Stochastic Simulation Optimization for Route ... - World Scientific

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Asia-Pacific Journal of Operational Research Vol. 35, No. 6 (2018) 1850045 (24 pages) c World Scientific Publishing Co. & Operational Research Society of Singapore DOI: 10.1142/S0217595918500458

Stochastic Simulation Optimization for Route Selection Strategy Based on Flight Delay Cost

Yong Tian College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, P. R. China National Key Laboratory of Air Traffic Flow Management Nanjing University of Aeronautics and Astronautics Nanjing 211100, P. R. China [email protected]

Bojia Ye∗ College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, P. R. China National Key Laboratory of Air Traffic Flow Management Nanjing University of Aeronautics and Astronautics Nanjing 211100, P. R. China [email protected]

Marc S´ aez Estupi˜ n´ a The School of Industrial Aerospace and Audiovisual Engineering of Terrassa Polytechnic University of Catalonia Terrassa, Barcelona 08222, Spain [email protected]

Lili Wan College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, P. R. China National Key Laboratory of Air Traffic Flow Management Nanjing University of Aeronautics and Astronautics Nanjing 211100, P. R. China [email protected] Received 27 May 2018 Revised 12 August 2018 Accepted 17 October 2018 Published 20 November 2018

∗ Corresponding

author. 1850045-1

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Y. Tian et al. The continuous and strong growth of the civil aviation in the world combined with the severe adverse weather problem have made necessary the collaboration between the different civil aviation agents to improve the management of the capacity-demand imbalances in the airspace. In this paper, we consider a stochastic simulation optimization problem for air route selection strategy based on flight delay cost. The problem takes consideration of airspace capacity and demand uncertainty, three strategies, including collaborative reroute strategy (CRS), full information reroute strategy (FIRS) and hybrid stated route preference strategy (HSR), are employed to mitigate the flight delay cost. To find the best strategy, a discrete event simulation model is built by Arena Software, and the Monte Carlo method combined with the OCBA simulation optimization technique is employed for assessing a common severe convective weather scenario in the Central and Southern China airspace. Simulation results imply that HSR schemes show better system-wide performance than CRS and FIRS, these benefits are supposed to come from the batch allocations method. Although the airline can receive full information in advance, FIRS does not show obvious advantage in reducing the total airborne waiting time than CRS. For the system-wide performance FIRS is better than CRS, but not as good as HSR. Keywords: Stochastic simulation optimization; air traffic flow management; route selection strategy; OCBA.

1. Introduction Civil aviation is still growing strong in the world, and its growth is even more accentuated in China, where every year has an increase of flights around the 10%, and the Chinese market has evolved from representing the 0.86% of the total flights in 1985, to represent the 10.24% of the world’s total number of flights in 2016 (ICAO, 2017). This growth, combined with the severe adverse weather problem, that is a major cause of congestion due to the fact that convective weather, winds, precipitation, and reduced visibility may make certain airspace regions un-flyable or require greater separation between flights (which means reducing capacity), have required civil aviation agents to find a solution to manage the capacity-demand imbalances in airspace and airports in order to reduce airborne holding and avoid overloading air traffic control (ATC) facilities (Li et al., 2016; CAAC, 2017). The air traffic flow management (ATFM) is the collaborative process that in recent years, although it has existed as a component of air traffic management (ATM) for several decades, is becoming pertinent even in regions without sustained overload conditions caused by dense traffic operations. It involves many measures to accomplish the mission of supporting a safe, efficient and expedited flow of air traffic. These measures are both long-term and short-term to resolve perturbations arising due to unpredicted weather and capacity disruptions. Their effectiveness relies on the amount, accuracy and timeliness of the information exchanged, resulting that human operators depend critically on technology enablers and Decision Support Systems (DSS) for making better informed and more effective decisions (Kistan et al., 2017). ATFM initiatives are being mediated by the most important official bodies in the civil aviation sector, such as the International Civil Aviation Organization (ICAO), that considers ATFM as one of their air navigation priorities (ICAO, 2016), the 1850045-2

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International Air Transport Association (IATA), which has engaged projects to promote ATFM in Asia Pacific, or the Civil Air Navigation Services Organization (CANSO). Also, the United States Federal Aviation Administration (FAA) with its US Next Generation Air Transportation System (NextGen) and the European Organization for the Safety of Air Navigation (Eurocontrol) with its research program Single European Sky ATM Research (SESAR) developed in collaboration with the European Union (EU), are also including significant ATFM components (EUROCONTROL, 2007; FAA, 2010). In China, the Civil Aviation Administration of China (CAAC) started the project known as the collaborative decision makingair traffic flow management (CDM-ATFM) system, and completed the construction of the first phase in 2014. There are many types of ATFM measures. ICAO, in its manual on collaborative air traffic flow management (ICAO, 2014), categorizes these types into strategic, pre-tactical and tactical phases of the ATFM timeline. Amongst all these techniques, the most typical are the ground delay (known as ground delay programs or GDP), MIT (Miles-in-trail), ground stops, rerouting and airborne holding. Extensive research about ATFM has been conducted for long time, and even more in last years, when the interest about these techniques has increased substantially. To start, the study performed by Ye et al. (2016), which is the starting point of this research, developed a discrete-event simulation model using Arena Software for evaluating the alternative collaborative route selection strategy. Also, another work performed by Kim and Hansen (2015) will also be recurrently cited in this research, a modeling framework which was developed to evaluate and compare allocation strategies, under different assumptions regarding the information that traffic managers may (or may not) have about airline flight costs. Several resource allocation strategies are introduced that feature different allocation rules and route preference inputs requested of flight operators. Finally, the work by Kistan et al. (2017) performs an evolutionary outlook of current ATFM techniques, also determines which ATFM research and development efforts hold the best promise for practical technological implementations. Several scholars have investigated different techniques to optimize current ones or simulate new ones for decade (Mukherjee and Hansen 2009; Sherali et al. 2011; Agogino and Tumer, 2012; Agustin et al. 2012a, 2012b). Recently, Bertsimas et al. (2014) have presented a binary optimization framework for modeling dynamic resource allocation problems, which allows modeling flexibility by incorporating different objective functions, alternative sets of resources and fairness controls, and is widely applicable in a variety of problems in transportation, services and engineering, and provides near optimal solutions fast for large-scale instances. Ozgur and Cavcar (2014) present a 0–1 integer programming model for air traffic flow management. The model is used for determining optimum departure times of aircraft to avoid aircraft conflicts and to balance capacity and demand on the airports. Standard air traffic control minimal procedural separations were set as conflict

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criteria, which has never been done before, and this makes it convenient for use in planning of flows in airspace sectors especially without surveillance system. Zhang and Mahadevan (2017) investigate a simulation based approach to optimize the aircraft rerouting process, by considering multiple sources of uncertainty. Sama et al. (2017a) addressed the real time optimization of take-off and landing operations at a busy terminal control area in case of traffic congestion using scheduling models solved to near optimality. Ivanov et al. (2017) propose a two-level mixedinteger optimization model to solve en-route demand-capacity imbalance problem and further improve airport slot adherence. Bolic et al. (2017) present an integer programming model for strategic redistribution of flights so as to respect nominal sector capacities, in short computation times for large-scale instances combining a tackling large-scale strategic flight planning using hard capacity constraints, while considering the whole network. Sama et al. (2017b) introduce new meta-heuristics based on variable neighborhood search, tabu-search and hybrid schemes, which are applied to a proposed framework to improve the solution by rerouting some aircraft in the terminal control area (TCA). Murca (2017) presents a robust optimization approach for metering aircraft departures under uncertainty in the taxi-out process. A mixed integer linear programming model for runway sequencing and scheduling that incorporates uncertainty sets for the taxi-out time is proposed to dynamically determine an optimal and robust sequence and schedule of aircraft release from the gate. Xu and Prats (2017) present an approach to implement linear holding (LH) for flights initially subject to ground holding, in the context of Trajectory Based Operations. The aim is to neutralize additional delays raised from the lack of coordination between various traffic management initiatives (TMIs) and without incurring extra fuel consumption. Most literatures introduced above have used different optimization models to solve the ATFM problem. Although the feedback have been incorporated into some of the optimization models, the resulting complexity and nonlinearity usually render the problem insoluble. Since the flight re-routing is an essential part of ATFM nowadays which can reschedule and reroute flights so that the delay time and costs caused by the capacity and demand uncertainty could be kept to a minimum (Agustin et al., 2012b), the objective of this research is to develop, simulate and analyze alternative route selection strategies to improve the effectiveness and performance of the airspace traffic flow. The rest of the paper is organized as follows. Section 2 introduces the air transportation simulation model which consisting of aggregate departure/arrival airports, flight routes, and sectors that could represents the upper air routes in Central and Southern China. Section 3 reviews three alternative route selection strategies which are the collaborative reroute strategy, full information reroute strategy, and hybrid stated route preference strategy will be presented. Section 4 presents the discrete simulation modeling with Arena and the applying of OCBA for simulation optimization. Section 5 discusses some results for a common scene where some severe convective weather is supposed to happen in the noon time. Finally, Sec. 6 concludes and outlines future work. 1850045-4

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2. Air Transportation Simulation Modeling 2.1. Airspace queuing network model The airspace reroute network model is adapted from previous work (Ye et al., 2016). The model consists of two aggregate departure/arrival airports, which are equivalent to the “virtual airports” and act as source and destination nodes in the airspace network model, different flight routes that the flights are able to take and en-route sectors modeled as multi-server queue, where the server’s number represents the capacity limitation of each sector, defined as the number of aircrafts that can fly in the sector simultaneously. The model also considers the capacity and demand uncertainty: for the first one, the sector traversal time has been introduced as a random variable that has an independent and identical distribution (IID), and a capacity changing event has been added. These two parameters are used to simulate sources of capacity uncertainty as the difference in abilities of varied air traffic controllers, the uncertainties in wind forecasting and aircraft performance modeling and multiple flow patterns. For the second one, inter-arrival times are created as IID random variables and a random flights’ demand with known mean and variance is constructed, to simulate the factors that may cause inaccurate predictions of demand, as pop-up traffics, changes in departure times and flight plans, cancellations, displacement of traffic, en-route wind and ATC-caused deviations. In order to capture the peaks and downs characteristic for the departures demand during the different periods of a day, a scheduled flight departures has been developed for this model. The upper air routes in Central and Southern China (CSC) airspace were also taken as an example of evaluation of alternative route selection strategies, where there is a primary upper air route (A461) which links two of the most important hub airports in China: Guangzhou Baiyun International Airport (IATA: CAN, ICAO: ZGGG) and Beijing Capital International Airport (IATA: PEK, ICAO: ZBAA). Then, some aggregate airports were represented, being Hong Kong International Airport (IATA: HKG, ICAO: VHHH), Shenzhen Bao’an International Airport (IATA: SZX, ICAO: ZGSZ) and ZGGG the most important ones. Also, there are more than 30 airways servicing central and southern China along this route segment. Thus, if some severe weather happens, an enormous number of flights may be affected. Many flights from these airports fly over CSC as shown in Fig. 1 of the airspace structure created in the original work. The CSC airspace was incorporated into queuing network model as follows: Let D represents the aggregate departure airports (e.g., ZGGG, ZGSZ and VHHH) where many flights schedule to fly over Central and Southern China along YIN-BUBDADAPRO-WHA-OBLIK. Let X represents the aggregate departure airports where some flights are scheduled to fly over Central and Southern China along three other routes: ONEMI-LLC-GOSMA-WHA-OBLIK, HUY-LIN-WHA-OBLIK, and ENH-YIH-WHA-OBLIK. Assume each air route is divided by the sector boundaries into route segments and named for the sector in which it belongs. Different route 1850045-5

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Fig. 1. CSC airspace structure.

GDP

YIN-BUBDA

BUBDA-DAPRO

DAPRO-WHA

AC03

AC14_1

AC15_1

BUBDA-LLC

LLC-LIN

LIN-YIH

YIH-ML

AC14_re

AC12_re

AC15_re

AC17_re

ONEMI-LLC

LLC-GOS MA

GOS MA-WHA

AC12_1

AC14_2

AC15_2

Airports D

Airports X

GDP

HUY-LIN

LIN-WHA

AC12_2

AC15_3

ENH-YIH

YIH-WHA

AC17

AC15_4

WHA-OBLIK

MIT

AC16

Airports A

Fig. 2. CSC airspace model.

segments belonging to the same sector are singled out by adding a number as a suffix. The CSC airspace network model is illustrated in Fig. 2, and “A” represents the destination airports for all the flights departure from D and X. Suppose some severe weather occurs in AC16, so portions of the capacity resources of AC16 become unavailable. Then the flights scheduled to fly over Central and Southern China through waypoint OBLIK may choose to join the alternative route YIN-BUBDALLC-LIN-YIH-ML through different waypoints or wait on the ground/en-route. The re-route CSC airspace model with GDP and MIT control points is illustrated in Fig. 2 and the bold lines represent alternative routes for flights. 1850045-6

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Stochastic Simulation Optimization for Route Selection Strategy Based on Flight Delay Cost Table 1. Route segments traversal time distribution. Sectors

Route segments

Traversal time distribution (second)

AC03

Capacity resource 12

AC03(YIN-BUBDA) AC12 1(ONEMI-LLC)

N orm(827, 568) 960 + 154 ∗ Beta(68.3, 197)

AC12

12

AC12 2(HUY-LIN) AC12 re(LLC-LIN)

N orm(1020, 230) N orm(980, 120)

AC14

30

AC14 1(BUBDA-DAPRO) AC14 2(LLC-GOSMA) AC14 re(BUBDA-LLC)

1270 + Logn(358, 115) 540 + Gamm(560, 3.02) 1180 + 75 ∗ Beta(14.5, 16.8)

AC15

25

AC15 AC15 AC15 AC15 AC15

AC16

15

AC16(WHA-OBLIK)

660 + 25 ∗ Beta(6.55, 15)

AC17

15

AC17(ENH-YIH) AC17 re(YIH-ML)

570 + 74 ∗ Beta(11.3, 23.2) 1170 + Beta(1.04, 1.01)

1(DAPRO-WHA) 2(GOSMA-WHA) 3(LIN-WHA) 4(YIH-WHA) re(LIN-YIH)

660 + 29 ∗ Beta(9.28, 17.2) 650 + 31 ∗ Beta(3.39, 16.6) 960 + Logn(354, 407) 830 + Logn(247, 305) Norm(620,20)

The appropriate traversal time distribution for each route segment and capacity resources for each sector is assumed to be a real integer number, as shown in Table 1. Consistent with reality, different route segments in the same sector share the capacity resources together. Based on maximum likelihood estimation principle, the parameters for each distribution are estimated using Arena Software Input Analyzer. According to the radar flight data statistic results, the CSC entry proportion from YIN, ONEMI, HUY, and ENY are set as 61.65%, 35.65%, 2.45% and 0.25, respectively. The procedure for creating the scheduled flight departures is as follows: All the flights departed from ZGGG, ZGSZ and VHHH from April 22, 2017 up to April 24, 2017 were recorded. These 5,151 flight records were used to determine the hourly number of flights. Once the overall hourly number of flights was calculated, it was necessary to determine which percentage of those flights were scheduled to fly over the airspace structure. A meaningful sample from the flight records were studied, and around the 60% of the departures use the CSC airspace structure. The developed flight schedule is shown in Table 2. 2.2. Flight operation delay cost model The goal of this part of the research was to update these values to have a better estimated flight cost model. To perform that, a sample of the flight data used in the scheduled flight departures section had been used. First, as the data included the aircraft information, the most representative aircrafts of each type had been selected according to the aggregate airports simulated. These aircrafts are the following ones: • A type: Airbus 330-200, Airbus 330-300 and Boeing 777-300ER • B type: Airbus 350 and Boeing 767 1850045-7

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Y. Tian et al. Table 2. Flight schedule. Time 00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00

Number of departures to to to to to to to to to to to to

01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00

26 20 17 21 11 8 40 58 65 59 57 56

Time 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

to to to to to to to to to to to to

Number of departures

13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 24:00

54 53 52 52 54 54 51 51 51 50 35 34

• C type: Airbus 320, Airbus 321 and Boeing 737 • D type: Bombardier Q400 and ATR 72. Once the aircraft types are defined, the rest of variables had been found according to them. The first one is the aircraft ratio, studied using the mentioned flight data sample, obtaining the flights’ percentage of each type of aircraft over the total flights in the sample. The results are 10% for type A, 25% for type B, 55% for type C and 10% for type D. For the seat number, a simple average between the most typical seat number configurations of the aircraft of each type have been performed. Load factor and Connecting/Non-connecting flight rate are shown in Table 3. Regarding the different unit time costs, the new values had been based on different research models (Ryerson and Hansen, 2013). In this study, they seek to quantify the fuel consumption impact on three operational performance measures: schedule padding, airborne delay and departure delay. Last two have a great importance to this research, and the findings of the mentioned work will be applied in it. Those findings include the statement that a minute of airborne delay leads to a fuel consumption that is about the 50% of the median fuel consumption per minute of the aircrafts. Also, it includes the statement that departure delay leads to a fuel

Table 3. Updated variables for flight cost model. Variable

Value

Aircraft type Aircraft ratio Seat number Unit time GDP fuel cost ($/min) Unit time airborne fuel cost ($/min) Unit time crew delay cost ($/min) Unit time passenger delay cost ($/min) Load factor Connecting/Non-connecting flight rate 1850045-8

A 10% 320 13 129.5 12 2.5

B C 25% 55% 260 160 10 2.5 125.5 52 10 8 2 1.5 Unit (0.75,0.9) 1:1

D 10% 80 1 24 6 1

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consumption that is about the 4% of the median fuel consumption per minute of the type B aircrafts and the 2.5% of the type C aircrafts. According to this, it was assumed a 5% for the type A aircrafts and a 2% for the type D aircrafts. Then, to apply these statements, the median fuel consumption per minute of each type of aircraft had to be calculated. The fuel cost per nautical mile in dollars and the cruise speed for each studied aircraft was noted down (Levy and Bassett, 2017; Sibdari et al., 2018). With these two variables, the cruise speed fuel cost per minute is a simple calculation, and is it assumed to be the median fuel consumption per minute. Finally, the median fuel consumption per minute was the simple average of the value for each one of the aircrafts of every type. Those values are 258.84 $/min for type A, 249.10 $/min for type B, 103.66 $/min for type C and 48.18 $/min for type D. Regarding the last two variables to be considered, the Unit time crew delay cost and the Unit time passenger delay cost, the values had been found based on the report European airline delay cost reference values prepared by the Department of Transport Studies of the University of Westminster (2011) for the EUROCONTROL’s Performance Review Unit. In this report, an extensive study of the costs

Table 4. Variables for flying cost model. Variables f k i Tf,k Tgf,k Taf,k TSCHf Tf,i Df,i Qf,g TMIT Qf,i Ni Vpf Ftf Sf Ldf Up Ucf Cf,k Vf f Vf g

Description A flight that is scheduled to fly through the target route segment A flight route with the same entrance and exit points but maybe different transit sectors A segment of the flight route and it is currently named by the sector it belongs to Estimated total delay time of flight f by choose route k after potential GDP Potential GDP time of flight f before choosing route k Estimated Airborne delay time of flight f by choosing route k after potential GDP Scheduled route transit time from flight planning for flight f Estimated transit time of the sector i for flight f in the normal situation, the mean value is used here Estimated extra delay time in sector i based on previous length of flight queues and sectors transit time The current length of flight queue in the aggregate airports with GDP for flight f The MIT time initialized by ARTCC for adjusting the imbalance in potential congestion sector The length of flight queue in the sector i before target flight joining the queue Number of airspace resources for the sector i Unit time passenger delay cost in flight f , include passenger and crew parts Flight mission type of f, 1 represents connecting flight Seat number of flight f Load factor of flight f Unit time delay cost per passenger Unit time delay cost of crew member in flight f Estimated total delay cost of flight f by s route k Unit time airborne fuel cost of flight f Unit time GDP fuel cost of flight f

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that delays create is performed, for a good number of different aircrafts of different types. The whole new variable values are shown in Table 4. Now we would like to introduce the model which will be used to compute the estimated delay cost of each flight. The estimated total delay time and estimated airborne delay time is shown in Eqs. (1) and (2). The estimated GDP delay time resulting from choosing route k and extra delay time in sector i for flight f is included in Eqs. (3) and (4). The calculation of estimated flight delay cost is shown in Eq. (5). Equation (6) reconciles the unit time passenger delay cost of a flight. The relative variables are defined in Table 4. Tf,k = T gf,k + T af,k − T SCHf , (Tf,i + Df,i ), T af,k =

(1) (2)

i∈j

T gf,k = Qf,k ∗ TMIT ,

(3)

Df,i = (Qf,i/Ni ) ∗ Tf,i ,

(4)

V pf = F tf ∗ (3 ∗ Sf ∗ Ldf ∗ U p + U cf ) + (1 − F tf ) ∗ Sf ∗ Ldf ∗ U p,

(5)

Cf,k = T af,k ∗ (V pf + V ff ) + T gf,k ∗ (V pf + V fg ).

(6)

3. Alternative Route Selection Strategy To implement and simulate different strategies from the ones performed in the previous work, three alternative strategies including collaborative reroute strategy (CRS), full information reroute strategy (FIRS) and hybrid stated route preference strategy (HSR) are introduced in this section. 3.1. Collaborative reroute strategy The CRS is one of the most recommended strategies from previous work (Ye et al., 2016; Sherali et al., 2011; Kotnyek and Richetta, 2006). Unlike the traditional reroute initiative given by TFM or airlines unilaterally, the airlines in this strategy will make the final decision based on ACC introduced MIT time and reroute percentage, and the More-Valuable-Flights Rerouted-First (MVRF) and Less-ValuableFlights Rerouted-First (LVRF) rules are taken by airlines based on the estimated flight delay cost model. This strategy is set as the baseline for comparing of different new route selection strategies in the study. 3.2. Full information reroute strategy According to the collaborative reroute strategy introduced above, the ultimate decision is the one made by airlines regarding which of their flights should be rerouted within the recommended search space in essence. As already commented, the MVRF 1850045-10

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and LVRF rules are the two decisions taken by airlines based on the current state of airspace. If the airline can receive full information in advance, the system performance may be improved accordingly. So the FIRS is proposed as the following one: suppose the airline can receive the information of both the current and future situation of the different routes its flight can fly over, regarding the current length of flight queue in each one of the sectors of each possible route, considering that it already knows the number of airspace resources for each sector and the mean value time for transiting them. Then, when a decision for that flight must be done, the estimated transit time for both route options (in the airspace simulated, although it could be between more route options using a more extensive airspace) is calculated and then the flight takes the route with minimum estimated transit time. 3.3. Hybrid stated route preference strategy The HSR is proposed based on the Collaborative Resource Allocation Strategies for Air Traffic Flow Management (Kim and Hansen, 2013), which consists of a mix of the full information optimal (OPT) and the first submitted, first assigned (FSFA). It maintains the reward structure of the FSFA, as it continues rewarding those who submit their information soon, but instead of doing it instantaneously, it does that in a batch allocation, meaning that all the flights information submitted in a short period of time are then allocated in the best global optimal allocation for those flights. The allocation batch time is the key parameter for this strategy. 4. Discrete Modeling and Simulation Optimization 4.1. Discrete simulation modeling with arena In this chapter, the building of the simulation models is explained. The program is coded by Arena Simulation, a discrete event simulation and automation software from Rockwell Automation (Kelton et al., 2004). Modeling constructs, which are called “modules” in Arena, are functionally arranged into a number of “templates” (A module contains logic, a user interface, and in some cases, options for animation.) Some important templates include the basic process template contains modules that are used for modeling arrivals, departures, services, and decision logic of entities, the advanced process template contains modules that are used to perform more advanced process logic and to access external data files in Excel, Access, and SQL databases, and the flow process template is used for modeling batch-processing operations. In this research, two simulation models were developed with several aspects in common. The first one was adapted from previous work which is used to simulate CRS strategy of the original work and the different routing choosing decision strategy FIRS, while the second one was used to simulate and HSR. Several resources had been used to develop these models, as part of the software learning process to 1850045-11

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Fig. 3. Arena simulation model.

finally master its use. Figure 3 shows the second Arena model with the three main parts. The left function part is the flights initialization, where they are created and assigned their variables according to the improved flight delay cost model that have been presented in a previous chapter. The middle function part is where the simulation of the flights is performed, with the different routes and the rerouting decisions are taken. The right function part is where the data is collected for the posterior treatment. 4.2. Simulation optimization with OCBA The alternative collaborative route selection can be approached as a stochastic simulation optimization problem, which refers to stochastic optimization using simulation. The goal is to find out the best strategy with suitable parameters to optimize the system metric defined above. There exists a large amount of literature on innovative methods for improving simulation efficiency (Zhang and Mahadevan, 2017; Thanos et al., 2017; Xu et al., 2015). Instead of performing the required simulation replications faster, some of these approaches apply variance reduction techniques to reduce the simulation variance. Among them, OCBA is a popular control-theoretic simulation technique that can intelligently determine the most efficient simulation replication numbers for all simulated alternatives (Xu et al., 2016; Chen, 2008, 2000). OCBA is a popular control-theoretic simulation technique that can intelligently determine the most efficient simulation replication numbers for all simulated alternatives (Gao et al., 2017; Chen, 2011; Lee et al., 2010; Chen, 2006). We employ a Monte Carlo approach for simulation and evaluating different route selection strategies, and introduce optimal computing budget allocation (OCBA) to improve the efficiency of simulation. The details of the simulation optimization procedure are as follows. The goal of our simulation is to select a route selection strategy associated with the best system performance cost metric, such as system total delay cost. Thus, we can consider this simulation optimization problem with the following objective function: min J(θi ) ≡ E[L(θi , ω)],

θi∈Θ

where Θ ≡ {θi , i = 1, 2, . . . , k} is the search space, θi is a vector of all the decision variables and also called a design. L(θi , ω) represents a sample performance estimate 1850045-12

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obtained from the output of one simulation replication for design i, and E[L(θi , ω)] is estimated using its sample mean E[L(θi , ω)] ≡

Ni 1 L(θi , ωij ), Ni j=1

ωij comprises the jth sample of the randomness ω for design i and Ni represents the number of simulation samples for design i. The simulation output is obtained as an average performance, so according to the central limit theorem, we can assume that the simulation output samples L(θi , ωij ) are normally distributed and independent from replication to replication. Under a Bayesian framework, a posterior distribution of the system performance metric J(θi ) can be constructed based on prior knowledge of the system’s performance and current simulation output. Let ˜ i ) denote the random variable whose probability distribution is the posterior J(θ distribution of design i. Thus the posterior distribution of J(θi ) is 2 ¯ i ), σi , ˜ i ) = p(J(θi ) | L(θi , ωij ), j = 1, 2, . . . , Ni ) ∼ N J(θ J(θ Ni which implies that we are more confident with the sample mean estimator when Ni increases as the variance decreases. For the alternative collaborative route selection problem, time is a valuable resource. Often, it is too expensive to conduct enough simulation replications for all candidate designs when the design space is large. However, to improve the simulation precision, we must increase the number of simulation replications for each design. The simulation output is assumed to be independent from replication to replication and the sampling across designs is also independent. For notational simplicity, define: Xij ≡ L(θi , ωij ). Denote by X i : the sample mean of L(θi , ω), the simulation output for design i; Xi =

Ni 1 Xij . Ni j=1

Si2 : the sample variance of L(θi , ω), the simulation output for design i. σi2 : the variance for design i, i.e., σi2 = Var(Xij ). In practice, σi2 is unknown beforehand and so is estimated by the sample variance. b: the design with the smallest sample mean metric; b = argmini {X i }. Define the probability of correct selection (P {CS }) as the probability that design b is actually the best design (i.e., with the smallest mean of system delay time). The 1850045-13

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P {CS} can be expressed using the Bonferroni inequality as: P {CS} = AP SC − B ≡ 1 −

k

˜ b ) > J(θ ˜ i )}. P {J(θ

i=1, i=b 2

˜ i ) ∼ N (J(θ ¯ i ), σi ), as Ni increases, the variance of J(θ ˜ i ) decreases, and so since J(θ Ni P {CS} increases. Define the OCBA-PCS problem as follows: max P {CS},

N1 ,...,Nk

s.t. N1 + N2 + · · · + Nk = T,

and Ni ≤ 0 .

Here, T denotes the total number of simulation samples to be allocated to k competing designs whose performance is depicted by random variables with means ¯ 1 ), J¯(θ2 ), . . . , J(θ ¯ k ), and finite variances σ12 , σ22 , . . . , σ 2 , respectively. As T → ∞, J(θ k the Approximate Probability of correct selection (APCS) can be asymptotically maximized when 2 σi /δb,i Ni = , i, j ∈ {1, 2, . . . , k}, and i = j = b, Nj σj /δb,j k Ni2 Nb = σb , σi2 i=1,i=b

¯ i ). Through optimal allocation ¯ b ) − J(θ ¯ i ), and J(θ ¯ b ) ≤ mini=b J(θ where δb,i = J(θ of simulation samples, it has been shown that OCBA can dramatically enhance

Table 5. Pseudo code for the main algorithm. INPUT INITIALIZAE

LOOP UPDATE

k, T, ∆, n0 (T − kn0 is a multiple of ∆ and n0 ≤ 5); l ← 0; Perform n0 simulation replications for all designs; N1l = N2l = · · · Nkl = n0 P WHILE ki=1 Nil < T DO PNil Calculate sample means J¯i = 1l j=1 L(θi , wi,j ), and sample standard Ni r l P Ni 1 ¯ 2 deviation si = l j=1 (L(θi , Wi,j ) − Ji ) , i = 1, . . . , k, using the new Ni −1

ALLOCATE

simulation output; compute, i = 1, . . . , k; find b = argmini J¯l . Increase the computing budget by ∆ and calculate the new budget allocation, N1l+1 = N2l+1 = · · · Nkl+1 , according to “ ” N l+1 s (J¯ −J¯ ) 2 (1) il+1 = s i (J¯b −J¯j ) , for all i = j = b, and Nj j j b s „ l+1 «2 Pk Ni l+1 = sb (2) Nb i=1,i=b s i

SIMULATE END OF LOOP

Perform additional max (Nil+1 − Nil , 0) simulations for design i, i = 1, . . . , k; l ← l + 1

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the simulation optimization efficiency (Zhang et al., 2016; Peng et al., 2013). The OCBA-based simulation optimization procedure is shown in Table 5. 5. Results and Discussion This section presents the results of a case study in which the capabilities of the alternative route selection strategies have been assessed. First, a brief outline of the scenario employed in the case study will be presented. Next, the OCBA algorithm will be used to maximize the probability of correct selection of strategy. Finally, the simulation results will be discussed relative to different route selection strategies. To begin with, let us consider a common scene where some severe convective weather is supposed to happen at noon local time in Central and Southern China. The capacity resource of AC16 is supposed to be reduced from 15 to 7 for 2 or 3 h (12:00–14:00 or 11:00–14:00), other sectors’ capacity being equal, as Table 6. Then, three alternative route selection strategy with five schemes including CRS, FIRS, HSR (5 min), HSR (10 min) and HSR (15 min) will be performed to minimize the system total delay cost. Here, HSR (5 min/10 min/15 min) represents the Hybrid State Route Preference strategy with a 5/10/15 min allocation batch. Three related metrics including AC16 total waiting time, total airborne waiting time and system total flying time will also be presented in the initial results. The programs running time for each replication is about 23 min for 24 simulation hours with 1,029 flight per day. Since we have considered the capacity and demand uncertainty in the simulation environment, the underlying problem becomes stochastic with some noise and randomness. Multiple simulation replications must be performed in order to get good estimation of different strategies. Initially, 5 simulation replications for each scheme were conducted to test different schemes, the means and standard deviations of the AC16 total waiting time, total airborne waiting time, system total flying time, and system total delay cost are selected as metrics displayed in Tables 7 and 8. It can be seen from the tables that different scheme shows different performance for almost all metrics. If we consider a metric with the minimum mean value as the best performance, a noteworthy finding is that all the best performances are proposed by HSR strategies. For example, HSR (5 min) proposed the minimum AC16 total waiting time for Scenario 2, and the minimum total airborne waiting time, system total Table 6. Sector capacity resource changing scenarios. Sector

Initial capacity (sorties/hour)

11:00–14:00 capacity (sorties/hour)

12:00–14:00 capacity (sorties/hour)

AC03 AC12 AC14 AC15 AC16 AC17

25 25 25 25 15 15

25 25 25 25 7 15

25 25 25 25 7 15

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Collaborative Reroute Strategy (CRS)

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AC16 total waiting 427 ± 311 time (min) Total airborne waiting 6,756 ± 3,178 time (min) System total flying 78,166 ± 3,898 time (min) System total delay 11,173,824 ± 309,195 cost ($)

Metrics


Metrics

9,940,747 ± 115,602

66,278 ± 396

75,794 ± 3,173

264 ± 136

5 min

2,505 ± 324

10,984,457 ± 437,211

9,661,643 ± 88,059

66,446 ± 932

5,666 ± 1,050

288 ± 156

10 min

9,571,541 ± 169,944

67,030 ± 1,283

8,133 ± 630

736 ± 260

15 min

9,689,343 ± 182,286

66,659 ± 990

5,766 ± 695

293 ± 166

10 min

9,577,607 ± 261,790

67,288 ± 1,408

8,453 ± 983

805 ± 267

15 min

Hybrid Stated Route Preference Strategy (HSR)

6,385 ± 3,055

320 ± 190

Full Information Reroute Strategy (FIRS)

Table 8. Scenario 2 11:00–14:00.

9,937,765 ± 236,415

66,304 ± 833

76,022 ± 3,163 10,866,384 ± 303,089

2,387 ± 493

375 ± 393

6,458 ± 2,764

455 ± 186

5 min


Table 7. Scenario 1 12:00–14:00. Full Information Reroute Strategy (FIRS)

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flying time for both scenario 1 and scenario 2. HSR (10 min) proposed the minimum AC16 total waiting time for scenario1. HSR (15 min) proposed the minimum system total delay cost for both scenarios. For better evaluation of different route selection scheme, using the Approximate Probability of Correct Selection by Bonferroni inequality (APCS-B) as the lower bound, the P {CS} of all the metrics were evaluated. Take scenario 1 for example, Table 9 shows that although HSR (10 min) scheme obtains the smallest mean of AC16 total waiting time, the probability of correct selection P {CS} is only 0.5573. Table 10 shows that HSR (5 min) scheme obtains the smallest mean of total airborne waiting time, and the P {CS} is as high as 0.9991. Specifically, HSR (5 min) scheme shows 100% better than HSR (10 min) and HSR (15 min) schemes. Table 11 shows that HSR (5 min) scheme also obtains the smallest mean of system total flying time, but the P {CS} is only 0.4560. However, HSR (5 min) scheme shows 100% better than CRS and FIRS schemes. Table 12 shows that HSR (15 min) scheme obtains the smallest mean system total delay cost, and the P {CS} is 0.8513. In general, no Table 9. Best strategy based on AC16 total waiting time for Scenario 1. Alternative strategy

CRS FIRS HSR (5 min) HSR (10 min) HSR (15 min)

AC16 total waiting time (min) Mean

Std.

Replications

P {J˜b < J˜i }

P {CS}

488 455 375 288 736

237 186 393 156 260

5 5 5 5 5

0.9425 0.9380 0.6773 — 0.9995

— — — 0.5573 —

Table 10. Best strategy based on total airborne waiting time for Scenario 1. Alternative strategy


Total airborne waiting time (min) Mean

Std.

Replications

P {J˜b < J˜i }

P {CS}

6,541 6,458 2,387 5,666 8,133

2,678 2,764 493 1,050 630

5 5 5 5 5

0.9997 0.9994 — 1.0000 1.0000

— — 0.9991 — —

Table 11. Best strategy based on system total flying time for Scenario 1. Alternative strategy


System total flying time (min) Mean

Std.

Replications

P {J˜b < J˜i }

P {CS}

76,575 76,022 66,304 66,446 67,030

2,641 3,163 833 932 1,283

5 5 5 5 5

1.0000 1.0000 — 0.6003 0.8557

— — 0.4560 — —

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Y. Tian et al. Table 12. Best strategy based on system total delay cost for Scenario 1. Alternative strategy


System total delay cost ($) Mean

Std.

Replications

P {J˜b < J˜i }

P {CS}

11,079,099 10,866,384 9,937,765 9,661,643 9,571,541

210,624 303,089 236,415 88,059 169,944

5 5 5 5 5

1.0000 1.0000 0.9975 0.8537 —

— — — 0.8513

scheme could propose the best performance for all the four metrics, and some more simulation must be conducted if we want get better evaluation based on the system total delay cost. Using the system total delay cost as the key performance measure, we increased the number of simulation replications step by step to improve the simulation precision. Both the OCBA algorithm and the equal allocation method were used to determine the best numbers of simulation replications for each scheme. Based on the initial 25 simulation replications results, extra 25, 50 and 75 computing budget Table 13. Extra number of simulation replications allocated by OCBA for Scenario 1. Number of extra replications

25 50 75

Number of replications allocated by OCBA and equal allocation Collaborative Reroute Strategy (CRS)


1 5 2 10 3 15

2 5 3 10 5 15

Hybrid Stated Route Preference Strategy (HSR) 5 min

10 min

15 min

2 5 4 10 6 15

9 5 19 10 28 15

11 5 22 10 33 15

P {CS} system total delay cost

0.8938 0.8720 0.9872 0.9367 0.9958 0.9758

Table 14. Extra number of simulation replications allocated by OCBA for Scenario 2. Number of extra replications

25 50 75

Number of replications allocated by OCBA and equal allocation Collaborative Reroute Strategy (CRS) 2 5 3 10 5 15

Full Information Reroute Strategy (FIRS) 1 5 3 10 4 15 1850045-18

Hybrid Stated Route Preference Strategy (HSR) 5 min

10 min

15 min

2 5 4 10 6 15

9 5 18 10 27 15

11 5 22 10 33 15

P {CS} system total delay cost

0.9653 0.8751 0.9949 0.9860 0.9988 0.9890


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Metrics

9,903,852 ± 190,551

69,910 ± 666

74,464 ± 3,793 10,800,581 ± 426,667

2,275 ± 397

351 ± 307

5 min

9,742,660 ± 95,886

66,539 ± 490

5,412 ± 389

10,071,444 ± 200,046

67,102 ± 1,224

75,982 ± 3,306

351 ± 340

5 min

3,314 ± 930

11,028,774 ± 385,811

9,605,830 ± 94,551

66,766 ± 421

8,135 ± 281

721 ± 200

15 min

9,843,814 ± 97,140

67,368 ± 1,139

6,210 ± 1,085

546 ± 405

10 min

9,686,283 ± 86,136

67,669 ± 1,502

8,951 ± 1,150

701 ± 497

15 min


6,301 ± 3,207

450 ± 313


578 ± 191

10 min


4,764 ± 3,452

440 ± 355


Table 16. Final results after simulation optimization for Scenario 2.


Metrics

Table 15. Final results after simulation optimization for Scenario 1.

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were allocated to each scheme in 2 scenarios to maximize the P {CS} based on the System Total delay cost in Tables 13 and 14. The replications for each scheme in the first rows were calculated by the OCBA while the replications in the second row were allocated equally. From the results of Scenario 1 in Table 13, we can see that the P {CS} based on the OCBA algorithm increases from 0.8513 to 0.9958 while the P {CS} based on the equal allocation method increases from only 0.8720 to 0.9758. Compared with the equal allocation method, the OCBA algorithm used about 25 less replications to achieve 95% correct selection which means 9.58 h (1/4 simulation time) were saved in this case. Similar results can be found in scenario 2, more than 25 replications were saved to achieve both 95% and 99% correct selection. The final results after simulation optimization are shown in Tables 15 and 16. For the system total delay cost, all three HSR schemes showed better performance than other two schemes, and the HSR (15 min) scheme proposed the minimum mean values for both 2 capacity-reduced scenarios with more than 99% correct selection. By applying the HSR (15 min) scheme for 2 scenarios, approximate 1,325,907 dollars (12.13%) and 1,440,561 dollars (12.95%) were saved respectively compared to CRS strategies, 1,194,751 dollars (11.06%) and 1,342,491 dollars (12.17%) were saved respectively compared to FIRS strategies. A noticeable point is that the HSR scheme with larger batch time seems to bring more economic benefits than the less batch time. For other time-related metrics, the HSR (5 min) scheme shows the best performances in almost all the aspects than other schemes in both the scenarios, including AC16 total waiting time, Total airborne waiting time and System total flying time. In addition, compared to other two HSR schemes, the time-related metrics seem to decrease with the increasing of the batch time, which implies that the flight delay cost may not be necessarily positive correlation with the flying time. In generally, the HSR schemes show better system-wide performances (System total flying time and system total delay cost) than CRS and FIRS, and these benefits are supposed to come from the batch allocations method. Although the airline can receive full information in advance, FIRS did not show obvious advantage in reducing the mean of AC16 total waiting time and total airborne waiting time than CRS. For the system-wide performance, FIRS seems be better than CRS but not as good as HSR. 6. Conclusion and Future Work In this work, we consider an alternative route selection problem in the context of Air Traffic Flow Management. The problem takes into airspace capacity and demand uncertainty, flight operation cost and severe convective weather which is mitigated by Collaborative Reroute Strategy, Full Information Reroute Strategy, and Hybrid Stated Route Preference Strategy (5/10/15 min). To find the best strategy, based on the queuing theory, we first modeled the aggregate departure/arrival airports, flight routes, sectors, and flight operation cost that represents the upper air routes 1850045-20

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in Central and Southern China. Then, a discrete event simulation model was built which can conduct route selection schemes by Arena Software. The Monte Carlo method combined with the OCBA simulation optimization technique was employed for assessing a common severe convective weather scene. Some interesting findings are as follows: the OCBA is a very effective simulation optimization algorithm for selecting the best reroute strategy. Compared with the equal allocation method, about 25 replications which implies 9.58 h (1/4 simulation time) could be saved for both capacity reduced scenarios to achieve the 95% correct selection. HSR scheme with larger batch time seems to bring more economic benefits than the one with less batch time, while the time-related metrics seem to decrease with the increasing of the batch time. HSR schemes in the two capacity-reduced scenarios showed better system-wide performances (System total flying time and system total delay cost) than CRS and FIRS, and these benefits should come from the batch allocations method. In addition, although the airline can receive full information in advance, FIRS did not show obvious advantage in reducing the AC16 total waiting time and total airborne waiting time than CRS. For the system-wide performance, FIRS seems be better than CRS but not as good as HSR. For future work, there are several possible directions to pursue. This work only considers the basic air traffic congestion scenario, extending the single congestion node to multiple congestion nodes with random severe weather durations is a suggested direction. The collaboration and competition among different airlines may be another interesting effort. Last but not least, as the current framework is for the upper air routes, the combination of terminal area sectors is of great interest. Acknowledgments This study was co-supported by the Natural Science Foundation of China (61671237), Natural Science Foundation of Jiangsu Province — China (No. BK20160798), and China Postdoctoral Science Foundation (2018M632308). References Agogino, AK and K Tumer (2012). A multiagent approach to managing air traffic flow. Autonomous Agents and Multi-Agent Systems, 24(1), 1–25. Agustin, A, A Alonso-Ayuso, LF Escudero and C Pizarro (2012a). On air traffic flow management with rerouting. Part I: Deterministic case. European Journal of Operational Research, 219(1), 156–166. Agustin, A, A Alonso-Ayuso, LF Escudero and C Pizarro (2012b). On air traffic flow management with rerouting. Part II: Stochastic case. European Journal of Operational Research, 219(1), 167–177. Bertsimas, D, S Gupta and G Lulli (2014). Dynamic resource allocation: A flexible and tractable modeling framework. European Journal of Operational Research, 236(1), 14–26. Bolic, T, L Castelli, L Corolli and D Rigonat (2017). Reducing ATFM delays through strategic flight planning. Transportation Research Part E: Logistics and Transportation Review, 98, 42–59. 1850045-21

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Biography Yong Tian is an Associate Professor with College of Civil Aviation in Nanjing University of Aeronautics and Astronautics. His research includes air traffic flow management and flight performance. He has published research papers in journals such as Transportation Research Part D: Transport and Environment, System engineering — Theory & Practice, Boletin Tecnico. Bojia Ye is an Assistant Professor with College of Civil Aviation in Nanjing University of Aeronautics and Astronautics. His research includes air traffic flow management and airspace management. He has published research papers in journals such as Chinese Journal of Aeronautics, The Aeronautical Journal. Marc S´ aez Estupi˜ n´ a is graduate student from Polytechnic University of Catalonia. His research includes air traffic flow management. He was a visiting student with College of Civil Aviation in Nanjing University of Aeronautics and Astronautics. Lili Wan is an Assistant Professor with College of Civil Aviation in Nanjing University of Aeronautics and Astronautics. Her current research includes Green Civil Aviation and Airspace Assessment and Planning. She has published research papers in journals such as Journal of Traffic and Transportation Engineering, Transactions of Nanjing University of Aeronautics & Astronautics.

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