Antoine Henry
email: antoine.henry@alumni.enac.fr

Daniel Delahaye
email: delahaye@recherche.enac.fr

Alfonso Valenzuela
email: avalenzuela@us.es

CONFLICT RESOLUTION WITH TIME CONSTRAINTS IN THE TERMINAL MANEUVERING AREA USING A DISTRIBUTED Q-LEARNING ALGORITHM

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Air traffic keeps increasing each year since the midtwentieth century. This increasing number of flights forces air traffic controllers to be more efficient. The capacity has to be improved in the TMA without impacting the safety. This means that controllers will have to resolve more and more potential conflicts between aircraft. In order to decrease the workload, most of international airports are equipped with softwares to assist them to manage traffic. These softwares, called arrival managers (AMANs), not only sequence aircraft on runways but also ensure a minimum separation between aircraft in the TMA. In summary, such tools organize the traffic in order to maximize the runway throughput by computing decisions for each aircraft which are delivered by the controllers.

The aircraft separation problem is complex since there are many decision variables inducing a large space state. By considering only speed and flight level as decision variables, a pre-sequence can be computed in the En-route airspace [START_REF] Abba-Rapaya | Coordinated Sequencing of Traffic on Multiple En-route Constraint Points[END_REF]. The generated flight instructions could be directly used by the controller, shaping a pre-sequence without any conflict when aircraft enter the TMA. Using this pre-sequence composed by aircraft entering at a certain time in the TMA, the algorithm should be able to solve conflicts in a heavy-loaded scenario. In the TMA, aircraft are usually controlled by speed regulation. When such decision are not enough, as when there are too much uncertainties, tactical vectorings are also assigned to some aircraft in order to solve the remaining conflicts. Such vectorings induce extra workload for the controller.

In order to reach the same objective, the Point Merge System (PMS) has been developed in the 90s. Such PMS consists in a circular leg in the TMA where aircraft are assigned to follow for a given amount of distance (2,3,4,..NM) in order to create efficient separations between aircraft. It is an efficient way to solve conflict problem when several Standard Arrival Routes (STARs) converge towards the same runway. This technique allows aircraft to add delay between each other by flying different paths. Some previous related works [START_REF] Liang | Multi-layer Point Merge System for Dynamically Controlling Arrivals on Parallel Runways[END_REF], [START_REF]Point Merge implementation A quick guide[END_REF] have used optimization algorithms for computing efficiently the amount of time aircraft have to stay in the PMS leg for building an optimal sequence at the runway.

The aim of this paper is to figure the best performance of a machine learning algorithm on sequencing and merging problem. Since this problem could be modelized as a Markovian Decision Process (MDP), the Q-Learning algorithm (QL) has been chosen for its simplicity and performance on these problems. It is a model-free reinforcement learning algorithm which finds the optimal policy corresponding to the maximum reward that an agent can get. This problem can be addressed in a centralized way by using global optimization approach [START_REF] Abba-Rapaya | Coordinated Sequencing of Traffic on Multiple En-route Constraint Points[END_REF] but the associated computation time may be too high. In order to reduce this computation time, a selective simulated annealing algorithm has been proposed in [START_REF] Deshmukh | Algorithmic Efficiency Comparison of Centralised and Distributed Arrival Management (AMAN) Problem In Terminal Airspace[END_REF] for which the computation can be divided by 20 compared with [START_REF] Abba-Rapaya | Coordinated Sequencing of Traffic on Multiple En-route Constraint Points[END_REF]. This approach still need some centralized communication between aircraft in order to be efficient.

In the current work, we propose a fully decentralized sequencing and merging algorithm based on a distributed Qlearning methodology, meaning every aircraft is considered as a learning agent. A difficult point is that every agent learns without being aware of the state or actions of others. This is why the QL used in this paper is not only distributed but also selected: all agents are not learning at the same time. Agents with the worst reward are considered critical, they learn before others. Furthermore, this problem is simplified by using a time decomposition approach [5] [6]. Instead of solving the problem for a whole day, the algorithm is applied to a set of time windows sliding along the day. This approach presents two main advantages. First, it considers aircraft in the near future for which uncertainty is reduced, thus increasing the validity of the decisions taken by the algorithm (as a matter of fact, it is irrelevant to take decisions in the morning for aircraft that will land in the evening). Second, taking into account aircraft in the next time window will reduce the size of the problems the algorithm will have to address. Therefore, the QL is run only on flights in a certain time window, which slides during the whole day.

This algorithm has been tested over 24-hour scenarios. These scenarios represent either a normal day at Paris Charles de Gaulle airport or heavily-loaded scenarios -with up to 50% more traffic. The results of the algorithm will be considered as satisfying when every conflict in a scenario will be solved, with a minimized average delay on aircraft.

The structure of the paper is summarised as follows. The next section presents mathematical modeling of this problem. The third section describes the Q-learning algorithm used to solve this problem. The fourth section presents benchmarks on Paris Charles de Gaulle airport.

II. MATHEMATICAL MODEL

This section describes the mathematical model of aircraft, network and decision variables.

A. Network

Based on the model developed in [START_REF] Ma | Integrated Optimization of Terminal Manoeuvring Area and Airport[END_REF], STARs are represented with a graph G(N , L ) where N is the set of nodes and L the set of links. Among the set of nodes one can identify two subsets: N e ⊂ N is the subset of entry points of the TMA and N r ⊂ N is the subset of runways. The final links connecting the runways are also grouped in a link subset: L r ⊂ L . The CDG current network is represented in figure 1. We propose in this study to feed both runways, 27R and 26L, by a double point merge system which will merge on initial fix of each runway (IF 27R -RWY 27R and IF 26L -RWY 26L, respectively).

For each aircraft, the procedure is flown at constant speed. This speed is the landing speed which, in this work, we assume, for simplicity, that depends on its wake vortex category.

The PMS structure is represented on figure 2. For each aircraft, the length of PMS arc will be considered as a decision variable for the algorithm.

B. Aircraft data

A flight f is characterized with the following information:

• V 0,f : the initial true air speed of the aircraft • t T M A 0,f : the initial entry time in the TMA

C. Decision Variables

For each flight f , the following decision variables are considered :

• the speed of the aircraft, V f • the entry time in the TMA, t T M A f • the runway assigned for landing, r f • the length of the merge point arc, l M P f Such decision variable have to meet some constraints which are now introduced.

Speed: The speed of the aircraft has to stay in a given range of the initial speed:

V f ∈ V 0,f + p∆V
with p the number of increments and ∆V the speed increment: p ∈ Z and p∆V ∈ ∆V min , ∆V max and:

• ∆V max the maximum speed increase from V 0,f that can be assigned to an aircraft; • ∆V min the minimum speed decrease V 0,f that can be assigned to an aircraft which depends on the wake vortex category. Entry time in TMA: The entry time decision corresponds to a delay which can be absorbed in the En-Route airspace before the aircraft enters the TMA. In this airspace, the aircraft can be slowed down or accelerated in a given range. As a result, the entry time in TMA of the aircraft could also change in a given range:

t T M A f ∈ t T M A 0,f + p∆T
with p the number of increments and ∆T the time increment:

p ∈ Z and p∆T ∈ ∆T min , ∆T max and:

• ∆T max , ∆T min the maximum and minimum time increments from t T M A 0,f that can be assigned to an aircraft. Runway: To keep a balanced flow between runways, it could be sometimes more appropriate to change the landing runway of an aircraft (r f ∈ N r ).

Length of merge point arc: As the network contains merge points, one of the decision variable, l M P f , is the length of the arc that an aircraft will fly in one of the merge point.

l M P f ∈ p∆L
with p the number of increments and ∆L the length increment: p ∈ N and p∆L ≤ L M P max and L max M P the maximum arc length that a merge point could have.

III. OPTIMIZATION ALGORITHM A. Markovian Decision Process

In this problem, each flight is a Markovian Decision process MDP{S, A, P a , R a }. All decision variables represent the state space S. It means that, for every aircraft, a state is defined by {speed, entry time in the TMA, PMS arc length, runway assignment}. In each state, the following actions are considered: A = {increasing/decreasing the speed, increasing/decreasing the entry time in the TMA, increasing/decreasing the PMS arc length, changing the landing runway, no action}. For states that are not direct neighbors of the current state, the transition function value is 0. For neighbor states, the transition function is an equiprobalistic one:

P a (s, s ′ ) = 0, if s' is not a neighbor of s 1 Card(A) , otherwise

B. Q-learning

The Q-Learning (QL) is a model-free reinforcement learning algorithm [START_REF] Watkins | Learning from Delayed Rewards[END_REF]. This means that the algorithm does not need a model of the environment, it only interacts with the environment without knowing it, see figure 3. It is also an off-policy algorithm: the policy only determines which stateaction pairs are explored. For a correct performance, policies need to ensure that every state-action pairs are continuously explored.

Every aircraft is considered as an agent, making it a multiagent Markovian Decision Process (MDP) problem. The QL has been well studied on MDP [START_REF] Sutton | Reinforcement learning: an introduction[END_REF]. The QL is used to learn the optimal policy of a certain MDP. This is done by computing the Q-function for each aircraft -representing the expected reward that an agent can receive if he takes a given action in a given state. The QL used is a distributed one, meaning that the reward of each agent is treated individually at each iteration. Therefore, they are considered as independent learners.

For each agent, the expected reward Q(s, a) in a given state s, for a given action a, is updated as follows:

Q(s, a)+ = α(R + γ max a ′ Q(s ′ , a ′ ) -Q(s, a)) (1)
with:

• s ′ the new state when the action a is taken in the state s;

• R the reward the agent will receive by making the action a in s; • α the learning rate;

• γ the discount factor. The expected reward Q(s, a) in a given state s, for a given action a is updated at each iteration considering an estimation of the optimal future value max a ′ Q(s ′ , a ′ ). This is done independently of the policy being followed. Precisely, this is a one-step QL since the estimation is only done by looking one iteration ahead.

The pseudo code of the Q-Learning is given in Section III-B.

Algorithm 1 Q-Learning Initialisation for each agent Q(•, •) = Q 0 Require: T 0 , β, T f , iterations while T ≥ T f do for i ≥ iterations do for agent ∈ critical flight set do
Choose action a from s using the Boltzmann strategy;

Take the action a, observe R and s ′ ; Update Q(s, a) for this agent according to (1);

s ← s ′ end for i ← i + 1 end for T ← β × T end while
In order to balance the ratio between exploration and exploitation, a softmax exploration (or Boltzmann exploration) has been used. For a state s ∈ S, an action a ∈ A and the temperature T , the probability π(s, a) to choose a in s is given by:

π(s, a) = e Q(s,a)/T a ′ ∈A e Q(s,a ′ )/T
The temperature at the iteration number k, is given by a geometric law of parameter β, i.e. T k = T 0 β k , with T 0 the initial temperature. This temperature set the trade-off between exploration and exploitation : a relatively high temperature will promote the exploration of the Q table, contrary to a low temperature which is in favor of the exploitation of the Q table.

In this distributed Q-Learning, every aircraft is considered as a learning agent and consequently has a Q-table. All the Q-tables are initialized at a Q 0 value chosen relatively low to enforce the state exploration. It is done on purpose since the reward -and the Q-table -of an aircraft depends on agents close to it (meaning which could be in conflict). Every agent is seen as an independent learner. Then, for a given agent, the choice of an action does not consider the chosen action of other agents but only their actual states. Therefore, between two decision makings of an agent, its environment could have been changed. In order to reduce this possibility, an agent could choose the specific action of doing nothing, since then, its state will not change.

C. Reward function

For each aircraft, a reward function is computed to be used by the reinforcement learning algorithm. The reward given at each state and action depends on other aircraft's state and is computed as the weighted sum of rewards described below. All rewards presented here are negative, therefore the function reward has to be maximized.

R =w rta (R rta + 5R runway )+ w conf lict ( R link + R node )
If an aircraft f does not land on r 0,f , its preferred runway, the reward added is 5 times the R runway weighed by w rta . This is equivalent to a 5 minutes penalty. w rta and w conf lict will be established in section IV.

Next, the different terms of the reward function are described.

Required Time of Arrival: All airlines have a schedule for each aircraft and on-time aircraft should have a better reward. Then, a reward corresponding to the absolute difference between the RTA and the real arrival time is added to every aircraft.

R rta = -|t RT A f -t arrival |
Runway Number: This model considers airport with two runways used for landing. Such as before, airlines have dedicate terminals, therefore their aircraft prefer to land on a runway close to the gate in order to reduce taxi time. R runway = 0, landing on the required runway, r 0,f -1, otherwise Conflicts: When an aircraft is flying on a network, loss of separation may only appears on nodes or on links. Then, our model considers two kinds of conflicts: link conflict when two aircraft do not respect the wake vortex category separation and node conflict when aircraft do not respect the 3 NM horizontal separation at merge points [START_REF] Ma | Integrated Optimization of Terminal Manoeuvring Area and Airport[END_REF].

Links Conflicts: For each link, at the entrance and the exit, the minimum separation between two aircraft f and g has to correspond to the table I. Assuming that s f,g is the separation minimum and d f,g is the actual distance between the leading aircraft f and the trailing g, see figure 4, the criticality of a potential conflict, C link , is proportional to the distance between aircraft. Overtakings are also computed, if this occurs, then d f,g < 0 and the criticality of the conflict is set to -1. C link is a piecewise linear and continuous function which is necessary for the learning algorithm: between two decision makings, the algorithm needs to know if the conflict is getting better or worst. Since C link could be close to 0 such as R rta , the learning algorithm could improve the R rta instead of resolving the conflict. In order to prioritize the conflict solving objective, the reward function for the link conflict is artificially set between -0.3 and -1 while preserving the linear variation using the formula:

C link =        -1, if d f,g < 0 - |s f,g -d f,g | s f,g , if d f,g < s f,g 0, otherwise
R link = -0.3 + (C link * (1 -0.3))
Node Conflicts: Even if there is no link conflict between two aircraft f and g, there still could be conflicts on nodes. In TMA, every aircraft has to be separated by 3 NM from others in order to respect the separation distance. But as [START_REF] Ma | Integrated Optimization of Terminal Manoeuvring Area and Airport[END_REF] shows, in many airports, thanks to the network geometry, the detection area could be reduced to a 2.2 NM radius circle, see figure 5. As for the links, the criticality of a conflict on a node is given by the formula:

C node = - 2.2-d f,g 2.2 , if d f,g < 2.2 0, otherwise
As for the links, the reward function used for a node conflict is artificially set between -0.3 and -1 while preserving the linear variation by the formula:

R node = -0.3 + (C node * (1 -0.3))

D. Sliding Window

In this problem, if an aircraft enters in the TMA many hours before another one, their decisions can be considered as independent. Therefore, it is not relevant to optimize the whole problem in one attempt. This is why we introduce a sliding window and run the optimization algorithm only on it. It reduces the number of irrelevant decision variables and the computational time [START_REF] Ma | Merging Flows in Terminal Moneuvering Area using Time Decomposition Approach[END_REF] [START_REF] Xiangwei | Sliding window algorithm for aircraft landing problem[END_REF].

Aircraft are classified into four groups, see figure 6:

• Completed, the latest landing time is before the starting time of the window; • On going, the earliest entry time is before the starting time of the window. For these, decisions have already been made • Active, the earliest entry time and the latest entry time is in the time window • Planned, the latest entry time is after the end of the sliding window

At each iteration of the sliding window, the optimization algorithm is run on active flights. The difference between the earliest entry time and the latest entry time for a given aircraft is about 7 minutes. Based on this, the sliding window wide has been fixed at 21 minutes (see table II). Also the time shift between two consecutive sliding windows has also been fixed to 7 minutes.

E. Critical Flight Set

Running the algorithm on every active flight in the sliding window is not efficient enough, some them have already a good reward and others have multiple conflicts. In order to speed up the optimization process, decisions are changed with a higher priority on aircraft with the worse reward. Those aircraft are indicated as critical flights.

Those critical flights are computed by using a threshold, which is compared to the reward. Aircraft in this critical flight set are these above 70% of the worst aircraft reward. Since these aircraft are learning, their rewards decrease and more and more aircraft are considered as "critical" as the average reward lowers.

Q 0 -150 α 0.1 γ 0.95 wrta 1 w conf lict 100 TABLE III THE QL PARAMETERS CHOSEN IV. APPLICATION A. Scenario
The benchmarks have been done on heavily-loaded scenarios but only considering LORNI and OKIPA entries. The initial fight set representing a regular day at CDG on those two entry points contains a total of 458 aircraft. However, in order to simulate extra demand, some of them have been duplicated and added to the initial set. In order to be coherent with the reality, aircraft have been added in regards with the density of aircraft in the initial set. The probability for an aircraft to be added at a high density time is higher than to be added at a low density time. The algorithm has been run on sets up to 50% bigger than the initial demand, i.e. 687 aircraft.

The maximum speed of in the TMA has been fixed at 250kts since they are below flight level 100. The minimum approach speed they can have depends on the wake vortex category: 220kt for heavy aircraft and 190kt for medium aircraft. This approach speed is a variable of the QL. This scenario does not contain light aircraft. After the merge point, in the final leg, the speed is fixed at 185kt for heavy aircraft and 155kt for medium aircraft.

For each different decision variable, different steps as been chosen : 10kt for the speed step, 20 seconds for the time step and 0.5 nm for the PMS arc length step. With that, the number of state possible is 5040 for a Medium aircraft and 2520 for a Heavy aircraft.

B. QL Parameters Optimized by Genetic Algorithm

As [START_REF] Tijsma | Comparing exploration strategies for Q-learning in random stochastic mazes[END_REF] shows, the Boltzmann exploration strategy required temperature parameters to be well chosen in order to perform well. To find the best combination of parameters, a genetic algorithm [START_REF] Michalewicz | Genetic Algorithms + Data Structures = Evolution Programs, ser. Adaptive computation and machine learning[END_REF] has been used. The QL parameters optimized by the genetic algorithm are the following: T 0 , T f , β, iterations, critical flight set threshold.

The other QL parameters is given by the table III. w rta has been set to 1 and w conf lict to 100 to ensure that the algorithm is first focused on conflict solving then on minimizing delays.

Evaluation: In this algorithm, an individual is a combination of Q-Learning parameters. To evaluate an individual, the QL is run 5 times with the corresponding parameters. The fitness associated to this individual is the average of final rewards of the five runs minus the standard deviation of these rewardsreminder, rewards are all negatives. This is done to not only optimize the best result that the QL can have but also the stability of the QL with these parameters. The pseudo-code of such evaluation is summarized in algorithm 2.

Algorithm 2 Evaluate an individual

procedure EVALUATE(individual) for i ← 1, j do ▷ j = 5 is enough to be precise Run the QL with the parameters given by the individual Observe the reward R i end for return The average of all R i minus the standard deviation of all R i end procedure Crossover: A uniform crossover has been chosen, for every child parameter, the value is randomly chosen between the two parents.

Mutation: For every parameter of every individual, the probability of a mutation is 0.2. The new value is chosen randomly in the parameter set.

The overall genetic algorithm is given in algorithm 3. In order to avoid the genetic algorithm to overfit the QL parameters, it has been run multiple times on different heavilyloaded scenarios. On some scenarios, every conflict has been solved and the algorithm couldn't go further. This is showed in figure 7, the critical flight set threshold parameter gives the same result in the range [0.7, 0.9].

Algorithm 3 Genetic Algorithm

C. Results

Figure 8 shows the value of the Q-function for an agent over iterations. Two exponential curves can be seen, these represent the exploitation part of the Boltzmann exploration strategy. This occurs at every sliding window when the temperature drops if, and only if, the aircraft has a so low reward that it is selected. Here, the red line separate the two different sliding windows. In this case, the Q-table was initialized to -150. This is why many values on this graph equal -150, it is the default value until this state and its neighbors have been more deeply explored.

Since the optimization is run only on worst aircraft first, the threshold drops all along the iterations. This means that more and more aircraft are selected in the critical flight set. Depending on the temperature at which aircraft enter in the critical set, the Boltzmann strategy allows the exploration to go more or less further. At the end of iterations, the temperature is very low and the best states discovered in the exploration part are now more likely to be reached. This bring the total reward of the sliding window to strongly improve (see figure 9).

The figure 10 represents aircraft rewards at LORNI for the first and the final state of a scenario. Each bar represents an aircraft, and the length of bars are proportional to the rewards -be aware, scales are different between the two graphs. If the aircraft is in conflict at some point, the bar is in red, in blue otherwise. The QL algorithm is very efficient on hot spots, since every conflict has been solved, the delay is now shared between all aircraft, maximizing the reward for each one.

Table V gives the average results over 10 iterations of the QL on a heavily-loaded scenario. The process was run on a 3.1GHz core i5 CPU with Java code. that aircraft have flown. The length step used is 0.5 nm. The average arc length for an aircraft in this scenario is 4.9 nm.

V. CONCLUSION Centralized AMAN has been extensively studied in the literature but few initiatives have been proposed for a decentralized version of such algorithm. This paper has presented an efficient decentralized sequencing and merging algorithm. A mathematical model, based on a network model, has been presented for which aircraft decision variables and constraints have been introduced. A distributed algorithm based on Qlearning has been proposed, for which parameters have been optimally tuned thanks to a genetic algorithm. This algorithm has been implemented by using a sliding window mechanism. It has been successfully applied to CDG airport for which demand has been artificially increased with a total of 687 aircraft landings. Conflict free solution for a full day of traffic has been computed in less than 30s which is really adapted for real time planning.

This approach is relevant for aircraft landing but is even more adapted for UTM, for which no centralized system is expected to manage the landing of many UAV at the same location.

In future work, such algorithm will be improved by taking into account uncertainties (wind, etc..) but also by using a more realistic aircraft model based, for instance, on BADA model.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Simplified STAR model at CDG: aircraft enter at LORNI or OKIPA. Merge points are located on both IF 27R and IF 26L

Fig. 3 .

 3 Fig.3. The agent -environment interaction in a Q-Learning : the agent does not know his environment but only the state and reward following an action

Fig. 4 .

 4 Fig. 4. Link conflict detection based on the comparison of distance between aircraft at the beginning or the end of a link with the separation minima

Fig. 5 .Fig. 6 .

 56 Fig. 5. Node conflict based on a circle detection area

Fig. 7 .

 7 Fig. 7. Genetic algorithm results on critical flight set threshold parameter, 150 individuals evaluated over 10 generations

Fig. 9 .

 9 Fig. 9. Evolution of the total reward (sum of all aircraft's reward) of a given Sliding Window, this could be seen as the learning curve of the algorithm over a certain sliding window Parameter Average Value Delay 75 sec Number of conflict 0 Runway change 5.3 Worst reward -8.7 Computational time 32 sec

Figure 11

 11 represents aircraft delays histogram. The time step used is the same as the time step used in the model: 20 seconds. The average delay of aircraft in this scenario is 73 sec.Finally, figure12gives the histogram of the arc length

Fig. 10 .

 10 Fig. 10. Reward for aircraft in the flight set at LORNI; aircraft in red are in conflict, in blue otherwise. Results are shown before optimization on the top and after on the bottom.

Fig. 11 .

 11 Fig. 11. Histogram representing the delay of aircraft in the scenario (687 aircraft)

TABLE I SEPARATION

 I MINIMA FOR LINK CONFLICT IN NM

TABLE IV THE

 IV BEST QL PARAMETER COMBINATION FOUND BY THE GENETIC ALGORITHMSelection: Individuals used to generate a new generation are those with the best fitness.

TABLE V AVERAGE

 V RESULT (COMPUTED ON 10 DAY OPTIMIZATION) OF THE QL WITH THE PARAMETERS FOUND IN THE PREVIOUS SUBSECTION (FOR 687

AIRCRAFT PER DAY).


Chunyao Ma

Sameer Alam

Qing Cai
email: qcai@ntu.edu.sg

Daniel Delahaye
email: daniel.delahaye@enac.fr

Sector Entry Flow Prediction Based on Graph Convolutional Networks

Keywords: air traffic, flow prediction, graph convolutional network, spatial-temporal

Improving short-term air traffic flow prediction can help forecast demand and maximize existing capacity by tactical air traffic flow management. Most existing studies in flow prediction lacks consideration of the dynamic, structural, and interrelated nature of air traffic flows in the airspace. Therefore, this paper proposes to predict sector entry flows based on graph convolutional networks, which consider the dynamic spatial-temporal features of air traffic from a graph perspective. First, we specify a sector entry flow based on its upstream and downstream sectors. Then, each entry flow is denoted as a node in a graph. The weighted edges between the nodes are learned from a Word2vec model based on air traffic flows among the nodes. With the weighted graph constructed and the temporal flows on the nodes extracted from the flight trajectories, an Attention-based Spatial-Temporal Graph Convolutional Network (ASTGCN) module is adopted to capture spatial-temporal features of recent, daily-periodic, and weekly-periodic flows in the graph. Finally, The outputs from the ASTGCN module based on the three features are fused to generate the final prediction results. The proposed method is applied on 164 sectors of French airspace for one-month ADS-B data )from Dec 1, 2019, to Dec 31, 2019) which includes 158,856 flights. Results show that, the proposed method outperforms the well established Long shortterm memory (LSTM) model, and demonstrates better capability in predicting rapid changes in traffic flow and has relatively smaller decrease in prediction accuracy as the prediction timewindow increases.

I. INTRODUCTION

Controlled airspace around the world is reaching its operational capacity as air transportation grows both physically and operationally [START_REF] Netjasov | Framework for airspace planning and design based on conflict risk assessment: Part 1: Conflict risk assessment model for airspace strategic planning[END_REF]. One of the key challenge confronted by air navigation service providers (ANSPs) is the imbalance between the limited airspace capacity and the increasing traffic demand, which is the major source of air traffic congestion that leads to traffic delays, economic losses, and potential safety issues [START_REF] Clarke | Determining stochastic airspace capacity for air traffic flow management[END_REF]. Although passenger demand during the outbreak of the COVID-19 pandemic almost came to a standstill, with traveling restrictions are being lifted gradually, air traffic demand is now on its way to ramping up [START_REF] Gudmundsson | Forecasting temporal world recovery in air transport markets in the presence of large economic shocks: The case of covid-19[END_REF]. This brief pause for the air transportation industry could also be an opportunity to develop and adopt new approaches to accommodate future air traffic growth.

In the presence of limited capacity, an accurate short-term air traffic flow prediction, i.e., 0-2 hour look ahead time [START_REF] Lin | Deep learning based short-term air traffic flow prediction considering temporal-spatial correlation[END_REF], in the airspace can be vital for Air Traffic Controllers (ATCs) about managing the forthcoming traffic flow situation and evaluating of control strategies [START_REF] Chen | A network-based dynamic air traffic flow model for short-term en route traffic prediction[END_REF]. In this way, tactical Air Traffic Flow Management (ATFM) [START_REF]ATM/501, 15th Edition, Procedures for Air Navigation Services[END_REF] measures can be planned and executed in advance in a more efficient manner to maximize the use of the existing airspace capacity [START_REF] Nosedal | An optimization model to fit airspace demand considering a spatio-temporal analysis of airspace capacity[END_REF]. For instance, ATCs can execute the agreed tactical measures, such as traffic re-routing and flight level allocation, in advance, to provide a smooth and efficient flow of traffic where demand is foreseen to exceed capacity or disruptions such as convective weather appears, to utilize the available capacity to the maximum extent [START_REF] Sridhar | Aggregate flow model for air-traffic management[END_REF].

II. RELATED LITERATURE

In current literature, there are mainly two types of shortterm air traffic flow modelling and prediction methods, i.e., trajectory-based method and aggregate method. Trajectorybased air traffic flow prediction is based on propagating the flight trajectories over time and using the predicted trajectories to count the future number of flights in the airspace [START_REF] Fernández | Dart: a machine-learning approach to trajectory prediction and demandcapacity balancing[END_REF]. However, research shows that the prediction error of the trajectory-based method increases exponentially as the forecast time horizon increases beyond 20 minutes, which may be caused by its sensitivity to various influencing factors, such as weather conditions, airspace restrictions, and human factors [START_REF] Lymperopoulos | Model based aircraft trajectory prediction during takeoff[END_REF]. Furthermore, the dimension of the trajectory-based method depends on the number of flights under consideration, which can requires huge computational costs and make such methods untenable in real world context.

Efficient ATFM demands prediction of the overall traffic flow situations in the specified airspace, instead of the temporal trajectory of individual aircraft. Thus, the aggregate air traffic flow models focus on predicting the overall distributions of the air traffic flow in the airspace [START_REF] Wei | Total unimodularity and decomposition method for large-scale air traffic cell transmission model[END_REF]. Since flights in the airspace are spatially aggregated, the computational cost can be reduced significantly comparing to the trajectory prediction based approaches. Moreover, without considering the individual behaviours of flights, the aggregated prediction methods are less sensitive to the uncertainty factors related to individual flights and a longer forecast time horizon with less prediction errors can be achieved.

Recently, the aggregated approach is widely discussed in the literature, which mainly predict air traffic flow based on probabilistic analysis or machine learning techniques. Based on the flights transition probability between adjacent air traffic control centers, a stochastic framework with Linear Dynamic System Model (LDSM) was developed by Sridhar et al [START_REF] Sridhar | Aggregate flow model for air-traffic management[END_REF]. The traffic flow is predicted as the flights count in each control center during a short term, e.g., a few hours, using the flights transition probability between adjacent centers extracted from historical data, the number of departure/arrival flights in the control center and the departure uncertainties. The major shortcoming of the stochastic framework is that it adopts Poisson distributions to model the departures at each time step, ignoring the fact that the departure traffic flow varies significantly during days, weeks and seasons under different traffic conditions. Gilbo et al. further explored the stochastic LDSM to predict the air traffic flow at the sector levels using a linear regression model [START_REF] Gilbo | A new model to improve aggregate air traffic demand predictions[END_REF]. However, their research mainly focused on improving the flow prediction results of the Enhanced Traffic Management System, without deeper investigation of the prediction mechanism of air traffic flow prediction.

Probabilistic based models for flight or airspace were also studied to illustrate stochastic features, such as flight speed and traffic density, of the air traffic and further used to predict the traffic flow [START_REF] Chen | A network based dynamic air traffic flow model for en route airspace system traffic flow optimization[END_REF]. However, the performances of probabilistic methods are affected by handcraft models or analyses, which makes it difficult to fully depict the real traffic situation and capture the sharp changes in the highly dynamic traffic flow.

In recent years, machine learning algorithms are started to be implemented in aggregated air traffic flow prediction [START_REF] Polson | Deep learning for short-term traffic flow prediction[END_REF]. In [START_REF] Lin | Deep learning based short-term air traffic flow prediction considering temporal-spatial correlation[END_REF], the authors discretized the airspace into small cubes and predicted the flight count in each cube. The prediction was achieved by a convolutional neural network and recurrent neural network to model the spatial and temporal correlations of air traffic flow. The main shortcoming of this model is that the disintegration of airspace into cubes ignores the structural features of the airspace, such as airway network structure and sectorisation schemes. This may limit the practical implementation of the prediction results in ATFM. In [START_REF] Zhang | Research on air traffic flow forecast based on elm non-iterative algorithm[END_REF], the authors adopted a Phase-Space Reconstruction Extreme Learning Machine (PSR-ELM) model to learn and predict the time series of traffic demand passing given waypoints in the airspace. In [START_REF] Gui | Machine learning aided air traffic flow analysis based on aviation big data[END_REF], by exploring ADS-B data, the authors adopted long Short-Term Memory (LSTM) and Support Vector Machine (SVM) to predict the air traffic demand between two airports. The limitation of such time-series models is that they fail to consider the effects that the air traffic network has on time-series flow at a single waypoint or airport pair, which may restrain the prediction accuracy of the models [START_REF] Dalmau-Codina | A machine learning approach to predict the evolution of air traffic flow management delay[END_REF].

Note that most of the current literature in air traffic flow prediction lacks considerations of the highly dynamic, structural and interrelated nature of air traffic flows in the airspace, such as considering the air traffic flow at different positions in the airspace as different time-series isolated from each other. This paper proposes to predict sector entry flows based on a graph-represented structure of air traffic, which intrinsically considers the dynamic spatial-temporal evolution of air traffic from a graph perspective. First, the sector entry flow prediction is formulated as a three-stage-flow prediction problem, which considers three stages of an entry flow: the upstream sector, the entry sector, and the downstream sector. Each sector entry flow is then represented by a node in the graph. Further, the interactions among the entry flow in the airspace are described by the weighted edges between nodes, which is modelled by a Word2vec neural network [START_REF] Church | Word2vec[END_REF] using the sequences of traffic flow transitions among the nodes. With the weighted graph constructed and the temporal flows on the nodes extracted from the flight trajectories, an Attention-based Spatial-Temporal Graph Convolutional Network (ASTGCN) module is adopted to capture spatial-temporal features of recent, daily-periodic, and weekly-periodic air traffic flows in the airspace.The outputs from the ASTGCN module based on the recent, daily, and weekly historical data are fused to predict the traffic flow on the nodes (sector-entry).

III. PROBLEM DESCRIPTION

A sector's capability in handling air traffic is not only determined by the number of the flights that can be served, but also influenced by the traffic complexity inside the sector, such as flight distributions and flight speeds [START_REF] Delahaye | Air traffic complexity map based on linear dynamical systems[END_REF], [START_REF] Prandini | Toward air traffic complexity assessment in new generation air traffic management systems[END_REF]. Thus, besides predicting the number of future flights entering a sector, it is also essential for air traffic flow predictions to provide the distribution of the upcoming traffic flow of the sector, such as the number of flights crossing the entry/exit points of the sector, the number of flights transiting through the air routes in the sector, or the number of flight passing certain waypoints in the sector. In recent years, the gradual implementation of Free Route Airspace (FRA) gives flights some freedom to plan their routes between an entry point and an exit point without referring to the ATS routes [START_REF] Samolej | Regular graph-based free route flight planning approach[END_REF]. Fig. 1 shows the one-day flight trajectories (red lines) in French airspace (sector boundaries shown as black lines), where the FRA has been implemented in nearly 50% of the airspace above flight level 195 [START_REF]Dsna france introduces free route airspace above 6000m[END_REF]. It can be observed from Fig. 1 that the majority of flight trajectories follows straight path and do not follow specific air routes in the airspace. The entry/exit points of flights into a sector are no longer fixed at certain positions at the sector boundary. Under this context, it is however impractical to predict air traffic flow on airways, fixed entry/exit points on sector boundaries, or waypoints.

Note that in the FRA, flights will remain subject to control from the sector ATCs. We can notice from Fig. 1 that most of the flows entering a sector are aggregated by their upstream and downstream sectors. Therefore, predicting the number of flights in the entry flow along with downstream and upstream information, i.e., where the flow is from and where it is going to, can provide ATCs an understanding of the emerging flow in a sector to develop flow control strategies.

Given the above analysis, this paper aims to predict the number of flights in the sector entry flows. An entry flow of a sector is defined as the flow entering the sector in which the flights have the same upstream and downstream sector. The prediction outcome will be the number of flights in each sector entry flow during a look-ahead time. For instance, flow "S1S2S3" represents one entry flow to Sector "S1", which is from Sector "S2" and going to Sector "S3". And this paper proposes to predict the number of flights in flow "S1S2S3" during a given look-ahead time.

IV. METHODOLOGY A. Methodology Overview

The proposed method to predict the sector entry flows comprises seven steps. The first step denoises the raw ADS-B data. The second to fourth steps organize the denoised ADS-B data and airspace structure data into a spatial-temporal graph. The rest three steps build the machine learning framework to learn from the spatial-temporal traffic information and make predictions about future traffic flow.

The flight information used in the paper is extracted from ADS-B data. It faces plenty of noises in measuring barometric altitudes, which is susceptible to variations in atmospheric conditions [START_REF] Ali | A study on geometric and barometric altitude data in automatic dependent surveillance broadcast (ads-b) messages[END_REF]. Therefore the first step is to remove the noises from the barometric altitude data. From the denoised ADS-B data, 4D trajectories of the flights is obtained i.e., time series data with geographic information. Therefore, in the second step, by referring to the airspace structure data, i.e., sector boundaries, we can map each 4D trajectory into a sequence of nodes at sectors boundaries and determine the corresponding times when the flight passes the nodes. In the third step, the nodes sequences are fed to a Word2vec model, which extracts the notion of relatedness across nodes and encodes each node into a numerical vector. By calculating the similarity between the vectors, we can quantify the relatedness between nodes, i.e., weights on the edges connecting the node pairs. In the fourth step, a spatial-temporal graph is built to describe the flow of air traffic in the airspace by combining the times series of flights on each node with the weights on the edges between nodes.

Based on the spatial-temporal graph established in the previous four steps, the last three steps adopt a graph-based neural network to achieve the prediction of the sector entry flow.

Step five organizes the spatial-temporal graph obtained in step 4 into a time series sliding over different time slices, from which the weekly, daily, and recent flow features can be extracted.

Step six adopts an ASTGCN module to capture the dynamic spatial and temporal patterns from the weekly, daily, and recent data. And in the seventh step, the outputs from the ASTGCN module of the three features are fused to obtain the air traffic flow prediction for the future time slices.

Following subsections details about data denoising, spatialtemporal graph construction, and the graph-based neural network to learn and predict air traffic flow.

B. Data Denoising

ADS-B data for aircraft surveillance can give highly accurate aircraft position and velocity information, providing a useful source for analytical solutions to effective and efficient airspace usage [START_REF] Ma | Airway network management using braess's paradox[END_REF]. However, ADS-B data still includes some noise in flights' geographic information, especially barometric altitude [START_REF] Mohleji | Modeling ads-b position and velocity errors for airborne merging and spacing in interval management application[END_REF]. The black line in Fig. 3 shows a flight trajectory extracted from the ADS-B data. Many spikes are observed in different phases of the flight, especially in take-off, cruise, and landing. This section will describe removing these spikes from the flight trajectory.

To remove the spikes from the cruise phase data, we adopt a median filter [START_REF] Amanipour | Median filtering forensics in compressed video[END_REF] that moves through the trajectory data one by one; and replaces each value with the median value of its neighboring data. The green line in Fig. 3 shows the denoised flight trajectory, in which the spikes in the cruise phase are smoothed after applying the median filter.

However, We cannot wholly flatten the noise in the altitude data by using a median filter, as a spike can still be observed at the initial part of the green curve. The cause of the altitude data busts during the take-off/landing phase may be the failure to change the necessary QNH [START_REF] Martinez | A boosted tree framework for runway occupancy and exit prediction[END_REF] setting during the takeoff/landing phase to the correct altimeter setting [START_REF] García-Heras | Analysis of the geometric altimetry to support aircraft optimal trajectories within the future 4d trajectory management[END_REF]. Thus, during the take-off/landing phase, the outlier data constantly show up over a relatively long time window, compared to the cruise phase during which the outlier data appear individually and are easy to be removed through a median filter. Given the constant occurrence of inaccurate barometric altitude data during take-off/landing, it is better to remove the trajectory data during these phases, i.e., below a certain flight level threshold, to avoid influencing the reliability of the research results. Therefore, we apply Robust Locally Weighted Scatterplot Smoothing (RLOWESS) [START_REF] Johnson | Sensitivity of holocene east antarctic productivity to subdecadal variability set by sea ice[END_REF], which uses locally weighted linear regression to smooth data, onto the filtered data (green line) to fit a smooth curve from which we can identify the overall trend of the trajectory. The blue line in Fig. 3 shows the smoothed curve after applying RLOWESS. By removing the corresponding data in the green line below a certain flight

C. Spatial-temporal Graph Construction

This section organizes the denoised flight trajectories and the airspace structure information into a spatial-temporal graph representation G = (V, E), where V is the set of nodes in the graph, and E is the set of edges indicating the connectivity between the nodes. This section consists of nodes extraction, edges generation, and graph construction.

1) Nodes Extraction: From the ADS-B data, 4D flight trajectories, containing the geographic information of flights over time, can be obtained. By intersecting the 4D flight trajectories with sector boundaries, it can be determined where and when a flight enters into each sector. An entry point of a flight into a sector can be described as a node defined by the entry sector, the upstream sector, and the downstream sector. More specifically, when a flight f k enters sector S i from sector S i-1 then goes to sector S i+1 , it belongs to the entry flow of sector S i described by the node S i S i-1 S i+1 .

Fig. 4 presents an example of nodes extraction from the trajectory of three flights. Flight f 1 and f 2 enter sector S 1 from sector S 2 , then go to sector S 3 . Therefore, according to the definition of entry flow in the Problem Description section, the two flights belong to the entry flow of sector S 1 represented by the node S 1 S 2 S 3 . Similarly, upon entering sector S 3 , the two flights are classified to the entry flow of S 3 represented by 2) Edges Generation: After determining the nodes, the next step is to construct the edges between the nodes. In this study, if two nodes are passed by a flight consecutively, they will be considered connected, and there will be an edge between them. Most current research in graph convolutional networks for traffic flow prediction either a binary graph [START_REF] Zhu | Ast-gcn: Attribute-augmented spatiotemporal graph convolutional network for traffic forecasting[END_REF] or set the edge weights according to the geometric distance between the nodes [START_REF] Guo | Attention based spatialtemporal graph convolutional networks for traffic flow forecasting[END_REF]. However, these simple representations of the weights may fail to capture many complex features in the graph, e.g., some edges are frequently traveled while some are seldom used, which may limit the ability of graph convolutional networks to learn from the features of neighboring nodes [START_REF] Xie | Attention adjacency matrix based graph convolutional networks for skeleton-based action recognition[END_REF]. Therefore, instead of adopting a simple representation of the weights, this paper proposes to learn the edge weights through the traffic data, i.e., the sequences of nodes generated from each flight trajectory.

Word2vec is a technique for natural language processing published in 2013 [START_REF] Church | Word2vec[END_REF]. It uses a neural network to model word associations by training from a text corpus. In this process, Word2Vec can build a vocabulary from the training text corpus and learn the vector representations of each word. The cosine similarity between the vectors can indicate semantic similarity between the words represented by those vectors [START_REF] Ma | Using word2vec to process big text data[END_REF].

Making an analogy between a node sequence and a text sentence with the nodes being the words in the sentence, the set of node sequences generated from the flight data can be regarded as the text corpus. Thus, by feeding the node sequences to a Word2vec model, we can obtain the vector representation for each node. Subsequently, the edge weights between nodes can be described by the cosine similarity between the corresponding vectors. In this way, the weighted edges between the nodes in the graph are determined.

3) Graph Construction: We have determined the nodes and edges for a graph in the previous two steps. For each node, based on the time of each flight passing it, we associate it with a time-varying traffic flow described by a sequence of flights on the temporal dimension. More specifically, if flights f 1 , f 2 , ..., f k pass the node S i S i-1 S i+1 at an increasing sequence of time t 1 , t 2 , ..., t k , the temporal flow on node S i S i-1 S i+1 can be represented by a sequence {(f 1 , t 1 ), (f 2 , t 2 ), ..., (f k , t k )}. The nodes with dynamically changing flow and the weighted edges between nodes constitute the spatialtemporal graph structure.

D. Sector Entry Flow Prediction

Given the spatial-temporal graph constructed in the last step, this section predicts the flows, i.e., the number of flights, passing the nodes in the graph during a future time slice.

With the temporal flight sequence recorded on each node in the graph G, we can determine a traffic flow time series for each node over different time slices. We use x i t ∈ R to denote the traffic flow of node i at time t. X t = (x 1 t , x 2 t , ..., x N t ) T ∈ R N denotes the traffic flow values of all nodes at time t. N is the number of nodes in the graph. χ = (X 1 , X 2 , ..., X τ ) T ∈ R N ×τ denotes the traffic flow values of all nodes over τ time slices. Therefore, the air traffic flow prediction problem can be specified as: given χ, traffic flow values at all the nodes on the graph over past τ time slices, predict future traffic flow sequences Y = (y 1 , y 2 , ..., y N ) T ∈ R N ×Tp of all the nodes on the whole traffic graph over the next T p time slices, where y i = (x i τ +1 , x i τ +2 , ..., x i τ +Tp ) ∈ R Tp denotes the future traffic flow of node i from τ + 1 to τ + T p .

As shown in Fig. 2, this paper incorporate three time series features, i.e., recent flow series, daily flow series, and weekly flow series, to predict the future traffic flow. The three features are designed to respectively model the recent, dailyperiodic and weekly-periodic dependencies of the historical data. Assume the sampling frequency is q times per hour, the current time is t 0 , and the prediction window size is T p . We extract three time series segments during the last T h hours, T d days and T w weeks as the input of the recent, daily-period and weekly-period feature respectively. Details about the three time series segments are illustrated below.

The recent segment is a segment of historical data adjacent to the predicting period, which is designed to capture the influence of the recent traffic evolution on the future traffic flows. This recent flow segment can be specified as:

χ h = (X t0-T h ×q+1 , X t0-T h ×q+2 , ..., X t0 ) ∈ R N ×S h , while S h = q × T h .
The daily-periodic segment is a time series of traffic flow over the past few days during the same time period as the predicting period, which is designed to capture the daily repeated patterns of air traffic flow. The daily segment can be specified as:

χ d = (X t0-T d ×24q+1 , ..., X t0-T d ×24q+Tp , X t0-(T d -1)×24q+1 , ..., X t0-(T d -1)×24q+Tp , ..., X t0-24q+1 , ..., X t0-24q+Tp ) ∈ R N ×S d , while S d = T p × T d .
The weekly-periodic segment is composed of the flow series on last few weeks, which have the same week attributes and time intervals as the forecasting period. It is designed to capture the weekly repeated patterns of air traffic flow. The weekly segment can be specified as: χ w = (X t0-7Tw×24q+1 , ..., X t0-7Tw×24q+Tp , X t0-7(Tw-1)×24q+1 , ..., X t0-7(Tw-1)×24q+Tp , ..., X t0-7×24q+1 , ..., X t0-7×24q+Tp ) ∈ R N ×Sw , while S w = T p × T w .

Each of the three time series feature will be fed to the ASTGCN module, shown in Fig. 2, respectively to model three temporal properties of air traffic flows. The ASTGCN module consists of a number of spatial-temporal blocks as well as a fully connected layer in the end to keep the output dimension the same as the forecasting target. A spatial-temporal block mainly consists of two mechanisms. First is the spatialtemporal attention mechanism which is employed to capture the dynamic spatial-temporal correlations in the traffic data. The second mechanism is the spatial-temporal convolution which uses graph convolutions and common standard convolutions to respectively capture the spatial dependencies from the neighborhood and the temporal dependencies from the time series. The spatial-temporal attention combined with the spatial-temporal convolution forms a spatial-temporal block. Multiple spatial-temporal blocks can be further stacked to capture larger range of dynamic spatial-temporal correlations.

Eventually, the outputs from the ASTGCN based on each of the three features are weighted fused to generate the final prediction results of traffic flow on the nodes, depending on the significance of the influence of the three features. The final prediction result after the fusion can be described as:

Ŷ = W h • Ŷh + W d • Ŷd + W w • Ŷw (1)
where • represents the Hadamard product. W h , W d and W w are the learned parameters to quantify the influence of the three features on the forecasting target.

V. EXPERIMENTAL STUDY

With the proposed method, we have carried out an experimental study on the French airspace using one-month ADS-B data from December 1, 2019 to December 31, 2019. A number of 158856 flights and 164 sectors in French airspace are included in the study. The prediction target is the hourly sector entry flows. The look ahead time investigated in this experiment ranges from 1 hour to 2 hours. The following sections presents the result of the experimental study.

A. Graph Construction

By intersecting the flight trajectories with the sector boundaries in the French airspace, we have extracted 6028 nodes for the traffic graph to represent different entry flows of the 164 airspace sectors. From the sequence of nodes on a flight trajectory, we have determined the edges in the graph.

The sequences of nodes are further fed to the Word2vec neural network to model the edge weights. Fig. 5 shows the constructed graph for the French airspace. Each red node in the graph denotes a sector entry flow, and the node's size is proportional to the size of the traffic flow passing through it. Each blue line represents an edge in the graph, while the line thickness is proportional to the edge weight.

C. Result Analysis and Comparison

We have compared the node flow prediction results of the proposed method with the state of art time series prediction model LSTM. Given there are over 6000 nodes in the graph, here we use a busy node in French airspace, node "LFBBP2-LFBBP1-LFBBP3", as an example to present the prediction result on the test dataset. According the node definition, node "LFBBP2-LFBBP1-LFBBP3" represents an entry flow of sector "LFBBP2", which is from sector "LFBBP1" and heading to sector "LFBBP3". Fig. 6 presents the traffic flow prediction result from 00:00 to 23:59 on Dec 30, 2019. The upper panel plots the prediction results for the next 1 hour (0-1 hour), while the lower panel plots the prediction for the next 1-2 hours. The red solid shows the true number of flights passing node "LFBBP2-LFBBP1-LFBBP3", the green dash shows the predicted value using the proposed method based on Graph Convolutional Networks (GCN), and the black dash shows the predicted value using LSTM. We can observe from Fig. 6 that both the proposed method and the LSTM model give forecasts that are close to the actual flow value in the coming 1 hour, while the proposed method can better capture the sharp increases in traffic flow. When the prediction window increases to 2 hours, the performance of the two models decreases. The Table I shows the average performance comparison between the proposed method and the LSTM model, including three metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE) and Root Mean Squared Error(RMSE). It can be seen from Table I that the proposed method achieves better performance in terms of all evaluation metrics. Fig. 7 shows the changes of prediction performance of the two models as the prediction window increases. Generally, when the prediction window is longer, the challenge of prediction becomes greater, consequently the prediction errors will increase. As can be seen from Fig. 7, LSTM can achieve good results in the shortterm prediction. However, with the increase in the prediction window size, the prediction accuracy drops dramatically. The reason of the sharp decrease in the performance of LSTM model may be that the LSTM model learns the correlations in the flow times series on the target node instead of the causal relationship between flows. Therefore its predictive power reduces sharply when trying to estimate the target at a later stage. As shown in Fig. 8, the predicted values using LSTM are highly correlated to the latest true value available in the input data. When the prediction window is 1 to 2 hours, we can observe a one-hour lag between the truth and the prediction of LSTM, while a zero-lag of the proposed method. The proposed method considers the spatial-temporal correlations which are more important in the long-term prediction. It has the potential to learn the causal relationship between flows from a graph perspective and produce good prediction results even when the prediction window is larger.

VI. CONCLUSION AND DISCUSSION

This paper proposed a method for short-term sector entry flow prediction based on graph convolutional networks. Each entry flow of a sector was defined as a three-stage flow based on the entry, upstream, and downstream sectors. The prediction of each sector entry flow in the airspace was modelled as the prediction of temporal features on each node in a graph. We adopted a Word2vec neural network to model the interactions among the sector entry flows in the airspace, i.e., the weighted edges between nodes, based on the transition of air traffic in the graph. The weighted graph and the temporal flow series (hourly, daily, and weekly flows) on the nodes were input to an ASTGCN module to capture spatial-temporal dependencies from historical data and produce the final flow prediction results. We carried out an experimental study using the proposed method in the 164 sectors of French airspace using the flight data from Dec 1, 2019, to Dec 31, 2019, including 158856 flights. Results showed that, compared with the LSTM model, the proposed method could better capture sharp increases in traffic flow. And as the prediction window increased, the proposed method had shown a slower drop in prediction accuracy, while the accuracy of the LSTM model decreased drastically.

This flow prediction method can provide the number of flights in a sector entry flow that comes from a particular upstream sector and goes to a certain downstream sector during a given future time slice. The prediction result can help ATCs better aware of the distribution of anticipated air traffic flows in the sector and develop control strategies, such as traffic re-routing and flight level allocation, in advance so that the air traffic flows can be handled in a more organized manner.

The prediction of air traffic flow in this paper only incorporates the feature of flight number in each entry flow. Various other factors can also influence airspace traffic situations, such as convective weather, airspace congestion, and operational restrictions. In the future, this traffic flow prediction method can be improved by taking more influencing factors into consideration to deliver a better prediction accuracy.

Fig. 1 :

 1 Fig. 1: Visualization of one-day flight trajectories in French airspace.

Fig. 2 :Fig. 3 :

 23 Fig. 2: Conceptual diagram of the proposed method for short-term sector entry flow prediction based on graph convolutional networks.

Fig. 4 :

 4 Fig. 4: An example of nodes extraction from the trajectory of three flights.

Fig. 5 :

 5 Fig. 5: The constructed graph for the French airspace. Each red node denotes a sector entry flow and each blue line denotes an edge in the graph.

Fig. 6 :

 6 Fig.6: Flow prediction result on node "LFBBP2-LFBBP1-LFBBP3" from 00:00 to 23:59 on Dec 30, 2019 (UTC). The upper panel plots the 0-1 hour prediction results, while the lower panel plots the 1-2 hours prediction results. The red solid shows the true flow values, the green dash shows the predicted values using the proposed GCN-based method, and the black dash shows the predicted value using LSTM.

Fig. 7 :

 7 Fig. 7: Prediction performance (MAE, MSE and RMSE) changes of the proposed GCN-based method and the LSTM model as the prediction window increases.

Fig. 8 :

 8 Fig. 8: Cross-correlation between the true values and the lagged (shifted) copies of predicted values. The horizontal axis shows the value of the time lag. The vertical axis shows the normalized value of the cross-correlation.

TABLE I :

 I Performance comparison between the proposed GCN-based method and the LSTM model using three metrics: MAE, MSE and RMSE.

	Look ahead	Metric	GCN	LSTM
		MAE	0.864	0.887
	0-1 hr	MSE	1.587	1.984
		RMSE	1.260	1.409
		MAE	1.402	2.016
	0.5-1.5 hr	MSE	3.384	7.956
		RMSE	1.839	2.821
		MAE	1.784	2.535
	1-2 hr	MSE	5.792	12.477
		RMSE	2.406	3.532

ACKNOWLEDGMENT

This research is supported by the National Research Foundation, Singapore, and the Civil Aviation Authority of Singapore, under the Aviation Transformation Programme. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore and the Civil Aviation Authority of Singapore.


Vincent Marguet
email: vincent.marguet@lcis.grenoble-inp.fr

Bogdan Gheorghe

Ionela Prodan
email: ionela.prodan@lcis.grenoble-inp.fr

Florin Stoican

Reliable motion planning and coordination for a team of aerial drones

Unmanned Aerial Vehicles (UAVs) technology starts to support the agricultural domain in monitoring the land for checking and countering the presence of parasites that can damage the crop.

To properly manage a UAVs team, equipped with multiple sensors and actuators, it is necessary to test these technologies and design reliable coordination strategies able to efficiently manage the team.

Motion planning strategy

The motion planning scheme we adopt is decomposed into offline optimal trajectories generation and online tracking.

Exploit the properties of B-spline curves

We consider the parametrization of the trajectories with B-spline curves, z(t) = PB d,ξ (t), ∀t ∈ [t 0 , t N ], with P the position matrix of the control points with appropriate dimension, Properties of B-splines:

1) Local support: B i,d,ξ (t) = 0, ∀t / ∈ [τ i ; τ i+d+1 )
2) Global partition of unity:

n i=1 B i,d,ξ (t) = 1, ∀t ∈ [τ d+1 ; τ n+1 )
3) Global convexity:

z(t) = n i=1 P i B i,d,ξ (t), ∀t ∈ [τ d+1 ; τ n+1 ) 4) Smoothness: B i,d,ξ (τ l ) ∈ C d-µ l at τ l ∈ ξ
P 1 = Q 1 P 2 = Q 2 P 3 = Q 3 P 4 P 5 P 6 = Q 7 P 7 = Q 8 Q 4 Q 5 Q 6
Approximation based on the Schoenberg operator

(P l,i M 1 ) T B i,d-1 (t)B j,d-1 (t)(P l,j M 1 )dt s.t.:               

Control of the Crazyflie

Consider the dynamical model of a quadcopter [2]:

ẋ(t) = Ax(t) + h ψ (t), with A = 0 3x3 I 3 0 3x3 0 3x3 , the state x = [ξ v] T = [x y z v x v y v z ] T , the input u = [T ϕ θ] and h ψ = 0 1x3 T (cϕ sθ cψ + sϕ sψ) T (cϕ sθ sψ -sϕ cψ) -g + T cϕ cθ T .
Online trajectory tracking Design a nonlinear predictive controller:

u * = min u N pred -1 s=0 ∥ξ(k + s) -z(k + s)∥ 2 Q + ∥u(k + s) -u eq ∥ 2 R + ∥ξ(k + N pred ) -z(k + s)∥ 2 P
with the reference z(k), the equilibrium input value u eq = [g 0 0] ⊤ and the prediction horizon N pred .

Experimental setup and tests at the Esisarium platform

  B d,ξ (t) the basis function and ξ = {τ 1 ≤ τ 2 ≤ ... ≤ τ m } a knot sequence. If m ≥ d + 2, we can define B-splines of degree d over the knot sequence [3].

  with multiplicity µ l and C ∞ otherwise.5) Convexity property:The curve lies within the union of convex hull defined by subsets of consecutive control points.

  locality property real curve quasy-interpolated curve Schoenberg-derived bounds Offline trajectory generation Solve the constrained optimization problem [1]:

  initial positions waypoint passing: ∀k ∈ {0; N }, P 1 B d (t k ) = w k communication maintenance with the previous agent l -1: A comm (P l -P l-1 ).B d (t) < b comm ∀l ∈ {2, n drones } communication maintenance with the ground station: A comm (P n drones -P osition base ).B d (t) < b comm

Scenario:

  Consider two drones which pass through a collection of waypoints while maintaining a communication range of 0.8m. Implementation specifications: B-splines of order 5, N pred = 20, sampling time for the controller of 0.1 [s], acquisition rate of the computed position and orientation of 34 Hz, mean computating time of the NMPC controller 55 [ms], initial thrust sent to the drones of 9.81 [N]. Actual motion of the two drones. Loco Positioning and Lighthouse Systems u * = [g 0 0] Change State x actual , x ref Units S.I. u * = [T ϕ θ]

* This work is supported by the French National Research Agency in the framework of the « Investissements d'avenir » program « ANR-15-IDEX-02» and the LabEx PERSYVAL « ANR-11-LABX-0025-01».


Hari Saravanabhavan

Seetha Raman
email: seetha.raman@spjain.org

K Maddulety
email: k.maddulety@spjain.org

Value Creation from the Impact of Business Analytics

Keywords: Big data, business analytics, culture, governance, strategy, technology, talent, business value, leadership

Digital transformation is a key imperative across multiple industries globally. One of the main tenets of digital transformation is improving the intelligence quotient in an organization in order to enable accurate decision-making. Intelligence in the digital era is fueled by data and .by the ability to analyze data in a way that generates meaningful insights, thereby making an organization competitive. Literature shows that the benefits of being analytically competitive are widespread and impactful across many organization functions like strategy, finance, marketing and operations; but this can be accomplished only if an organization has the right level of capability for adopting and executing analytics initiatives. Data, leadership, people skills, culture and governance are capabilities that are essential for successful analytics endeavors in an organization. This study is focused on building an end-to-end perspective comprising input factors and outcomes of being analytically competitive.

Introduction

In coming years, the most intelligent organizations will need to blend technology-enabled insights with a sophisticated understanding of human judgment, reasoning, and choice. Those that do this successfully will have an advantage over their rivals (Schoemaker, P. J., & Tetlock, P. E. 2017). The Authors further state, a relatively new phenomenon, the Global intelligent enterprise is shaped by the growing power of computers and big data, which provide the foundation for operations research, forecasting models, and artificial intelligence (AI). An analogy to this, is Sam Palmisano, IBM CEO's, coining of the term "Globally Integrated Enterprise" (GIE)in his 2006 article where he terms it as this emerging business model that is built completely on the base of data and analytics. Prominent researchers within the field use the following definition of Business Analytics (BA): a combination of data, tools and technology, analysis and quantitative and qualitative methods used to build statistical, mathematical or computer-based models that can provide organizations with better insights to drive intelligent fact-based decisions [START_REF] Davenport | Thinking for a living: how to get better performances and results from knowledge workers[END_REF].Thomas Davenport introduces his latest publication Analytics 4.0 by stating that artificial intelligence (AI) is intrinsic to analytics; This statement emphasizes the significance of business analytics in an organization [START_REF] Davenport | Artificial intelligence for the real world[END_REF] culminating to AI.

A review of the literature indicates that the value of BA is in its strategic competitive advantage (Sprongl,2013) and that business analytics is also a means for improved performance (Whitelock,2018). Various studies expand the value of BA to include the supply chain, research and development, pricing and human capital interventions [START_REF] Davenport | Thinking for a living: how to get better performances and results from knowledge workers[END_REF]. Multiple articles also refer to the causal relationship between BA and organization performance, including an improvement in financial outcomes [START_REF] Jamshi | Causal linkage among business analytics, supply chain performance, firm performance and competitive advantage[END_REF] [START_REF] Rouhani | The impact model of business intelligence on decision support and organizational benefits[END_REF]. However, in order to realize the impact of BA, organizations need to have the right capabilities for gaining these benefits. The studies point towards analytics capabilities being adapted from the capability maturity model for software [START_REF] Paulk | A history of the capability maturity model for software[END_REF]. Research reveals that more than 150 versions are being studied in order to try and establish a BA maturity framework [START_REF] Chuah | A review of business intelligence and its maturity models[END_REF].

Research objective

The Capability Maturity Model (CMM) was first introduced by Watts Humphrey in 1988 at the Software Engineering Institute which then empowered organizations to gain an understanding of software process development and were able to improve their capabilities (Paulk et al., 2018). The CMM allowed organizations to measure their software process development and enable them to improve their capabilities. Since its introduction, there has been a steady growth of maturity models applicable to various domains. The objective of this paper is to build a preliminary understanding of a standardized global BA capability framework from existing literature that can create value for organizations. Thus, the Research questions (RQ) being addressed herein are: RQ1: What are the significant variables contributing towards the BA framework? RQ2: What are the potential outcomes from deploying a BA capabilities framework in an organization?

Scope of the Study

Maturity models have been developed for both BA and BI separately (Ariyarathna, K., & Peter, S., 2019) An exhaustive study of maturity models brings out two distinct concepts, namely, Business Analytics and Business Intelligence maturity models. What distinguishes the two concepts is that BI builds analysis based on past data as support for decision-making, while analytics also have predictive capabilities that can analyze and suggest future changes ahead of time [START_REF] Davenport | Thinking for a living: how to get better performances and results from knowledge workers[END_REF]. BI and BA have emerged as strategic differentiators for organizations globally. Cloud, AI and other advancements such as Internet of Things (IOT) are also quickly converging to the larger analytics canvas; however, this qualitative research is focused on studying business intelligence and business analytics capabilities and their impact on a firm.

Research Methodology

Research methodology helps to bridge the gap of understanding in a structured and systematic manner [START_REF] Saunders | Reporting and justifying the number of interview participants in organization and workplace research[END_REF]. Research methodology is the science of studying techniques, based on which, the researcher can decide what study is to be conducted. Additionally, it includes logical, productive and planned steps that help lead to a better understanding of a phenomenon (Zikmund, 2009). The research methodology in this study details the existing core variables identified through an exhaustive literature survey.

Searching and reviewing of literature for BA and BI maturity models laid the foundation of this study. Over twenty related models or studies were found from Google Scholar, Emerald Insight, Research Gate and IEEE Xplore Digital Library and after an initial screening nine were selected for further assessment. Finally, variables were identified. The researchers do not claim this to be entirely exhaustive; however, the papers selected and reviewed considerably represent the wide-ranging body of the research work accomplished in this area. The review focuses on research institutes' papers and conference papers within the period of 2009-2020.

Background

BA has been an evolving science and has manifested into a critical component in the world of business. There are multiple capability models that have been studied in the past that take their inspiration from the Capability Maturity Model for software [START_REF] Paulk | A history of the capability maturity model for software[END_REF]. The models from the literature have been segmented into four types, as represented below.

Real-World Models (Case-Study Based)

Thomas Davenport and Harris [START_REF] Davenport | Thinking for a living: how to get better performances and results from knowledge workers[END_REF] recommended a framework for analytics maturity based on extensive real experiences of an organization in their journey of building analytics capabilities. They advocated the concept of analytics competitor, the highest level of utilising analytics within an organization to drive strategic value from business analytics investments. The framework emphasises five dimensions for analytics capability building: data and technology, enterprise, leadership, targets and techniques, Analysts (DELTA) based on various case studies. Although empirical evidence shows that BA systems bring benefits to organizations [START_REF] Kohavi | Data mining tasks and methods: Classification: decisiontree discovery[END_REF], few studies provide a sound theoretical basis for understanding how and why these benefits are achieved. The resource-based view theory discussed in the next section provides this theoretical base.

Theoretical Resource-Based Models

Studies indicate multiple theoretical models that have been researched to build analytics capability within firms. One of the widely cited models is the Business Analytics Capability Framework (BACF) developed by Cosic [START_REF] Cosic | A business analytics capability framework[END_REF] that helps organizations to evaluate their current Business Analytics initiatives. BACF arrived after an in-depth study of more than 50 publications. The framework refers to 16 variables that are clustered into four major capability areas, namely people, culture, technology & governance.

Another framework that builds an interesting perspective in BA capability is the Analytics Processes Maturity Model commonly referred to as APMM. (Grossmann, 2018). The APMM identifies analytics intervention within the firm processes into six key areas: Building analytic models, Deploying analytics models, Managing and operating analytics infrastructure, Protecting analytics assets through policies and procedures, Operating an analytics governance structure and Driving analytics strategy within the organization Based upon the maturity of these processes, the APMM divides organizations into five maturity levels and the framework contributes very significantly in differentiating Analytics Maturity Level (AML) between organizations.

Business-Intelligence Models

BI has existed for a long time, and there have been multiple studies that have worked to establish the maturity factors for Business Intelligence. An exhaustive paper [START_REF] Chuah | A review of business intelligence and its maturity models[END_REF] indicates that there are over 150 versions of BI models that have been studied in the past. From the vast number of models, the dominant variables that emerge are culture, strategy, business understanding and enablement along with data and skills.

Consulting-Led Models

Given the importance of BI and BA in the digital era, there have been significant studies done by Tier 1 consulting firms to understand the analytics maturity factors and the value of analytics initiatives for an organization. Studies by McKinsey (McKinsey, The Age of Analytics) (McKinsey, Building an Advanced Analytics Organization) point towards similar factors, as described earlier in the theoretical models, such as data, process management and culture as well as to more practical variables such as picking the right use cases that were not referred to in the previous frameworks. Additional interesting studies on analytics by AT Kearney (a study referred to as The Analytics Impact Index) and by Deloitte (a study referred to as The Analytics Advantage) point to organization structure (Analytics Centre of Excellence) as being a key component in driving analytics capability beyond the other factors described in the studies that were mentioned earlier. In summary, the emerging pattern of variables from various models is mentioned below:

1. DELTA model [START_REF] Davenport | Artificial intelligence for the real world[END_REF]: Data, Enterprise Leadership, Targets, Analysts, Technology, Techniques 2. BACF [START_REF] Cosic | A business analytics capability framework[END_REF], APMM [START_REF] Grossman | A framework for evaluating the analytic maturity of an organization[END_REF] Observations from the literature review of multiple capability models highlight four recurrent independent variables that can drive the dependent variable 'BA capabilities' in an enterprise. These four variables are:

• Leadership (Management, vision and strategy)

• Information technology (data, tools and systems)

• Human capital (talent, skills and competency)

• Organization (structure, process, culture and governance).

Leadership (Management Vision and Strategy)

The analytics maturity of an organization depends on the outlined strategy [START_REF] Raber | Using Quantitative Analyzes to Construct a Capability Maturity Model for Business Intelligence[END_REF] as well as the level of executive leadership and support [START_REF] Cosic | A business analytics capability framework[END_REF].

In his book competing on Analytics, Thomas Davenport characterizes an analytics competitor as an organization that champions analytics from the top. The literature reveals the following critical success factors:

• Top-down support -the top-down leadership and executive support needed to drive an analytics agenda within an organization [START_REF] Davenport | Thinking for a living: how to get better performances and results from knowledge workers[END_REF]). • The type of industry and size of the firm -the nature of industry is a strong determinant in the BA capability of a firm. Digital natives such as Google and Amazon have a higher disposition towards analytics initiatives compared to the traditional firms (Sharon, M. S. D., & Aggarwal, V). Studies also indicate that within an industry, the larger a firm, higher is the analytics maturity level. Therefore, industry and size are important to be considered from a competitive perspective (Muller O. et al 2018). • Analytics strategyfirms that have a clear and well-defined analytics strategy and road map have higher business analytics capability levels compared to organizations that have a tactical approach to the competency (AT Kearney)

IT (Data, Tools and Systems)

The digital world throws up various types of unstructured data (beyond the well-known structured data component) such as image data, speech data and text data (Lemon, Verhoef, 2016) that needs to be managed well prior to analysis. There are multiple interesting views or categorization on the dynamic state of data; a common one is referred to as the seven 'V' by Vincent Whitelock [START_REF] Whitelock | Business analytics and firm performance: Role of structured financial statement data[END_REF]) and it classifies data under one of seven 'V' dimensions. In analytics terms, the key imperatives on the data front need to be: 1) Is the data relevant?2) Do we have enough volume of data? 3) How accessible is the data? 4) Does the data reflect all types of sources?5) Can the data be trusted? Enabling technology is defined as an ecosystem that allows for the storage and processing of data inputs using multiple hardware and software processes, such as ETL and governance capabilities, either internally or through partner systems [START_REF] Seddon | How does business analytics contribute to business value?[END_REF]. Tools are the functionality provided by the technology ecosystem that allow the organization to access, manage and analyze data effectively and efficiently (Seddon et al., 2017).

Human Capital (Talent, Skills and Competency)

As data becomes more available, the ability to analyze and drive insights from data is becoming more critical (McAfee &Brynjolfsson, 2012).This requires human skills and expertise that are extremely dynamic and ever-increasing. Human skills in the business analytics domain include technological skills, business skills and management skills. These skills also emphasise the importance of being able to translate and communicate insights and values to the executives in an organization [START_REF] Cosic | A business analytics capability framework[END_REF]. Davenport emphasises the need to not only recruit people with analytics skills but to also recruit people who have the ability to explain complex outcomes to decision makers in simple business terms [START_REF] Davenport | Thinking for a living: how to get better performances and results from knowledge workers[END_REF]. A common term used to address the combined skill set is data sciences; according to a survey by McKinsey [START_REF] Espinosa | The big data analytics gold rush: A research framework for coordination and governance[END_REF], data sciences is one of the most coveted professional jobs of the digital era. Being a data scientist entails having a broad perspective, from data to analysis to outcomes, which combines quantitative numbers analysis with qualitative insights and focuses on delivering business results within the organization.

Organization (Structure, Process, Culture and Governance)

A well-reputed study by AT Kearney, a leading consulting firm, assigns the highest weights to the factor of organization that is composed of cross-functional data-driven decision-making, embedding analytics within the processes, tightly articulated roles and responsibilities and key constructs around building internally vs. outsource/partner(AT Kearney, The Value of Analytics, 2019).In a study of 25 business intelligence and analytics models [START_REF] Foshay | A comprehensive diagnostic framework for evaluating business intelligence and analytics effectiveness[END_REF],65% of the models emphasised the need for robust processes, 40% of the models reinforced the need for a formal organizational structure to enable business analytics, 60% of the models highlighted governance as a key aspect and 40% of the models valued the concept of cost-benefit analysis, thereby pointing towards the overall significance of the organization factor in business analytics capabilities. Another framework that focuses on the process aspect of BA capability is the Analytics Processes Maturity Model (APMM) (Grossmann, 2018). The APMM identifies analytics intervention within the firm processes into six key areas building analytic models, deploying analytics models, managing and operating analytics infrastructure, protecting analytics assets through policies and procedures, operating an analytics governance structure and driving analytics strategy within the organization.

Findings

The literature review thus validates that these four variables indeed enhance the impact on BA capabilities of an organization. It is now important to analyze these variables from the value creation standpoint.

Analysis

Big data and BA can lead to more informed insight, that in turn can result in better decisions and hence, greater performance gains (Sharma et al., 2014, A large proportion of empirical studies assume a direct relationship between big data and business analytics capabilities and performance outcomes, or through mediating organizational capabilities [START_REF] Wamba | Big data analytics and firm performance: Effects of dynamic capabilities[END_REF]. A combination of the four variables' (Leadership, IT, Human Capital and Organization) drives BA capabilities that creates value.

Leadership

In an issue on leadership development, Harvard Business Review (Ashkenas & Manville, 2018) aptly describes leadership as uniting people around an exciting, aspirational vision and as building a strategy for achieving the vision by attracting and developing the best possible talent to implement the strategy and relentlessly focusing on results in the context of the strategy. Studies indicate that the importance of leadership for BA is the same as any other function [START_REF] Grossman | A framework for evaluating the analytic maturity of an organization[END_REF].Successful analytics endeavours depend on multiple factors, including strategy and leadership. Successful companies have built a role around Data and analytics commonly referred to as the Chief Data Officer or Chief Analytics Officer thereby placing critical importance on the strategic leadership aspect for the competency. Another research study on five diverse reputed global brands, Ebay, Cancer LinQ, Walmart, Deutsche Bank and UPS [START_REF] Grover | Creating strategic business value from big data analytics: A research framework[END_REF],demonstrated that, with strong leadership as a moderating/driving factor, these organizations achieved:

• Functional benefits -financial performance, growth, revenue, cost reduction and customer retention • Strategic benefitsreputation, satisfaction and market leadership

IT

Business analytics or Big Data Analytics (BDA) is often referred to as a 'new paradigm of knowledge assets' (Hagstrom, 2012, p. 2), or 'the next frontier for innovation, competition, and productivity' (Manyika et al., 2011, p.1). This is possible due to the adoption and use of data, tools, technologies, infrastructure and platforms for a firm's operations to achieve and sustain competitive advantage.

Another key component of the IT solution is to have a clear information agenda that can enable BA initiatives to drive the necessary outcomes. A well-acknowledged and comprehensive study by MIT Sloan (Lavelle. S et al., 2011) on big data and analytics charted information agendas as visions and road maps that can align IT with analytics and business needs. The IT agenda spans information governance policies and tools and data architecture, including structured and unstructured data, data relevance and currency, master data management and analytics tool kits that support reporting and visualization in advanced analytics.

Human Capital

Talent is a critical driver in building a competitive advantage and helping organizations innovate with analytics [START_REF] Ransbotham | Minding the analytics gap[END_REF]. Talent refers to the competence to deliver BA in a big data environment. Talent capability for BA is a combination of technical skills, technology understanding, business knowledge and domain.

An interesting quantitative study of service analytics which is categorized as a dynamic capability shows how talent capability mediates the relationship between technology, information and firm performance [START_REF] Akter | How talent capability can shape analytics capability in the big data environment[END_REF]. Another study's findings indicate that the outcomes of BA are significantly driven by talent capability, which can be achieved by maintaining a balance of hiring external people with sound analytical skills and of upskilling the existing team through customized training programs (Ransbotham, et al, 2015).

Organization

In a study entitled 'Building an Analytics Organization', McKinsey describes an analytics organization (department) as an ecosystem that is enabled by deep functional expertise and that provides access to data, tools and technology and fosters talent development to deliver business outcomes. It has the responsibility to govern and encourage an analytics culture across the company. Similarly, a study (Krishnamoorthi, S., & Mathew, S. K. 2018) using a case study methodology proved that Organization variables contribute positively to BA capabilities that in turn deliver positive business performance.

Another study (Espinosa, J. A., & Armour, F, 2016) provides a valuable framework that serves as an ecosystem for capturing the essential elements of an organization that enable big data/business analytics outcomes.

Results

The effective outcome of BA capability driven by the four variables impacts four key areas:

• Financials, which includes profitability, cash flow management and risk mitigation.

• Operations/shared services, which includes optimization, human-resource effectiveness, improving IT effectiveness and mitigating cyber-security challenges. • Sales marketing and customer management focused on acquiring and retaining customers, improving customer experience, marketing Return on Investment optimisation product-portfolio management. • Strategic imperatives around increasing market share, market growth and competitive advantage.

Conclusions

Globally, firms are investing in business intelligence and business analytics with the objective of gaining a competitive advantage in an intensifying market. However, to gain this advantage, firms need to focus on building the right maturity levels and stay invested in the journey of analytics. Higher the maturity of the capabilities, better is the quality of analytics and broader are the impacts for the organization.

Discussions

This research paper is based on qualitative research from relevant papers and is validated using secondary data. A conceptual framework identifying relevant factors contributing towards BA capability within an organization has been outlined and the study also provides a preliminary view on the value creation by implementing the framework. This research contributes to the global BA and BI practice and helps organizations in their path of becoming Globally Integrated Enterprises

Recommended Contribution of Theory (Integrated Model)

Previous papers have successfully drawn out the contribution of BA to individual theories -TOE framework (Nam, D. et al, 2019)) and the TAM framework (Brock, V. F., & Khan, H. U. 2017). However, given the wholistic nature of the analytics function there is a potential opportunity to validate the framework towards an integrated model (Wilber. K, 1997) The Integral model emphasises that in the new world, the sum total of multiple theories is successfully applied to achieve a superior outcome.

Limitations and Scope for Future Research

BA is an extremely dynamic subject, and it covers a wide variety of competencies under its span. In addition, analytics maturity is a concept that is derived from the capability model, and there is no standard industry level framework to assess maturity. Given this background, the interpretation of BA factors and related variables on maturity may tend to be subjective, depending on the user approach. The preliminary impact of BA is

clearly tangible and needs to be further studied by industry, geography and functions using primary data in order to harness the optimal value from the competency.