Capacity Planning Based on Scenario Tree and Passenger Motion Equation (IKIA and MIA)

Transcription

1 Journal of Geotechnical and Transortation Engineering Volume 1 Issue 2 Caacity Planning Based on Scenario Tree and Passenger Motion Equation (IKIA and MIA) Shabaniveri et al. Received 7/23/2015 Acceted 8/12/2015 Published 12/15/2015 Corresonding Author: H.Shabaniveri; hesam@shabaniveri.com Caacity Planning Based on Scenario Tree and Passenger Motion Equation (IKIA and MIA) Hesam Shabaniveri Urban Planning, Lusofona University, Lisbon, Portugal hesam@shabaniveri.com Amir Reza Mamdoohi Transortation Planning, Tarbiat Modares University, Tehran, Iran armamdoohi@modares.ac.ir Mahmoud Saffarzadeh Civil and Environmental Engineering Faculty at Tarbiat Modares University, Tehran, Iran saffar_m@modares.ac.ir Abstract Demand for air travel has increased in quantity and quality, lie reflight services and communications systems, necessitating more serious attention to air terminal caacity lanning. Caacity lanning, esecially when uncertainty exists about future levels of assenger demand is also considered, becomes even more comlex. The roblem of random, multistage and nonlinear modeling must be adated to include a multi-commodity networ flow structure which shows the flow of assengers at terminals. In this aer a caacity lanning aroach is utilized based on the concets of scenario tree and motion equations of assengers, and imlemented for assenger terminals of the two major International Airorts (IKIA & MIA) in Tehran, Iran. Results of mathematical rogramming model for these case studies indicate that increasing the caacity of the assenger terminal in IKIA can increase the roductivity of the existing sace and the whole airort which is also very economical. At MIA, it would be necessary to increase the effective width of corridors and to increase number of rocessing stations. Keywords: airort assenger terminal, caacity lanning, Multistage Stochastic Programming, Imam Khomeini International Airort, Mehrabad International Airort 1. Introduction The nature of air transortation is different from other modes of transortation, e.g. airorts may be considered the most imortant comonent since they tend to be the bottlenec of the system. Major bottlenecs are at airort assenger terminals since the total caacity of the system deends on the maximum volume of assengers who can use the airort. Considering the increasing demand for air travel, assenger terminals need to satisfy this demand, otherwise these terminals will serve as bottlenecs reducing the caacity of the airort meaning that the rest of the airort facilities will not be fully utilized. One way to increase caacity is to increase the number of assenger terminals [1]. However acquiring land on which to build a new terminal often is not ossible due to high costs. Building also increases the number of rogrammable terminals without necessarily romoting otimal oeration. The airort assenger terminal lays a vital role in lanning different features such as assenger volume, location and number of outut gates, hallways and corridors and emergency exits. Efficient use of airort caacity was analyzed by Fernandes & Pacheco [2], considering assenger demand, and the time required to develo caacity to maintain high standards of service that assengers need. One main objective in the analysis of airort terminal caacity is to minimize assenger delay. Therefore, an essential comonent of the caacity lanning model is to accurately estimate the time it taes for assengers to traverse assageways and delay times at rocessing stations. It is also imortant to reduce delays and costs resulting from reductions in waiting time of flights and to lower travel duration [1]. A stochastic version of the general networ design roblem has been studied by Riis & Andersen [3] and Andrade et al. [4] within the context of telecommunication networ design. In these studies, two-stage stochastic rogramming models with linear costs are described. Riis & Andersen extend this aroach to the multieriod case, using a two-stage model [3]. Another two-stage stochastic model based on the Steiner tree roblem is described by Guta et al., where a linear rogramming rounding aroximation algorithm is roosed as a solution rocedure[5]. Most efforts to solve such roblems have been roblem-secific since there are no ractical general urose algorithms for multistage stochastic integer rogramming roblems. The roblemsecific efforts are based on decomosition rocedures through 53

2 Journal of Geotechnical and Transortation Engineering vol. 1 (2) column generation [6, 7]. The deterministic equivalent of a stochastic integer roblem can be solved by branch and bound methods [4], however for most roblem formulations, this multistage structure leads to a large number of integer variables, leaving the roblem extremely difficult to solve. In this aer, a assenger terminal caacity lanning based on scenario tree and motion equation of assengers is alied: a multistage stochastic integer rogramming model for the caacity lanning roblem for airort terminals is addressed. We calculate waling and waiting (rocessing) delays searately and develo delay time aroximates for each of the two case studies (namely Terminal 1 of Imam Khomeini International Airort- IKIA- and Terminal 2 of Mehrabad International Airort- MIA): the origin and destination of rocesses are considered in the calculation of the total time, which includes assenger waling time. Efficient use of existing terminals will determine the bottlenec caacity of airorts in coordination with the various facilities for assengers. 2. Research Methodology To consider all delays at the terminal, roblem formulation and mathematical modeling in this research is decomosed into two hases: the first includes the time that assengers are moving (waling) between different stations (rocessing or service stations) within the assenger terminal; and the second includes the time that assengers are waiting at these stations to receive service. Characteristics and behavior of assengers at terminals, including waiting halls, rivate rooms, rocessing stations, and servicing, are also taen into account as design comonents. If aviation industry forecasts [1, 3] over the coming decades are realized, worldwide RPK will grow at an average rate of aroximately five ercent er annum over the next 20 years, resulting in about 8 ercent increase er year in assengers [8]. Based on these figures, flight schedules over one year were used to estimate assenger arrival rates in this research. Sola et al. determined three aroximations to reresent the shae of a ea to estimate the maximum queue length. In this aer, we calculate waling and rocessing delays searately and develo delay time aroximates for each of the two areas under study. Validity of the time functions are then analyzed by comaring them with simulation results based on the actual airort, terminal number 1 of IKIA and terminal number 2 of MIA. Waling time is calculated using equation 1 [1]: terminal as described by the system equilibrium concet of Wardro [10]. A scenario tree is a viable way of taing the underlying dynamic stochastic data over time and discretizing it to solve a roblem. Each stage in a scenario tree denotes the stage of time when new information is available to the decision maer. The stages might include a number of eriods in the lanning horizon, not necessarily corresonding to time eriods [1] The scenario tree of this research (Fig 1) has three stages, each with two assenger tyes that enter or exit the terminals, while it has four combinations of assenger demand in future: low-low, low-high, high-low, and high-high. Three eochs, each 5 years long, are considered to have a forecast for next 15 years. Moreover, each arc in this tree has its secific robability, indicating the robability that each node and arc may occur. Table 1 shows LL, HL, LH and HH robability for the three stages, based on which: Lowest robability is associated with LL scenario. Probability changing rate is equal to 5 ercent for LL scenario. Strongest scenario is HH which also increase during the 3 stages [11]. Software acages MatLab and Rocwell Arena 13.5 were used for simulation uroses. In the second hase, all the formulas obtained from the first (otimization roblem) were fed into Lingo 8.5 software acage to solve the roblem. For validation of the simulation rocess, (surveys of) actual assengers at different stations in the assenger terminals were used. Table 1: Probabilities in the Scenario Tree of the Research [11] Pen LL LH HH HL S (1) where, ф is the density of assengers (assenger er square meters) and S is the average waling seed of assengers (meter er second). Maximum delay estimation at the rocess stations (as a function of flow and caacity) assuming a deterministic aroximation with varying arrival rates and constant rocess rates based on fluid aroximations was suggested by Newell [9]. Simulation with Arena is an effective tool for assessing the delay time functions in rocessing stations [6]. Considering a multicommodity flow networ, different tyes of assengers corresond to different commodities. Using this model, several objective functions can be considered. For examle, the model could minimize the worst case scenario of the maximum total time sent in the system by a assenger who is routed through the networ regardless of the route. Another objective could be to minimize the maximum delay at each assageway and rocessing station. We assumed that the assenger flow during ea demand eriods is distributed otimally among alternate routes within the airort Fig.1: Scenario Tree scheme for IKIA and MIA airorts [11] The research integer model is based on the model resented by Sola et al. (2009) and modified according to the roblem size for the secific case studies. The mathematical rogramming roblem is to minimize the objective function (z) resented in equation 2 [1]. ρ ω minimize z= å å f t (.)+ n nl nl å å f t (.) n nl nl (2) nî T lî A nî T lî A P w s.t. x n,ij- x =0 n,, iï{ O D R} å å (3) j V:(i,j) A j V:(i,j) A å x n,ij=d in n,, i O j V:(i,j) A (4) 2 54

3 Shabaniveri et al. å x = å d n, K, i D (5) d j V:(i,j) A ' i O å x = å d n, K, i D (6) d j V:(i,j) A ' i O å x = å å x n, K, i D (7) n.ji ' ' n,i,j j V:(i,j) A ' ' i R j V:(i,j) A å å å x = x n, K, i D n.ji ' ' n,i,j j V:(i,j) A ' ' i R j V:(i,j) A (8) å d å å (9) j O jn ' å x n,ij-u ' ' =0 n, (i,i) A n,i i, j V:(i,j) A ' ' d K jn ii ' j O u + å ε =u n, l A (10) 0 1 ml nl m P(n),m n u nl-fnl 0 n, l A (11) (1-c )f -u 0 n, l A (12) nl nl nl Q (x nl,u nl,f nl,ε nl) 0 n,,l (13) x,u,f,ε,u,w 0 n,,l (14) 0 0 nl nl nl nl 1 1 V { 0,1 } n N,n 0, l nl (15) Networ node balance (or flow conservation) constraints are reresented by constraints 3 to 7. Constraints 8 and 9 indicate overall caacity of the networ. Constraint Number 10 shows that flow in nodes and arcs is deendent on time. Constraints 11 and 12 roviding for conditions under which the caacity of rocessing stations is between the average and maximum flow. Constraint 13 shows a vector that rovides additional constraints on the networ. Constraints 14 and 15 show the decision variables of the roblem. 3. Research Case Studies The emirical case of this research includes two of the main airorts in Tehran, caital city of Iran: namely Terminal 1 of Imam Khomeini International Airort (IKIA) and Terminal 2 of Mehrabad International Airort (MIA). These most congested terminals are selected due to their large number of flights and since access to technical information and flight schedules for these airorts were also available. Data for the years 2010 and 2011 are used regarding these airorts and their assengers and based on them, redictions for the next 5 and 20 years are conducted [11] IKIA assenger terminal No. 1 Based on assenger distribution at IKIA assenger terminal No. 1 (Figure 2) for ea hour traffic for the first hundred ea hours of the year, the busiest time of the year with 3125 assengers is on 7th of Aril from 03:45 to 04:45 hours. The thirtieth and fortieth busiest time haen on 27th of March (with 2116 assengers) from 04:35 to 05:35 hours, and on 3rd of May (with 2027 assengers) from 03:45 to 04:45 hours, resectively. This terminal will also be busy for 144 hours in Aril, 23 hours in June, 21 hours in March and in August, and 10 hours in May and Setember (Table 2) [11]. Fig.2: Passenger Distribution at IKIA Passenger Terminal (V-axis: Passenger number, H-Axis:1st 100 ea hours) Dearture ea hour of this terminal for 100 ea hours indicates that the busiest hour of the year (with 1964 assengers) is on 27th of March from 04:35 to 05:35 hours. The thirtieth and fortieth busiest time is on 22 August (with 1481 assengers) from 06:20 to 07:20 hours, and on 26th of March (with 1447 assengers) from 07:55 to 08:55 hours, resectively. The same measures for Arriving assengers of this terminal are 2698 assengers, on 7th of Aril from 03:35 to 04:35 hours. The thirtieth and fortieth busiest time occur on 30th of March (with 1534 assengers), and on 31st of Setember (with 1470 assengers), resectively (Table 2) [11]. Table 2: Probabilities in the Scenario Tree of the Research [11] tye 1 st 30 th 40 th BTP DBTP BTP DBTP BTP DBTP IKIA T 3125 Ar Mar May 3 D 1964 Mar 1481 Aug Mar A 2698 Ar Mar Se 31 MIA T 2779 Dec Jan Dec 30 D 1983 Mar 1659 Jun Mar A 1883 Mar Mar Jul 9 Where T=Total, D=Dearture, A=Arrival, BTP is Busiest Time Passengers ; DBTP is Date of Busiest Time Passengers MIA assenger terminal No. 2 MIA has six assenger terminals, one of which (number 2) has an area of square meters with 32 chec-in counters. The busiest time of the year with 2779 assengers is between 12:45 and 13:45 hours on 4th of December (Figure 3). With 2134 assengers, the thirtieth hour occurs on 22 January between 12:25 and 13:25 hours. The fortieth hour with 2097 assengers occurs on 30 December between 13:15 and 14:15 hours. The busiest times of this terminal include 141 hours in December, 37 hours in January, 10 hours in February, 7 hours in October and 4 hours in March and August [11]. 3 55

4 Journal of Geotechnical and Transortation Engineering vol. 1 (2) Table 4: Passenger Terminal Facilities for IKIA and MIA MIA IKIA Fig.3: Passenger Distribution at MIA Passenger Terminal (V-axis: Passenger number, H-Axis:1st 100 ea hours) From Table 2, it can be observed that the busiest time of the year for dearture at MIA with 1983 assengers occurs on 14th of March between 6:35 and 7:35 hours. The thirtieth ea hour with 1659 assengers occurs on 17th of June between 5:55 and 6:55 m. There were 1624 assengers at fortieth ea hour on 10th of March between 6:15 and 7:15. Rush hours of this terminal arrival are rather uniform with a gentle sloe. The busiest time of year, with 1883 assengers on 22nd of March occurs between the hours of 22:55 and 23:55. The thirtieth and fortieth with 1434 and 1416 assengers, resectively, occur on 21st of March between 8:00 and 9:00 hours and on 9th of July between 23:30 and 00:30 (Table 2) Other characteristics of IKIA & MIA As another inut set of arameters of the lanning roblem, each airort secial characteristics and roerties including facilities, area, and number of gates as well as length and width of corridors need to be considered. Table 3 resents these characteristics for IKIA and MIA as alied in model estimation. Some other observations secific to these terminals are: gates at IKIA are located in such a way that at ea hours (large aircrafts), they cannot wor at full caacity; and in MIA Terminal No.2, there is no assort control because it oerates for only domestic flights [7]. Table 3: Passenger Terminal Facilities for IKIA and MIA Tye of facilities IKIA counters MIA counters Total Active Total Active Chec in Passort Police Gate Baggage Model Results For estimation of assenger arrival equations to each terminal, simulation was adoted for higher recision. Using Arena software acage, we studied assenger arrival rates and estimated the arrival equations as resented in Table 4. The best fit for these equations was observed to have Beta distribution [11]. There is, naturally, a difference (although not very large) between the estimated equations as exected, due to e.g. different number of assengers and different nature of these terminals. Exression * * BETA(4.85, 1.7) BETA(4.08, 1.55) Square Error Chi-Square Test Results Number of intervals Degrees of freedom Test Statistic -value < < Model calibration results for delay function at IKIA and MIA based on Sola et al. method are shown in Table 5 for different functions [1]. It can be observed that the half-ellitical function (equation 16) and the arabolic function (equation 17) are the more roer delay functions for IKIA for MIA, resectively: 3 T0 2 te ( f u) u (1 2 c) f (16) 4cuf T0 ( f u) (17) t 3u cf c 1 f (18) f where, f is the arrival rate, T0 is the time when the arrival rate dros below the average arrival rate, c is a constant, u is the area between caacity and triangular arrival rate curve, t is the maximum time sent for the arabolic aroximation of ea at rocess station, and te is the maximum delay in half-ellitical aroximation. Table 5: Passenger Terminal Facilities for IKIA and MIA Airort Simulation Triangular Parabolic Half ellitical IKIA MIA For arriving assengers, a double node reresents the origin. In the first test model, only unidirectional flow was assumed, however by aroximating delay times using the seed density relation (1), bidirectional flow was integrated into the larger model. It was assumed here that density is based on flow in both directions. The lengths of the assageways were measured directly. For each customer tye, a triangular curve was assumed for arrival rate (demand) at the initial rocessing and the downstream stations [7]. Details of delay time estimation were alied from Saffarzadeh & Braasma s research [2]. All other arameters were determined based on forecasts and actual measured ea demand levels at IKIA and MIA. U to three stages were studied with the multistage models. LINGO software was used to erform the standard branch and bound rocedure. Comutations were erformed on a PC with an Intel Pentium GHz rocessor and 4 GB of internal memory. A relative tolerance of was used, while a time limit of 3600 s (one hour) was imosed on the number of iterations. The standard branch and bound did not roduce an otimal solution within the one-hour time limit for roblems on the small networ. However, the time for the branch and bound rocedure increases 4 56

5 Shabaniveri et al. with increasing roblem size and number of nodes for two airorts. In all instances the standard branch and bound erforms well. We can conclude that the standard branch and bound erformed well under all scenarios, including those where in-flow rates were the highest. The reason is the size of the roblem that made it different from Sola et al. s roblem condition. Actual 15 year traffic forecasts at IKIA and MIA were the basis for the demand levels in the test models. 5. Conclusions and Recommendations In this aer, by focusing on air terminal caacity lanning, a multieriod stochastic lanning roblem under uncertainty was addressed. Based on the concets of scenario tree and motion equations of assengers, assenger terminals of the two major International Airorts (IKIA: Imam Khomeini International Airort & MIA: Mehrabad International Airort) in Tehran, Iran were considered as the case studies. Mathematical rogramming models for IKIA and MIA case studies include and variables and and 14021constrains, resectively (for horizons of 5, 10 and 15 years). Nonlinear (MINLP) lanning roblems were solved by branch and bound method using LINGO software acage. Results indicate that increasing the caacity of the assenger terminal in IKIA can increase the roductivity of the existing sace and the whole airort which is also very economical. Potential current caacity of IKIA can be used for emergency caacity (for the next 5 years). However, IKIA also needs to exand its terminal in the next 10 years at Chec-In areas and gates. At MIA, different arts of the rocess and waling stations need to be exanded: It would be necessary to increase the effective width of corridors and to increase number of rocessing stations (exanding its gates and security checs). This terminal was observed to oerate 89% of its nominal caacity during ea hours, resulting in a level of service of F. Develoment of MIA terminal after the first 5-year eriod would be ossible only in certain directions of motion. Thus, managers should consider other facilities near this terminal. Overall, emirical results for the IKIA and MIA roblems (with various numbers of stages) suggest that the roosed model can be alied as a owerful tool for caacity lanning at airort terminals. The question is whether there is a relationshi between the otimal exansion decisions and the exected future demand at a given decision oint. In summary, our recommendations and suggestions for further research are: 1- Behavior analysis can be used for a more detailed consideration of the rocessing stations. Image and video rocessing would be an effective tool in this regard. 2- For a more realistic situation for a terminal, both air field and land field should be considered in the analysis. Thus, we suggest a study on airfields of these two major airorts of Iran. 3- It is recommended that further research tae into account the costs to develo various scenarios, and thus extending the model to an economical otimal as well. 4- Although exansion will increase delay of waling and transfer of assengers between stations in the airort, facilities such as electrical vehicle, edestrian conveyor and arc shae stations can be useful. Moreover, level of service will increase, too. References [1] Sola S., Clare, J. P. and Johnson, E. L., Airort Terminal Caacity Planning, Transortation Research Part B, Vol. 43, No. 6, , [2] Saffarzadeh M. and Braasma, J.P., Otimum Design and Oeration of Airort Passenger Terminal Buildings, Transortation Research Record: Journal of the Transortation Research Board, Vol. 1703, No. 1, , [3] Riis M. and Andersen, K.A., Multi Period Caacity Exansion of a Telecommunications Connection with Uncertain Demand, Comuters and Oerations Research, Vol. 31, No. 9, , [4] Andrade R., A. Lisser, N. Maculan and Plateau, G., Telecommunication Networ Caacity Design for Uncertain Demand, Comutational Otimization and Alications, Vol. 29, No. 2, , [5] Guta A., Ravi, R. and Sinha, A., LP Rounding Aroximation Algorithms for Stochastic Networ Design, Mathematics of Oerations Research, Vol. 32, No. 2, , [6] Lulli G., and Sen, S., A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Alication to Stochastic Batch-Sizing Problems, Management Science, Vol. 50, , [7] Shabaniveri H., Mamdoohi, A.R. and Saffarzadeh, M., Stochastic Planning Aroach in Airort Passenger Terminals, Journal of Traffic and Logistics Engineering, Vol. 1, No. 1,. 1-5, [8] Macintosh A. and Wallace, L., nternational Aviation Emissions to 2025: Can Emissions Be Stabilised without Restricting Demand? Energy Policy, Vol. 37, No. 1, , [9] Newell, Gordon Fran. Alications of queueing theory, No. 2nd ed [10] Wardro, J. G.; Whitehead, J. I., Corresondence. Some Theoretical Asects of Road Traffic Research. ICE Proceedings: Engineering Divisions, Vol. 1, No. 5, , [11] Shabaniveri H., Model of Evaluation of Airort Passenger Terminal Caacity Planning, Transortation Master of Science Thesis, Islamic Azad University, Science and Research Branch, [12] Kelton W. D., Sadowsi, R.P. and Swets, N.B., Simulation with Arena, McGraw-Hill Boo Comany, Acnowledgement The authors wish to exress their gratitude to Paul Hooer, Amir Jalilvandnejad, Asghar Fallah Sheihlari and Hamed Boroumand for their invaluable technical assistance, and to Pars Hayan Laboratory for roviding financial suort. 5 57