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					             AIR TRAFFIC RUNWAY ALLOCATION PROBLEM USING
                             ARTMAP (ART1)

                                                     Krishan Kumar1
               1
                   Invertis Institute of Management Studies, Bareilly, India (kumar_krishana@yahoo.com)

                                               Ravendra Singh2
        2
            Department of CSIT,IET, MJP Rohilkhand University, Bareilly, India (rsingh_iet@rediffmail.com)

                                                    Zubair Khan3
                   3
                    Department of Computer Science, IIET, Bareilly, India (zubair_762001@yahoo.com)

                                                         Ajai Indian3
                   3
                       Invertis Institute of Management Studies,Bareilly (indian_ajai123@rediffmail.com)


                                                         ABSTRACT
                   The biggest of the ATC challenges is the continuing rise in traffic volumes and which
                   is increasing the movements of airbuses around the airport due to busy runways. This
                   air traffic congestion is increasing the running cost of flights due to unwanted
                   movement of airbuses around the airport and it will also increase the chances of the
                   airbus collision. Such type of problem can be solved either by increasing runway’s
                   capacity which is very costly or by means of providing some artificial intelligence
                   solutions to optimize the utilization of existing capacity. So for optimum utilization of
                   existing resources, some researchers have given the genetic algorithm based solutions
                   but these solutions are not able to minimize the average arrival delay of the air traffic
                   less than 11.25 minutes. In this paper we have proposed Adaptive Resonance Theory
                   ART (ART1) algorithm to produce optimize solution. Our result shows that the
                   average arrival delay of 9 flights using ARTMAP has been minimized to 10.55
                   minutes.


                   KEYWORDS- ATC (Air Traffic Control), ATM (Air Traffic Management), Adaptive
                   resonance theory



1   INTRODUCTION                                                   detection and alert systems to reduce cost & delay, as
     Today as we know that Air Traffic is going to                 well as improved ground guidance systems will
increase day by day and creates traffic congestion,                increase situational awareness both in the cockpit and
delay of flights at airport and hence loss to air                  on the ground. Trial and error or cut and try methods
industry due to increase in running cost. However,                 for finding the answers to a problem are well accepted
continuing rise in traffic volume can be solved by                 in every field of science. The success rate of the cut
increasing the existing capacity and will require                  and try approaches depends greatly on the experience
investment in new automated systems and                            the user has with the problem under consideration.
infrastructure. Improving the current systems will                 Artificial Intelligence areas like Artificial Neural
provide a short-term solution. Artificial Intelligence             Networks, Fuzzy Logic, & Genetic Algorithm
techniques constitute an optimized methodology                     constitute an optimization methodology effective for
effective for solving discontinuous, non-convex, non-              solving discontinuous, non-convex, non linear or non-
linear, or non-analytic problems.                                  analytic problems. This research explores the
     Airport ground operations and en-route ATM                    application of such techniques to a non-analytic
Safety is being enhanced through the implementation                event-related air traffic control problems that of run-
of improved tools for enhancement in conflict
way assignment, sequencing and scheduling of arrival
flights at an airport with multiple runways.
     Today survey of Federal Aviation Administration
(FAA) shows that average arrival and departing
traffic both are experiencing delays of 15 minutes or
more, and a lot of research [3],[4],[5],[6] has been
done till now. In order to minimize the fuel
consumption and total cost for a flight, we have
planned a new tool in java language using ART map
which solves the problem of congestion and landing
on the airport in a most economical and efficient
manner. This tool will proved to be a great assistance
for ground controllers and provide them optimized
solutions. The major problem of landing at the busiest
runways can be solved by calculating the total waiting
time and fuel cost an aircraft spend while waiting to
land on runway. This method can be applied to
modern ATC’s where ground controlling is the major
cause of concern and hence we can minimize the
average delay. In this paper there is a busy airport          Figure 1: Nine aircrafts are waiting to land on three
with three runways.                                           runways

2     PROBLEM DESCRIPTION                                         A simple scenario has been arbitrarily generated
                                                             for evaluation of the two schemes with nine flights
     Consider a busy airport with three runways and 9        and three runways. For identification purposes, the
flights are waiting to land. The ATC problem                 call signs of the flight numbers from 1 to 9 are given
discussed in this paper has concerns with the runway         by s1, s2, s3, s4, s5, s6, s7, s8, s9.
assignment and scheduling of x arrival flights to y               Matrix for eta values (in minutes) is given by
runways.

2.1   Assumptions                                                              16 11      8
    The problem is formulated with the following                                 4     16 8
conditions:                                                                      5    6   7
1. For each of flight arrival, an expected time of                             15     6 17
   arrival (eta) to each runway is available as the            eta [9][3] =    15    11 13
   minimum time to get to the runway. Any restriction                          16     8   9
   in aircraft performance and flight pattern is                                4    16 13
   assumed to have been included in the determination                          15     6   7
   of these expected times of arrival (eta) values. The                          5    6   7
   schedule time of arrival (sta) of a flight to a runway
   can not be earlier than the corresponding eta.            Where the rows represent the flight numbers and
2. All the flights scheduled to land on a runway have        columns represent runway numbers.
   to observe specific separation rules between the          sta [ 9]= {16, 27, 28, 19, 23, 21 ,25 ,20, 24}
   leading aircraft and the trailing aircraft based on the
   aircraft types                                            (We have taken 9 values in the above array, which
                                                             means we are taking only one value out of three
3. When a flight is scheduled to a runway, the delay         values on three runways)
    as a result of the schedule is defined as the
    difference between the schedule time of arrival          3 METHODOLOGY USED
    (sta) and the expected time of arrival (eta) among
    all the runways for that flight.                              Earlier in 1999 Chang and P.K. Menon used four
                                                             [3] genetic search schemes, out of which section third
                                                             to explore the different characteristics associated with
the different base to formulate the genetic search.          match.) If the ratio of ║x║ and ║s║ is greater than or
Genetic search methods represent a logical approach          equal to the vigilance parameter, the weights (top
to cut and try search methods. Continuing                    down and bottom up) for the winning cluster unit are
improvements in the computational power of desktop           adjusted.
machines make genetic search method a practical                   However, the ratio is less than the vigilance
methodology for finding the answers to difficult             parameter; the candidate unit is rejected, and another
problems. But these solutions are not able to                candidate unit must be chosen. The current winning
minimize the delay less than 11.25 minutes. So we            cluster becomes inhibited, so that it cannot be chosen
are proposing an Adaptive Resonance Theory based             again as a candidate on this learning trial, and the
solution to minimize the delay by using ART1.                activations of the F1 units are reset to zero. The same
                                                             input vector again sends its signals to the interface
3.1 Algorithm                                                units, which again send this as the bottom-up signal to
                                                             the F2 layer, and the competition is repeated (but
     A discussion of the choice of parameter values
                                                             without the participation of any inhibited units).
and initial weights follows the training algorithm. The
                                                             The process continues until either a satisfactory match
notation we use is as follows:
                                                             is found (a candidate is accepted) or all units are
                                                             inhibited. The action to be taken if all units are
n- number of components in the input vector.
                                                             inhibited must be specified by the user.
m- maximum number of clusters that can be
     formed.
                                                             3.3 Training Algorithm
bij-bottom-up weights (from F1(b) unit Xi to F2
     unit Yj).                                                   The training algorithm an ART1 net is presented
tji- top-down weights (from F2 unit Yj to F1 unit            next. A discussion of the role of the parameters and
     Xi).                                                    an appropriate choice of initial weights follows.
ρ- vigilance parameter.                                      Step0. Initialize parameters:
s- binary input vector (an n-tuple).
x-activation vector for F1 (b) layer (binary).                       L > 1,
║x║ norm of vector x, defined as the sum of the                      0 < ρ ≤ 1.
    components xi.                                                   Initialize weights:
                                                                     0 < bij(0) < L / L- 1 + n ,
3.2 Description                                                       tji(0) = 1.
                                                             Step1. While stopping condition is false, do
     A binary input vector s is presented to the F1 (a)
                                                                     Steps 2-13.
layer, and the signals are sent to the corresponding X
                                                             Step2. For each training input, do steps 3-12.
units. These F1 (b) units then broadcast to the F2
                                                             Step3. Set activation of all F2 units to zero.
layer over connection pathways with bottom-up
                                                                    Set activations of F1(a) units to input
weights. Each F2 unit computes its net input, and the
                                                                    vector s.
units compete for the right to be active. The unit with
                                                             Step4. Compute the norm of s:
the largest net input sets its activation to 1; all others
                                                                                 ║s║= ∑ si
have an activation of 0.We shall denote the inbox of
                                                             Step5. Send input signal from F1(a) to the F1(b)
the unit as j. This winning unit becomes the candidate
                                                                    layer: xi = si.
to learn the input pattern. A signal is then sent down
from F2 to F1 (b) (multiplied by the top down
                                                             Step6. For each F2 node that is not inhibited:
weights). The X units (in the interface portion of the
                                                                     If yj ≠ -1, then
F1 layer) remain “on” only if they receive nonzero
                                                                     yj = ∑ bij*xi.
signals from both the F1 (a) and F2 units [figure (2)].
     The norm of the vector x (the activation vector         Step7. While reset is true, do step 8-11.
for the interface portion of F1) gives the number of         Step8. Find J such that yJ ≥ yj for all nodes j.
components in which the top-down weight vector for                  If yj = -1, then all nodes are inhibited and
the wining F2 unit tj and the input vector s are both 1.
(This quantity is sometimes is referred to as the
                                           Figure2: Basic Architecture of ART1



                                                              bij: bottom-up weights (from F1(b) unit Xi to F2 unit
this pattern can not be clustered.
                                                              Yj).Used to store different clusters values. Permissible
Step9. Recompute activation x of F1 (b):
                                                              range is given by
        xi = si*tji.                                          0 < bij(0) < L / (L – 1 + n) sample value 1 /( 1 + n).

Step10. Compute the norm of vector x:                         tji: top-down weights (from F2 unit Yj to F1 unit
               ║x║ = ∑ xi.                                    Xi).Used to store runways assignment for different
 Step11. Test for reset:                                      flights.
           If ║x║ / ║s║ < ρ, then yj = -1 (inhibited          ρ - vigilance parameter.(For deciding the learning
node J) (and continue executing Step 7 again)                 node).
          If ║x║ / ║s║ ≥ ρ,
                                                              s - binary input vector (an n-tuple). Input array to
 Then proceed to Step 12.                                     store different input values.
Step12. Update the weights for node j (fast learning):
                                                              x - activation vector for F1 (b) layer (binary).
    bij(new) = L*xi / L-1 + ║x║ , tji (new) = xi.
                                                              Output array to decide the learning node.
Step13. Test for stopping condition.
                                                              ║x║ - norm of vector x, defined as the sum of the
3.4 Parameters Used                                           components xi.
                                                              Full algorithm is coded by using core java.
n: number of components in the input vector.     Used
as a sequence of flights.
                                                              Now the algorithm works as follows in our case:
m: maximum number of clusters that can be formed.
                                                               Initialize parameters:
Used as a runway assignment.
                                                                      L =50
                                                                       ρ=0.8
                                                                      Initialize weights:
                                                                      bij(0) =0.2
       tji(0) = 1                                          4 CONCLUSION AND RESULTS
                                                                Our main objective of allocating runways to
     We have taken 9 flights in all and 3 runways at
                                                           flights (table2) and hence minimizing congestion and
an airport. Each flight is presented as an input pattern
                                                           minimizing the arrival delays in minutes (table3,
one by one in a sequence and the top down weight
                                                           figure3) is successfully achieved. The use o Adaptive
matrix is updated in which each row is taken as the
                                                           Resonance Theory (ART1) instead of Genetic
runway number. The flight sequence is defined by the
                                                           Algorithm has drastically reduced the arrival delay
following table1:
                                                           and hence cost. The computation time required is
                                                           reduced 6000 generations to 50 generations as
                                                           compared with genetic techniques (table4, figure4)
     Binary Input pattern          Flight Number
                                                           and result so obtained are more accurate and
             0001                    flight1 (s1)          optimum. Implementations for all the iterations is
             0010                   Flight2 (s2)           done by using java development tool kit (jdk1.6)and
                                                           on Pentium IV processor. Implementation time is 30
             0011                   Flight3 (s3)
                                                           minutes for 50 iterations.
             0100                   Flight4 (s4)                     For the particular sequence 918653472 at 50
             0101                   Flight5 (s5)           generations following runway assignment is found
                                                           (shown by table2)
             0110                   Flight6 (s6)
             0111                   Flight7 (s7)
             1000                   Flight8 (s8)            S. No   Sum4 (as per      Flight      Allocated
                                                                    input sequence)   Number      Runway
             1001                   Flight9 (s9)            1       4                 s1          R1
                                                            2       15                s2          R3
                                                            3       15                s3          R3
Table1: Input Sequence Pattern as per Flight                4       15                s4          R3
Sequence                                                    5       15                s5          R3
                                                            6       15                s6          R3
                                                            7       15                s7          R3
     After the completion of one sequence pattern
                                                            8       15                s8          R3
different delay values are calculated for that pattern.     9       15                s9          R3
Flights are assigned to the runways on the basis of top
down weight matrix. Flights are arranged in sequence       Table2: Runway Allocation
starting from first row for first flight, second row for
second flight and so on. Now whatever the value of             Air Traffic Control System Command Center
the runway number in that row, the flight is assigned      says that general arrival/departure delays are 15
to that runway. That sequence pattern to be selected is    minutes or more. Departures are experiencing air taxi
on the basis of delay value that is calculated and is      delays of 16 to 45 minutes and also arrivals are
then compare with the other delay values and the           experiencing airborne holding delays of 16 to 45
minimum one is selected.                                   minutes. Traffic destined to this airport is being
We have taken the following assumption in our case         delayed at its departure point. Departures are
for runway numbers:                                        experiencing taxi delays greater than 45 minutes
                                                           and/or arrivals are experiencing airborne holding
         Runway 1->0001, 0100, 0111                        delays greater than 45 minutes. So we can say that our
         Runway 2->0010, 0101, 1000                        results are far better.
         Runway 3->0011, 0110, 1001
                                                           5 FUTURE WORK
and rest of the sequence left up to 1111.
This means that if the value in the first row of top            This technique can be further implemented to air
down matrix is 0101 then flight number 1 will land at      and local control of ATC to provide the optimum air
runway 2 and so on.                                        traffic control at the busiest airport. Also the first
     The delay values are calculated by subtracting        module, which we implemented with this problem
the expected time of arrival (eta) for a flight at a       can be combined with second module by using
runway and scheduled time of arrival (sta) for that        adaptive resonance theory (ART2) to get the best air
flight on the scheduled                                    traffic simulation tool. Further work will concentrate
                                                           in refining the modeling and the global criteria to
                                                           optimize, taking into account for example take-off
sequencing needs of approach sectors or priority
levels for slotted departures.                                                                Average Landing Time Chart Using ART map

                                                                                         16
                                                                                         14
                  Sequence of Flights and




                                                        Delay(in minutes)
                                                                                         12
  Generations     Corresponding Average Delay in                                         10
  (Iterations)    Minutes                                                                 8
        5         485291673:15                                                            6
       10         148569327:15                                                            4
                                                                                          2
       15         163297548:14.5555555
                                                                                          0
       20         362579481:14.5555555                                                        0     20          40       60        80          100    120
       25         167834592:14.5555555                                                                               Generations
       30         854173692:14.2222222
       35         275194368:14
       40         879156342:14                        Figure3: Results according to our proposed ART1
       45         498175362:14
       50         918653472:13.7777777
       55         315864972:13.7777777                                                   35
       60         437295168:12.1111111


                                                        Average Arrival Delay(minutes)
                                                                                         30          30.25
       65         781569423:12.1111111
       70         187569423:11.2222222                                                   25
       75         871564932:11.2222222                                                   20                  19
       80         381659247:10.5555555
                                                                                         15
       85         718596432:10.5555555                                                                               13.5 13.5 13
                                                                                                                                           11.25
       90         841569723:10.5555555                                                   10
       95         381549628:10.5555555                                                    5
      100         921567413:10.5555555
                                                                                          0
                                                                                              0          2000           4000            6000         8000
Table3: Delay according to our proposed ART1
                                                                                                                     Generations



                                                      Figure4: Results according to V.H.L. Chang
                                                                          & et. al. [3]

    Generations        Fitness value (Delay)
      1000                         30.25              REFERENCES
      2000                          19
                                                      [1] Gail A.Carpenter, Stephen Grossberg, Adaptive
      3000                         13.5
                                                           Resonance Theory MAP.
      4000                         13.5               [2] Yang Yuying, Shi Xizhi, Li Guoyi, Rules from
      5000                          13                    fuzzy adaptive resonance theory map, Progress in
      6000                         11.25                  Natural Science May 1999, Vol.9 No.5, p.382.
                                                      [3] V.H.L. Chang, Crawford, P.K.Menon, Air Traffic
                                                          Control Using Genetic Search Techniques,
Table4: Delay according to V.H.L.Chang & et. al.[3]       Optimal synthesis palo alto California, May 1999,
                                                          Vol.9 No.5, p.382.
                                                      [4] Nathan L. Kleiman, Stacy D. Hill, Simulation
                                                          optimization of air traffic delay cost, IEEE Winter
                                                          Simulation Conference, Proceedings of the 30th
                                                          Conference on Winter simulation Washington,
                                                          D.C., United States, Pages: 1177–1182,Year of
    Publication: 1998,ISBN:0-7803- 5134-7.
[5] Delahaye and Elliot, Genetic Algorithm for Air
    Traffic Assignment, European ECAI 94, 11th
    Conference on Artificial Intelligence.
[6] B. A. Peters, J. S. Smith, D. J. Medeiros, and M.
    W. Rohrer, eds. David W. Hutchison, Stacy D.
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    with Constraints, Proceedings of the 2001
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[7] Heinz Erzberger, The Automated Airspace
    Concept, 4th USA/Europe Air Traffic
    Management R&D Seminar, December 2001.
[8] Erich Gamma, Richard Helm, Ralph Johnson, and
    John Vlissides. Design Patterns: Elements of
    Reusable Object-Oriented Software. Addison-
    Wesley, Reading, Massachusetts, 1995.
[9] Tom G. Reynolds and R. John Hansman.
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    and future air traffic control environments. 21st
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    2002.
[10] David C. Zhang. Collaborative arrival planner:
     Its design and analysis using object modelling.
     Master’s thesis, Massachusetts Institute of
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[11] H. Rezberger, T.J. Davis and S. Green, De
      sign of center-TRACON Automated System,
      Proceedings of the 56th AGARD
      Symposium on Machine Intelligence in Air
      Traffic Management, Berlin Germany, 1993
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[12] Gail A. carpenter, Stephen Grossberg John H.
      Reynolds, ARTMAP: Supervised Real-Time
      Learning and Classification of Nonstationary
      Data by a Self-Organizing Neural Network

				
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About UBICC, the Ubiquitous Computing and Communication Journal [ISSN 1992-8424], is an international scientific and educational organization dedicated to advancing the arts, sciences, and applications of information technology. With a world-wide membership, UBICC is a leading resource for computing professionals and students working in the various fields of Information Technology, and for interpreting the impact of information technology on society.