Table 3. Calculaton of the parameters for graphcal approach, example In order to enable comparson of the results from FAA s graphcal approach to analytcal model results, we observe apron areas X, Y and Z separately. We have: For apron area X: 5 1 C mn 60, 60 6, 5arcraft/h x 0, , ,13 55 (share of wde-body/nonwde-body arcraft f we observe only flghts of arlne X, s 87/13 %) For apron area Y: 3 C 60 4, 5 arcraft/h y For apron area Z: 1 C , 4 arcraft/h z (arlne 1Y 35and Z operate all flghts, 100%, wth nonwde-body arcraft) Capactes by apron area calculated from graphcal approach (expressed n movements/h) are double then values calculated analytcally (expressed n arcraft/h). As a quck approxmaton, on can multply the dynamc capacty of the apron by two to convert t to movements per hour, as the occupancy of a stand s assocated wth two movements on the runways, an arrval and a departure (De eufvlle and Odon, 003). If we apply that approach, then we get the same result (by X, Y and Y area) as obtaned from graphcal approach. evertheless, the fnal result from graphcal approach s defntely wrong. As dscussed before, capactes of ndvdual areas cannot be summed. Each area restrcts total apron capacty to the certan level, dependng on mx of users n demand. Capacty restrcton set by each apron area has to be calculated n respect to share of each arlne n total demand (respectvely 55%, 30% and 15% for arlne X, Y and Z) and mnmum adopted as total apron capacty: C C x y Cz C mn,, mn 11,8;15;,8 11, 8 0,55 0,3 0,15 arcraft/h Speakng of transformaton arcraft/h nto movements/h, De eufvlle and Odon (003), except multplyng by two to transform arcraft/h nto movements/h, suggest more prudent approach. It takes nto consderaton that demad dstrbuton at the arport s such that contans perods durng whch there are consderably more arrvals than departures, and vce versa. More realstc approach to obtan the equvalent capacty expressed n terms of movements per hour s do dvde apron capacty to the largest fracton of arrvals n the traffc mx durng ceratn tme nterval. For example f we have 65% of arrvals and 35% of departures, equvalent apron capacty (from prevous example) n movements/h would be: 11,8 18, movements/h (nstead 11,8 3, 6 movements/h). 0,65 Dscussed analytcal apron models are sutable for quck capacty estmaton for small aprons havng smple sze and user restrctons. For apron areas that have flexble layouts n respect to arcraft types that can be accommodated and/or dfferent users of apron areas (ether by arlne, or type of traffc) ths calculaton can be qute tedous. Apron becomes much more complcated to model wth ncluson of more complex user restrctons, sze restrctons, dfferent turnaround tmes, buffer tmes, etc. Anyway, these models can serve as a good bass for furter mprovement n analytcal apron modellng feld. All these examples assume that all stands are fully utlzed. In order to get a better (more realstc) estmate of apron capacty, calculated values should be multpled wth stand utlzatons factor. Horonjeff and McKelvey

7 1114 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) (1994) nclude utlzaton factor n the calculaton. For each group of stands, stand tme suppled have to be larger or equal to stand tme demanded. For th group of stands: t C (1) In the expresson represents percentage of tme n an hour that the stands from th group can be used by all arcraft that can use stands from group. So, apron capacty s: C mn( C ) where restrcton set by the group of stands s: C (13) t Another approach for gettng more realstc estmaton s to add postonng tme and buffer tme together wth stand occupancy tme to obtan stand blockng tme. De eufvlle and Odon (003) defne Stand Blockng Tme (SBT) as sum of Stand Occupancy Tme (SOT), Postonng Tme (PT) and Buffer Tme (BT). Frst value depends on sze of arcraft, flght dstance, arlne, busness model (low-cost, tradtonal, general avaton, etc.). SOT ranges from 0mn (small regonal arcraft) to 4h (wde-body ntercontnental flghts). PT can range form mn to 10mn dependng on whether arcraft s pushed back or t does power n /power out. BT between two consecutve users of the same stand s somethng that s desrable to plan at the arport to absorb dsturbances n flght schedule. Dependng on the local crcumstances t can range from several mnutes to an hour. 3. Apron Capacty Envelope Apron modelng was left n a shade of runway modelng snce runway system s consdered to be major arport capacty constrant. Analytcal runway modelng for runway maxmum throughput capacty estmaton s set by Blumsten n Blumsten developed model to calculate landng (arrval only) sngle-runway capacty. Many extensons are developed up to now for calculaton of departure and mxed operatons capacty, for sngle runway and multple runways, for dfferent procedural and technologcal changes. The common way to llustrate maxmum throughput capacty for a gven confguraton of the runway system and gven demand structure s runway capacty envelope, Fgure. departures arrvals apron capacty (arcraft/h) 5 Sch.fl. stands + 6 ALL fl. stands schengen/other flghts share (%) Fgure. Runway capacty envelope, sngle-runway Fgure 3. Apron capacty envelope, example 3 It contans 4 typcal ponts, representng dfferent arrval/departure shares. Pont 1 represents capacty of arrvals only. Pont represents, so called, departure free capacty, consders addtonal departures whch can be performed wthout any changes n arrvals separatons. Pont 3 represents capacty under 50/50% arrvals/departures share, and Pont 4 s departures only capacty. In the lterature there s nothng smlar to llustrate apron capacty. Ths paper suggests possble shape(s) of apron capacty envelope to llustrate apron capablty to accept gven demand. A runway capacty envelope gves maxmum throughput capacty for one runway system confguraton, for gven demand structure, but dfferent share of arrvals and departures. Runway capacty s expressed n movements/h.

8 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) Smlarly to that apron capacty envelope could represent maxmum throughput capacty of the certan apron confguraton and gven demand structure (fleet mx, share of dfferent arcraft classes) for dfferent share of users. Apron capacty s expressed n arcraft/h. Example 3: An apron has 11 stands of whch 5 stands are avalable only for Schengen flghts and 6 stands are avalable for all rotatons (Schengen and Other). Average stand occupancy tme for Schengen flghts s 45mn, and for Other flghts (non-schengen/non-schengen and mxed Schengen/non-Schengen) 50mn. If we assume demand of 50% Schengen flghts and 50% of Other flghts apron capacty s 13,9arcrfat/h. Apron capacty change wth user structure change n total demand s shown n the Fgure 3. Fgure 3 s an example of apron capacty envelope. Wth apron confguraton change the shape of apron capacty envelope changes. Fgures 4 and 5 represent set of apron capacty envelopes for dfferent apron confguraton (dfferent number of stands avalable for Schengen flghts and stands for all flghts). As number of stands for all flghts ncrease, flexblty of apron s hgher and apron s less senstve on user mx n total demand (Fgure 4). And opposte, as the number of exclusve use stands (only for Schengen flghts) ncrease, apron s more senstve on share of dfferent users n total traffc, Fgure 5. apron capacty (arcraft/h) 5Sch/6All 4Sch/7All 3Sch/8All Sch/9All 1Sch/10All schengen/other flghts share (%) apron capacty (arcraft/h) 5Sch/6All 6Sch/5All 7Sch/4All 8Sch/3All 9Sch/All 10Sch/1All schengen/other flghts share (%) Fgure 4. Set of apron capacty envelopes, ncrease n number of mxed use stands, example 3 Fgure 5. Set of apron capacty envelopes, ncrease n number of exclusve use stands, example 3 Ths s only smple example to show possble llustraton of apron capablty to accept for dfferent demand structure, and how t changes wth apron operatonal constrants changes. In ths example demand structure s gven n share of Schengen/Other flghts. Dependng on the polcy of stand usage at the apron t can be expressed n respect to other users, e.g. arlnes/allances. If we have combned restrctons (dfferent types of users, arcraft sze) there are many possble combnatons that could be analyzed. But, not all of them are n the scope of out nterest. For the purpose of comparson between dfferent scenaros we can observe set of selected segments of apron capacty envelope. Example 4: An arport has an apron of 11 stands, of whch 5 stands are for Schengen flghts and 6 are for Other flghts. At Schengen apron 3 stands are desgned for arcraft class 1 and stands for arcraft class. Apron for Other flghts s conssted of 1 stand for arcraft class1, stands for arcraft class and 3 stands for arcraft class 3. Table 4. Demand structure and average stand occupancy tmes, example 4 Table 5. Fleet mx by the users, current and future demand, example 4 fleet mx by users (%) avg. stand number of share n user arcrfat class occupancy user arcraft current future stands populaton (%) tme (mn) class Schengen Other flghts Schengen Other flghts Share of flghts (by type of flght and arcraft class) and average occupancy tmes are gven n the Table 4. Demand consst of 40% Schengen flghts and 60% Other flghts. 70% of Schengen flghts are operated by arcraft

9 1116 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) class 1 and 30% wth arcraft class. 15% of Other flghts are operated wth arcraft class 1, 50% wth arcraft class and 35% wth arcraft class 3 (Table 4). Let s assume that ncrease n Schengen flghts s predcted for the future, as well as change n fleet mx. Three demand scenaros are nvestgated: 50/50, 60/40 and 70/30 share of Schengen/Other flghts. Fleet mx by users are gven n the Table 5. Three possble Scenaros are consdered as a response to demand change n the future. Scenaro 1 assumes changes n layout at Schengen apron. One small stand for arcraft class 1 s wden to accept arcraft class. So, we have small and 3 mddle-sze stands n ths scenaro. Scenaro assumes changes n operatonal constrants. Layout s the same as n the current state, but second termnal s also allowed to accept pure Schengen flghts, all stands for Other flght are avalable for Schengen flghts at the same tme. Scenaro 3 ncludes both changes n layout (the same n Scenaro 1) and operatonal constrants changes (as n Scenaro ). We have more flexble apron then n basc scenaro wth one wder stand n the pure Schengen area. Apron capacty envelopes (not complete, but relevant segments) are gven for n the Fgure 6, for basc and three proposed scenaros. apron capacty (arcraft/h) basc scenaro1 scenaro scenaro3 current AC 0 50/50 60/40 70/30 schengen/other flghts share (%) Fgure 6. Set of apron capacty envelopes for dfferent scenaros, example 4 Blue lne n Fgure 6 shows how exstng apron (basc scenaro) reacts on changes n demand. For the 50/50% share t wll provde somewhat hgher capacty (by 11,4%) then wth current demand structure (uder whch we have underutlzed Schengen apron). Wth further ncrease of Schengen flghts share, apron capacty falls under current capacty level (dashed lne, Fgure 6), and contnue decreasng wth ncrease of Schengen flghts share. Changes n apron capacty (n %) relatve to current capacty level (10,6 arcraft/h) are gven n the Table 6 (column 1, for Basc Scenaro). Table 6. Apron capacty changes (n %) relatve to current apron capacty level (10,6 arcraft/h), example 4 Sch/Oth flghts share Basc Sc Scenaro 1 Scenaro Scenaro 3 50/50 11,4 6,0 1,5 6,0 60/40-7, 7,9 31,4 46,5 70/30-0,4 9,6 43,0 51,5 In all three Schengen/Other flghts share cases, Scenaro 1 provdes hgher apron capacty (than current level, and than Basc Scenaro as well) for gven demand structures (pnk lne, the Fgure 6; column, Table 6). Although better than Basc Scenaro, Scenaro 1 responds well on Schengen share ncrease to the certan level, after whch msmatch between share of stands by the users and share of users n demand appears and apron capacty decreases. In Scenaro (red lne, the Fgure 6) the apron capacty s smlar to Scenaro 1 for 50/50 and 60/40 mx of Schengen/Other fghts. Wth more sgnfcant ncrease n Schengen flghts (70/30 mx), Scenaro s much better

10 Bojana Mrkovc / Proceda Socal and Behavoral Scences 0 (011) then Scenaro 1 due ts flexblty n use. For 70/30 mx case Scenaro provdes apron capacty by 43% hgher than current capacty (column 3, Table 6), aganst 9,6% n Scenaro 1. As expected the most sgnfcant mprovement we have n Scenaro 3 whch consders both changes n layout (the same as n Scenaro 1) and operatonal constrants changes (as n Scenaro ). Apron capacty envelop (relevant segment) for Scenaro 3 s presented by green lne n Fgure 6. Scenaro 3 provdes capacty ncrease from 6% to 51% (Table 6, n column 4) dependng on Schengen/Other flghts mx. For comparson of the scenaros t s also mportant to consder the cost of changes at supply sde (e.g. extenson of the apron area, or changes nsde termnal buldng regardng securty zones to enable flexble termnal apron usage). The best scenaro(s) are those whch provde acceptable capacty/demand match under acceptable cost. 4. Concluson Exstng analytcal apron models calculate dynamc apron capacty based on apron layout (number of stands per arcraft class and per stand users) and weghted average turnaround tmes for all arcraft demandng servce. They are sutable for quck capacty estmaton for small aprons havng smple sze and user restrctons. For of apron areas that have flexble layouts n respect to arcraft types that can be accommodated and/or dfferent users of apron areas (ether by arlne, or type of traffc) ths calculaton can be qute tedous. Apron becomes much more complcated to model wth ncluson of more complex user restrctons, sze restrctons, dfferent turnaround tmes, buffer tmes, etc. Sometmes average tmes are good approxmaton of turnaroundtmes, as t s the case for low cost arlnes, whch bussness model s such that t requres short turnaroundtmes, and they fly from pont-to-pont. On the other hand tradtonal arlnes, dependng on the range of flght can have turnaroundtmes form 0mn to several hours. Typcal turnaround tmes for a range of arcraft and flght types become longer as flght dstance ncrease. To provde more realstc estmates of apron capacty postonng and buffer tmes have to be taken nto consderaton and/or, utlzaton factor of apron area. Transformaton of apron capacty n movements/h s mportant n order to make t comparable to runway capacty, but more mportant s to defne correct relatonshp between these two elements. Ther functonal relatonshp depends on many factors lke: type of arport (e.g. hub, non-hub), domnant market segments (e.g. scheduled, charter, low-cost, general avaton), arfeld elements desgn, etc. Future work s drected towards creatng flexble apron model capable of delverng apron capacty envelopes for more complex apron confguratons wth ncluson of other parameters that provde for more realstc (rather then overestmated) apron capacty. Acknowledgement Ths research work s supported by the Mnstry of Scence, Republc of Serba, under the research programme n technologcal development, Project TR References Ashford,.J., Wrght, P.H. (199) Arport Engneerng (3 rd edton). John Wley & Sons Inc. Hoboken, Unted States, (Chapter 7) De eufvlle, R., Odon, A. (003) Arport Systems- Plannng, Desgn and Management. McGraw-Hll, ew York, Unted States, (Chapter 10) Federal Avaton Admnstraton (1983). Advsory Crcular 150/5060, Arport Capacty and Delay Horonjeff, R. (1975) Plannng and Desgn of Arport ( nd edton). McGraw-Hll, ew York, Unted States, (Chapter 5). Horonjeff, R. and McKelvey F.X. (1994) Plannng and Desgn of Arports (4 th edton). McGraw-Hll, ew York, Unted States, (Chapter 8). Horonjeff, R., McKelvey F.X., Sproul, W.Y. and Young, S.P. (010) Plannng and Desgn of Arports (5 th edton). McGraw-Hll, ew York, Unted States, (Chapter 1).