ATM Network Performance Evaluation And Optimization Using Complex Network Theory Yalin LI 1, Bruno F. Santos 2 and Richard Curran 3 Air Transport and Operations Faculty of Aerospace Engineering The Technical University of Delft (TUD), Kluyverweg, The Netherlands With the continuously increase in air transport demand, it is foreseen that the current structure of air transportation systems will reach its limit in the next years. To regulate the flow of air traffic and use of airspace in a safe, cost-efficient, environmental-friendly way will be a challenging task for Air Traffic Management (ATM) systems. This paper addresses this challenge by presenting an innovative framework to evaluate and optimize ATM network performance. In our definition of ATM network we consider nodes to be airports or waypoints with limited capacity (i.e., aircraft per unit of time crossing that node), segments to be tracks between airports and waypoints, and the flow to be the set of aircraft using the ATM system in a given period. The framework proposed integrates a stochastic simulation model based on network flow theory, which simulates the performance of the network under different demand conditions, a performance assessment structure based on complex network theory and an optimization model used to maximize the network capacity, in terms of total flights using the network. The decision variables consist on the distribution of the capacity over the nodes of the network and the definition of the layout of the network i.e., set of segments and nodes made available for air traffic. The development of the framework is part of the Ph.D. project of the first author and in this paper we present the first results of this research. A sample network based on a real ATM network will be used to test and validate the framework. Preliminary results already illustrate the significant impact of network optimization in the ATM system overall capacity and performance. Conclusions drawn from these preliminary results and future research developments will be discussed at the end of the paper. KEYWORDS: ATM Network, Complex Network Theory, Network Optimization, Flow Simulation 1 Phd Candidate, Control and Operations, Y.Li-12@tudelft.nl. 2 Assistant Professor, Control and Operations, B.F.Santos@tudelft.nl. 3 Professor, Control and Operations, R.Curran@tudelft.nl.
I INTRODUCTION Air traffic demand has been steadily growing in the past years, increasing congestion both on the ground and on the skies. This is particular the case in North America and Europa but also in Asia where the air transport is growing at a fast speed. The air traffic management (ATM) systems, i.e., the systems that safely process aircraft in the sky as they fly and at the airports where they land and take off, are suffering from an increasing traffic pressure. In some of these regions, there is the urgent need to improve capacity without compromising safety or sharply increase costs. Effective planning and management of airspace resources will be necessary premise to solve the existing challenges. A big amount of previous studies had been done to understand and reduce traffic congestion of networks, but in most of these studies there is a basic assumption that network is homogeneous. This seams not the case of ATM networks where hierarchy processes seem to take place. In this paper we turn our view into the complex network theory, with which we can analyze the network from a topological perspective. Since the concept of complex network had been put forward, this area has gained large popularity. In the end of 1950s, Erdos and Renyi came up with a new way to build network. In this network, the connection of two nodes is decided by possibility. This network, called random network, has been treated as the most suitable network to describe real world systems (Erdos and Rényi, 1960). As the information technology developed, researchers found a lot of real networks are neither regular nor random, but in between. In these studies, two important concepts emerged the concept of small-world networks, i.e., a network in which most nodes can be reached from every other by a small number of hops or steps (Watts and Strogatz, 1998); and the concept of scale-free networks, i.e., a network in which a fraction of the nodes in the network having more connections to other nodes than the rest of the nodes and that this fraction follows a power law when plotted for all nodes in the network (Barabasi and Albert, 1999). Several researchers have used complex network theory and, in particular, these two concepts to analyze air transport networks. For instance, some researchers proved that real airport networks can be described as small-world network (Guimerà et al, 2005, Zhang et al, 2010). As to the air traffic domain, most of the researches using complex network theory have focus on analyzing the network structure and behavior, and are not applied to optimization of the network. The study of optimization of the air traffic system gains more and more relevance with the need to enhance ATM systems capacity. With favorable en route network modeling and simulation assessment methods, the performance of the air traffic network can be evaluated. Following a structured and comprehensive approach, this performance can be improved via the redistribution of ATM resources or changing the layout of the network used by the ATM system. Therefore, in this paper we present an innovative ATM network simulation and optimization framework based on complex network theory. The framework proposed integrates a stochastic simulation model based on network flow theory, which simulates the performance of the network under different demand conditions, a performance assessment structure based on complex network theory and an optimization model used to maximize the network capacity, in terms of total flights using the network. At this point in time, the optimization model is still not implemented in a constructive way, in which the search for the optimal network is done in a rational process. Instead, in this paper we use a trial-and-error approach with the purpose to show how new network solutions can lead to different network performance, validating the use of a comprehensive optimization model in future works. This paper is organized as follows. In the following section, we discuss the methodology proposed. The illustration of the type of results obtained with the proposed methodology is presented in Section 4, with the use a simple test work and a case study network representing part of the ATM network of China. The results are discussed in the same section. A summary of the paper and directions for future work are provided in the final section. 2.1 NETWORK MODEL II METHODOLOGY We define our ATM network as a two-dimension network, with nodes and segments (Fig.1). There are two categories of nodes, airports or waypoints. The segments simply represent the segments between airports and waypoints. A flow of aircraft between airports is assumed to happen during a given period of simulation. This flow is constrained by the capacity at both airport and waypoint nodes. The airport node capacity (CA) is considered to be the number of aircraft that can take off per time unit. The way point capacity (CW) is considered to be maximum number of aircrafts that can cross the waypoint per time unit. These capacities are based on the number of resources allocated to control the traffic at each airport and waypoint.
Fig. 1 Schematic diagram of an ATM network 2.2 SIMULATION PROCESS The simulation of the aircraft flow in the network is done via an iterative process (Fig. 2). This iterative process is based on the simulation tool proposed by Yang et al (2008) and can be describe as follows: Fig. 2 The simulation of the network The input consists the network structure, including the number of airport nodes, waypoints and segments; the capacity at the nodes (CA, CW); and the flow proportion, i.e., what is the percentage of flights to be generated in the network which are specific to the flow between each origin-destination (OD) airport pair. An iterative process of generating flights and tracking their flow in the ATM network. In total, this process is repeated T time-steps that cover the simulation period. Every time step involves the following process: o o Random generation of R flights, choosing the OD airport pair based on the flow proportion (Fig.3). The choice of the OD pairs follows a roulette approach, where each OD airport pair has a slice proportional to the flow proportion of the flights between those airports. Move all flights forward in the network, simulating their flow (Fig.4). This is done assuming that each aircraft will follow the shortest path. It starts the journey at the origin airport (being inserted in the network in the respective node) and it ends the journey at the destination airport (it is removed from the network when reaches the respective node). As time steps evolve, the aircraft will follow their path and transfer from node to node in the network based on a predefined standard aircraft speed. When an aircraft reaches a node, the simulation will judge if the number of flights at the node is larger than the node capacity or not. If so, the aircraft will be wait at the node in the next time step; if not, the aircraft can continue its path. o Compute the performance and all require data to monitor the performance of the network. The output of the iterative process is the set of performance indicators and all other data captured in each iteration step of the process. This can include, e.g., the number of aircraft at each node; the time each aircraft has been in the network; the number of served aircraft movements; and the number of aircraft movements still waiting to be generated.
Fig.3 The process of generate aircraft (left) and the schematic diagram of roulette (right) Fig. 4 The process of forward aircraft (left) and the schematic diagram of aircraft transferring and waiting (right) As time goes by, the simulation will record the data in the network and when the network has congestion the simulation will stop and output the Rc and other results we want. 2.3. NETWORK PERFORMANCE The output of the iterative simulation process can be used to assess the network performance. The number of aircraft in the network, R, is recorded at each time step of the simulation. There is a critical value Rc, when R = Rc, a phase transition will take place from free flow to congested traffic. We can think this value is the maximum capability of a system handling its traffic. For R<Rc, the numbers of generated and removed aircraft are balanced, and the network will be in a steady free traffic flow. For R>Rc, there will be traffic congestion with the number of aircraft accumulating. To characterize the phase transition and to measure this critical value we compute an order parameter, which can be considered as a proxy indicator of the network performance: C N p ( R) lim, t R t
Where, η is the order parameter; C is the average capacity of all the nodes; N () t is the total flight number in the network at time-step t and N N ( t t) N ( t) is the variation of flights in the network from time-step t to time-step t there is no congestion; when more. p p p t ; and is the average value during t R R c p. When η =0, R R c, meaning that, η will grow rapidly, which means the aircraft are accumulating more and 2.4 OPTIMIZATION The performance of the ATM system can be improved if a better allocation of resources or a variation of the network layout is possible. To do this, we present a concept of an optimization model which can make use of the simulation process and the network performance assessment to enhance the ATM performance (Fig. 5). Currently, this optimization model is still not fully implemented. Thus, in this paper we will use a trial-and-error approach, assuming that we can have three ways of doing improving the network: 1. The first one is by relocating the sum capacity of the nodes. In this case, we assume that there are already resources and costs associated with the operation of the ATM system and that we do not want to change these resources and costs. Our aim is to find a better way of operating the system without putting more effort. 2. The second one is by assuming that these resources and costs can be increased, increasing the capacity in some (congested) nodes of the network. This can help us to discuss how to invest in the ATM system, increasing the total number of available resources and the costs associated with the operation. 3. The third way is by changing the network structure, i.e. adding or removing nodes and segments in the network. The trial and error approach is done by assuming a set of these network changes in a new feasible ATM system solution, and testing the impacts on the network performance. Fig. 5 The ATM network optimization model followed III MODEL APPLICATIONS Two ATM networks were used to validate the proposed simulation and optimization framework: a small test network with a simple structure and a case study network representing part of ATM network of China. The first network will be useful to easily display the results of our framework and to facilitate the discussion of the conclusions that can be draw. The case study network will be used to illustrate the potential application of the framework to a real case study. This section is divided in two sections, one for each ATM network used. 3.1 THE TEST NETWORK Fig.6 shows the structure of the small test network. We use it to valid our method in the beginning of our study. Each node has an ID. The test network has 15 nodes, from 1~10 are airports and 11~15 are waypoints, and 25 segments. We use it in the simulation and got the result of the order parameter (which has been defined in 2.1), which shows the phase transition point, i.e. the value of Rc in this network. In fig.6 we assumed that in all
the airports, CA=8 and in all the waypoints, CW=2. These capacity values are just come from assumption to make our simulation run. Thus, at this reference situation, Rc=7. We compare the process of flights accumulating in the network of R=7 and R=8, and found that when R=8, the total number of flights keeps growing, and the one of R=7 stays in a relative stable situation (see fig.7). Some nodes has a large number of waiting queue, like ID7, when R>Rc. That means they are easy to have congestion and they both have large degree, which is the number of connection at the node (the size of red bubbles representing the degree). We can make an assumption that the larger the degree is, the more likely the congestion will be. Fig. 6 The test network with node ID (left) and the phase transition point R c of it (right) Fig. 7 The total number of flights when R=7 and R=8 (left), and 13 the extend of congestion when R=8(right) We then came up with several thinking of optimization of the network capacity, i.e. get higher value of Rc. The first one, we can think that the sum of all the node capacity is the total network resources. We assumed that if we keep the total number same, but change the way to allocate it, there are changes in the Rc of the network. Fig.8 shows how Rc changes with the value of CA and CW. There are also 3 parallel lines, and the number on each line is the sum of the capacity. Every point on each line has the same sum of capacity. We use the data from the lowest line i.e., the points (CA2; CW6), (CA5; CW4), (CA8; CW2) to look deep into the network and valid that the relocation of the network resources will help to get better result. And in fig.9 we clear see that after the optimization, the network got higher Rc. Although the results of (CA2; CW6), (CA5; CW4) both have higher Rc, (CA2; CW6) and (CA8; CW2) have cross in R=38. This shows that when more and more flights generated in the network, the congestion becomes much severe in (CA2; CW6), while the (CA8; CW2) will keep at a stable level. When look into the total flight number, we found that after the optimization, it also has a big growth, and after a while, (CA2; CW6) and (CA5; CW4) become separated and the latter one seems to have a relative high value.
Total Flight Number Fig. 8 Changes in the R c of the network while CA and CW changing (the values in white are the sum of all the nodes capacity) 2 CA2-CW6 CA5-CW4 CA8-CW2 1000 CA2-CW6 CA5-CW4 CA8-CW2 1 500 0 0 20 40 R (number of flights generated per time unit) 0 0 200 400 Time Fig. 9 The phase transition, R c (left) and the total flight number growth of the capacity relocation (right) For the second method, we changed a particular node capacity. From fig.7, we clearly see that ID7 is the most congestion point. We found it is not only an airport but also a waypoint. So we separately changed CA and CW of it. After changing, we can see from fig.10 that how the method worked. In this optimization, we took (CA2; CW6) as the reference situation. We found that no matter we enhanced the CA or CW of ID7, the Rc of the network both grew, and the order parameter gradually converges together. That means if we keep increasing the flight generate rate, the congestion level will eventually be same. While in the total flight number of the network, after optimization the value is higher than the reference situation, and changing the CW of ID7 seems to have a little better result.
Total Flight Number 2 CA2-CW6 CA(7)6 CW(7)10 1000 CA2-CW6 CA(7)6 CW(7)10 1 500 0 20 40 R (number of flights generated per time unit) 0 0 200 400 Time Fig. 10 The phase transition (left)and the total flight number (right) And when we look deep into how the waiting number of the flights changed, we found that at the same time, the extend of congestion became smaller. Fig.11 shows that there are still congestion points, but the congestion becomes small and more focus and still occurs at high degree nodes (the size of red bubbles representing the degree). Fig. 11 The extend of congestion of each node of changing the capacity of node 7 before (left) and after (right) The third way is changing the network structure. We have tried adding a segment (ID 5-10) and deleting segments (ID 2-7, 7-10) and found that they all have made some changes of the network performance. Fig.12 is how Rc changed with CA and CW. The lower surface is from the origin network, i.e. the three-dimensional view of fig. 8. Those above are the performance after changing the structure. We can find that the performance is better than the origin one.
Fig. 12 The performance of adding a segment (ID 5-10, left) and deleting segments (ID 2-7, 7-10, right) (the lower one in each figure is the origin network) 3.2 REAL WORLD BASED NETWORK As the method worked for the test network, we want to apple to real world network. Form the data of real ATM network of China, the simulation will cost too long and not able to see how the performance changes when we optimizing the network. We took a relatively isolated part from the network (see fig.14), and use this as a part of case study of the research. The network, which is going to be used has 77 nodes, with 12 airports, and 113 segments, and is shown in fig.13. Fig. 13 The real ATM network of China and the sample network For the validation of our method, we also use the sum of node capacity as the total network resources. Fig.14 shows how Rc changes with the value of CA and CW. As we don t have the real data of the capacity at each node, we only assumed every airport and every waypoint have the same capacity and let the CA and CW change from 1~50. There are also 3 parallel lines, and on each line the number is the sum of the capacity, and every point on each line has the same sum of capacity. We picked three groups of data from the intermediate line i.e., (CA7; CW23), (CA20; CW21), (CA38; CW18) to look deep into the network and valid that the relocation of the network resources will help to get better result. Fig. 15 shows the phase transition and the total flight number growth of the three pairs of CA and CW. From the figures we can identify that Rc changes with the way we relocate the resources of the network. And with the growth of flight generate rate, after R>Rc, the level of congestion also grows similarly. Moreover, the total flight number also grows in similar way. But the higher Rc is, the larger flights number will be. Fig. 16 is a group of data, when R=80 and at the same time, when the
network will definitely have congestion. Still congestion occurs at nodes with larger degree (the size of the bubble represents the degree). But the trend is with a larger Rc, congestion seems smaller than the others. Fig. 14 Changes in the R c of the network while CA and CW changing (the values in white are the sum of all the nodes capacity) Fig. 15 The phase transition (left) and the total flight number growth (right) of the capacity relocation (a) (CA7; CW23) (b) (CA20; CW21)
(c) (CA38; CW18) Fig. 16 The change of extend of congestion at each node(ca7; CW23), (CA20; CW21), (CA38; CW18) Later we tried to change the capacity of several particular nodes. From the extend of the congestion, we found that ID21, 48, 56 are the busy nodes. Thus we enhance the capacity at this nodes. As they are all waypoints, we changed the CW of the three nodes from 23 to 30. Fig.17 shows Rc has significant growth and the total fight number maintain at a similar level. But from fig.18, the extend of congestion changes a lot, especially the congestion place moved to other direction. Fig. 17 The phase transition (left) and the total flight number growth (right) Fig. 18 The change of extend of congestion before(left) and after(right) enhance several nodes capacity At last, we added several segments in the network, segments (ID 75-56, 75-52, 75-66), the new network have 116 segments(see fig.19).
Fig. 19 The network with 3 potential segments (dash lines in grey) Using this new network we obtain the difference of Rc between the two network, which showed in fig.20. The Rc of the network had become better and the total flight number became larger. In fig.21 the congestion at different nodes became less after we added the segments. This shows that the optimization also works to real network. Fig. 20 The phase transition (left) and the total flight number growth (right) Fig. 21 The change of extend of congestion after adding segments IV CONCLUSION
In this paper we address the challenge of improving ATM systems performance, by presenting an innovative framework to evaluate and optimize ATM network performance. The framework proposed integrates a stochastic simulation model based on network flow theory, which simulates the performance of the network under different demand conditions, a performance assessment structure based on complex network theory and an optimization model used to maximize the network capacity, in terms of total flights using the network. After explaining the simulation and optimization framework, we tested the applicability of the framework using a simple test network and a case study network based on a part of the Chinese ATM system. These two networks helped us to validate out method and to illustrate the type of results that can be obtained with the framework. From the results we present in this paper, we can confirm that our method is useful to optimize the ATM network. The development of the framework is part of the Ph.D. work of the first author of the paper. Thus, it is one work still under development. Future research will definitely involve the development, implementation and testing of a full ATM network optimization model. The simulation of the complete Chinese ATM network is also planned. REFERENCES Erd s P, Rényi A. Publications of the Mathematical Institute of the Hungarian Academy of Science, 1960, 5: 17 Watts D J & Strogatz S H:Collective dynamics of small-world networks [J]. Nature, 1998, 393:440-442. Barabási A L, Albert R. Emergence of scaling in random networks[j]. science, 1999, 286(5439): 509-512. Guimerà R, Mossa S, Turtschi A, et al. The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles[j]. Proceedings of the National Academy of Sciences, 2005, 102(22): 7794-7799. Zhang J, Cao X B, Du W B, et al. Evolution of Chinese airport network[j]. Physica A: Statistical Mechanics and its Applications, 2010, 389(18): 3922-3931. Yang H X, Wang W X, Wu Z X, et al. Traffic dynamics in scale-free networks with limited packet-delivering capacity[j]. Physica A: Statistical Mechanics and its Applications, 2008, 387(27): 6857-6862.