International Journal of Business
Management & Research (IJBMR)
ISSN 2249-6920
Vol. 3, Issue 4, Oct 2013, 105-112
© TJPRC Pvt. Ltd.
INNOVATION IN AIR TRAFFIC STRATEGY USING GAME THEORY
SEEMA V. LATHKAR1& U. B. JANGAM 2
1
Asst Professor and Head, Department of Engineering Sciences, Saraswati college of Engineering ,University of mumbai,
Navi Mumbai, Maharashtra, India
2
Research guide, Principal Science College, kalian, Maharashtra, India
ABSTRACT
Air Traffic control Strategy (ATCS) of the longer term permits for the likelihood of free flight, within which craft
select their own best routes, altitudes, and velocities. The safe resolution of mechanical phenomenon conflicts between
craft is important to the success of such a distributed system. During this paper, we present a technique to synthesize
incontrovertibly safe conflict resolution maneuvers. The strategy models the craft and therefore the maneuver as a hybrid
system and calculates the maximal set of safe initial conditions for every aircraft in order that separation is assured within
the presence of uncertainties within the actions of the opposite aircraft. Samples of maneuvers victimization each speed
and heading changes are figured out thoroughly.
KEYWORDS: Altitudes, Automatic Dependence Surveillance-Broadcast, Temporal Order of Vehicles
INTRODUCTION
AIR transportation systems are subjected with soaring demands for travel. The annual traffic rate within the India
is predicted to grow by 2–3% annually for a minimum of consequent fifteen years [1]. This National Airspace System
(NAS) design and management will not be ready to expeditiously handle this increase as a result of many limiting factors
as well as the subsequent.

Inefficient airspace utilization: presently, the airspace is extremely stiffly structured and craft area unit forced to
travel planned jet ways in which. This is often usually not optimum and disallows craft to fly on to the destination
and make the most of favorable winds. This downside is especially evident in water routes that are experiencing
the best demand growth (for example, nearly 10% [1] annually across the Asia).

Accrued traffic management (ATC) workload: Separation among craft likewise as vectoring craft so as to avoid
weather hazards is performed centrally by ATC. In full areas, like the regions near urban airports mentioned as
Terminal radar Approach controls, controllers alter their serious work by keeping craft in holding patterns outside
the this system.

Obsolete technology: the pc technology utilized in most ATC centers is sort of thirty years previous [2].
Communication is restricted to full speech between the craft and ATC. Navigation is performed by flying over
mounted points.
In view of the on top of issues, the aviation community is functioning toward an innovative idea referred to as
Free Flight [3]. Free Flight permits pilots to decide on their own routes, altitude, and speed. User preference would be
restricted solely in full airspace or to forestall unauthorized entry of special use airspace (such as military airspace). Free
Flight is probably possible as a result of enabling technologies like world Positioning Systems (GPS), datalink
communications like Automatic Dependence Surveillance-Broadcast (ADSB) [4], [5], Traffic Alert and Collision rejection
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Seema V. Lathkar & U. B. Jangam
Systems (TCAS) [6], and powerful on-board computation. Additionally, tools like NASA’s Center-TRACON Automation
System (CTAS) [7] and MITRE’s URET [8] can call support tools for ground controllers in an endeavor to scale back
ATC work and optimize capability.
The higher than technological advances can change the present ATC system to accommodate future traffic
growth: subtle on-board instrumentality will enable craft to share a number of the work, like navigation, weather
prediction, and craft separation, with ground controllers. So as to boost the present standards of safety in associate degree
unstructured Flight setting, conflict detection and determination algorithms are very important. Such algorithms would be
used either on the bottom by traffic management or within the air by the Flight Management System (FMS) of every craft.
In the projected Free Flight airspace, every craft is enclosed by couple of virtual cylinders [4], the protected zone
and also the alert zone, shown in Figure 1. A loss of separation between 2 aircraft happens whenever the protected zones of
the craft overlap. If the alert zones overlap, either ATC is notified regarding the potential conflict, or the aircraft exchange
device and intent data so as to predict and resolve the conflict. The radius and also the height of the en-route protected zone
over U.S. airspace is presently 2.0 maritime mi and 2000 foot (1000 foot below 25 000 foot, 5000 foot over oceanic
airspace), severally. The scale of the alert zone, presently below dialogue, depends on numerous factors as well as velocity,
altitude, accuracy of sensing instrumentality, traffic scenario, aircraft performance, and average human and system
response times.
Current analysis endeavors in conflict prediction and determination embody [9]–[13]. Conflict prediction might
be spatial, temporal, or probabilistic. Spatial and temporal approaches, like [11] and [13], calculate the multidimensional
coordinates of a potential conflict. Probabilistic approaches, like [9] and [10], assume random uncertainty within the
measured data and confirm the likelihood of collision.
Figure 1: Defining Zones as a Base for Game Theory Algorithm
The work of [11] and [12] formulates conflict resolution as an optimum management drawback, whereas [13]
treats the matter} as an umbellate improvement problem. The computer program of CTAS permits controllers to manually
alter craft trajectories to resolve conflicts in on the way airspace [14]. TCAS [6] provides resolution advisories (flight level
changes) to pilots concerned in two-aircraft conflicts; but these advisories don't seem to be formally verified. (Conflict
prediction and determination are the foremost vital modules that are in would like of augmentation and verification within
the current implementations of CTAS and TCAS.)
In [10] an attainable future design for traffic Management (ATM) is conferred. In our paradigm, aircraft are
allowed to self-optimize within the spirit of Free Flight, communicate state associated intent information to every
alternative utilizing an ADS-B circuit for conflict prediction, and coordinate with one another to resolve potential conflicts.
Innovation in Air Traffic Strategy Using Game Theory
107
State and intent information might be unsure. Coordination among the craft is within the style of maneuvers that are finite
sequences of flight modes like heading, altitude, and speed changes for every aircraft. These kinds of maneuvers are
habitually utilized in current air traffic management practice since they're simply intelligible by pilots likewise as simply
implementable by on-board autopilots that regulate the aircraft to heading and speed set points. The most thrust of our
conflict resolution algorithms is to verify that a maneuver with success resolves the conflict by computing the set of initial
conditions that the maneuver is safe, wherever safety implies that separation is maintained. Within the presence of finite
uncertainty within the state or intent information, we tend to take a worst case approach and verify that the worst case
system flight is safe.
The flight mode shift occurring in every maneuver is sculptural by a finite-state automaton with the relative
aircraft configuration dynamics residing inside every flight mode. A conflict resolution maneuver is so sculptured by a
finite state automaton interacting with a group of continuous management systems, leading to a hybrid system. The
interaction and data exchange of all of the aircraft concerned within the maneuver leads to a multi-agent hybrid system.
There are many approaches to hybrid system modeling, verification, and controller style (see, as an example, [6]–[9]). The
computer science approach is to increase models of finite-state automata to regular automata [20], linear hybrid automata
[21], and hybrid input/output automata [2].
Linear hybrid automata model or abstract the continual dynamics by differential inclusions of the shape and verify
properties of the ensuing abstracted system [3]. Specifications are verified for these models employing either model
checking, that thoroughly check all system trajectories, or deductive theorem-proving techniques, that prove the
specification by induction on all system trajectories. During this framework, controller style has conjointly been developed
[7], [8]. Machine-driven machine tools are developed for each model checking [9] and theorem proving.
Management abstractive approaches to modeling, analysis, and controller style for hybrid systems have extended
the speculation of projectile systems to incorporate distinct modes of operation. Modeling approaches embrace those of [2].
Analysis and style techniques extend existing management techniques, like stability theory, best management and
management of discrete-event systems, to hybrid systems. Our conflict resolution algorithms are within the spirit of model
checking, however we have a tendency to use management abstractive deductive) techniques to calculate the accessible
region for hybrid systems with general nonlinear dynamics.
Our methodology calculates the most important controlled invariant set of the complement of every aircraft’s
protected zone, taking into consideration the uncertainty of the actions of the opposite craft. So as to work out this safe set
of states, we 1st develop a way to work out the controlled invariant subsets for continuous systems within the presence of
disturbances. A natural framework for this sort of drawback is zero-sum non-cooperative dynamic scientific theory. During
this framework, unsure info regarding neighboring craft is treated as a disturbance. For a 2 craft example, presumptuous a
saddle resolution to the sport exists, every aircraft chooses a best policy presumptuous the worst doable disturbance. This
can be intended by the work of, during which game abstractive strategies are used to prove safety of a group of maneuvers
in Intelligent Vehicle route Systems.
At intervals its safe region of operation, the craft could style its mechanical phenomenon to optimize over
different criteria, like fuel potency or tokenish deviation from route. At the boundary of its safe region, the craft should
apply the actual management that keeps it out of its unsafe region. Thus, we are naturally diode to a change control-based
protocol that is least restrictive. An additional elaborated description of this multi objective methodology is also found in.
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Seema V. Lathkar & U. B. Jangam
The resultant hybrid system is safe deliberately, as we have a tendency to illustrate with 2 versions of a stimulating
example of two-aircraft conflict resolution within the horizontal plane.
Figure 2: Illustrative Control Strategy for Algorithmic Logic Build-up
TRAFFIC SIGNAL CONTROL PROBLEM FORMULATION
We contemplate the matter of finding the best coordinated stoplight set up for a bunch of signalized intersections
over a given time horizon. A tangle instance is outlined by specifying the topology of the traffic network, the time horizon,
yet because the time-dependent origin-destination flows over now horizon. Specially, for each origin-destination try within
the network, the temporal order of vehicles’ departures from the origin for the destination and also the route they take area
unit probable to be familiar. The goal is to reduce the common time period toughened by all drivers within the network
throughout the given time horizon (we use the terms “driver” and “vehicle” interchangeably).
We formulate this coordinated traffic signal control problem as a discrete optimization problem, where the
planning horizon is divided into N time periods of equal length of ± seconds, and the decision variables are the signal
phases1 prevailing during each of the N time periods, at each of the I signalized intersections2. The following notation will
be used in describing the coordinated traffic signal control problem:
² I = f1; 2; : : : ; Ig: set of signalized intersections;
² N = f1; 2; : : : ;Ng: set of time periods (each time period
is ± seconds long);
² Si = f1; 2; :::; Sig: set of permissible signal phases forintersection i, i 2 I;
² si;n 2 Si: a decision variable representing the signalphase at intersection i during time periodn.
The problem can be formally written as:
min AVERAGETRAVELTIME(fsi;n; i 2 I; n 2 Ng)s.t.
si;n 2 Si; 8i 2 I; 8n 2 N
Where the mapping from the vector of decision variables, fsi;ng, to the objective value is signified by the function
AVERAGETRAVELTIME(¢), which replicates the presentation measure we conferred above. The reliance of this
function on the resolutions made in the problem, i.e., the signal timing plans over the planning horizon, is intrinsically
multifaceted and have neither critical depiction nor known structural properties. In result, we are faced with a difficulty of
optimizing a “blackbox” function. In exacting, in our research, all task assessments are endowed with by a traffic
simulation program, as portrayed in subsection V-B.
Innovation in Air Traffic Strategy Using Game Theory
109
In the worst case, all joint decisions, with number bounded by (maxifSig) N¢I , need to be enumerated and
evaluated so as to seek out an optimum answer to assure world optimality. For a sensible size downside, this is often not
possible. Therefore, we take the approach of looking for a top quality domestically optimum answer instead. Still,
considering the quality and scale of the matter, it's not obvious however even this could be achieved at intervals cheap
time. Within the next section, we are going to propose the utilization of a game hypothetic approach to resolve our
perplexity.
MOTIVATION FOR A GAME-THEORETIC APPROACH
In this section we in short describe the motivation and therefore the intuition behind using game theory in
resolution coordinated stoplight management issues. Though some game theory-related terms area unit mentioned
throughout this section, their formal definitions are postponed to consequent section. The intuition behind our approach is
stressed here. Recall that the choice variables in our drawback are the signal phases prevailing throughout every of the N
time periods at every of the ‘I’ signalized intersections. The quantity of joint choices is so bounded by (maxifSig) N¢I .
The problem quickly becomes stubborn as we increase N and/or I. However, if we have a tendency to decompose the
matter into smaller sub-problems, we may be able to notice a sufficiently smart resolution in a very affordable quantity of
your time.
The decomposition of the matter is accomplished by assumptive that every signal in each amount is a freelance
decision maker. By adopting this decomposition, the centralized decision problem, with (maxifSig) N¢I possible decisions,
can then be transformed into (N ¢ I) sub-problems, each with at most maxifSig possible decision alternatives. The effect is
to reduce an exponential to a linear number of alternatives to consider. However, if we decompose the problem without
considering the interactions among these independent decision makers, we are just solving (N ¢ I) isolated signal control
problems over very short time horizons, and there is no coordination among traffic signals. In order to effectively
incorporate coordination of an outsized range of call manufacturers, we tend to communicate game theory that originates
from political economy. modern game theory was created when von Neumann and Morgenstern in 1950 and quickly
became a preferred tool in explaining and predicting behavior of teams of rational call manufacturers (players in game
theory terminology) once their well-beings are related to the joint actions of all call manufacturers (players). If every head
that controls a fundamental measure for a symbol is viewed as a player within the game, and therefore the average period
of all vehicles within the traffic network is viewed as a standard payoff for each player, the coordinated light management
drawback will then be described as a game of identical interests. The notion of an answer to a game is that of a Nash
equilibrium, that for a game of identical interests are often viewed as a coordinate-wise native optimum. Intuitively, a joint
call could be Nash equilibrium if no individual player will improve its payoff by unilaterally deviating from the first joint
call. Note that in a very game of identical interests, Nash equilibrium isn't essentially a world optimum. it's well-known
that finding author equilibria could be a laborious problem. One in every of the earliest algorithms used to realize Nash
equilibria is a repetitive method referred to as fictitious play.
The primary pitfall of fictitious play (FP) is that generally it doesn't converge to the equilibrium. However,
Monderer and stargazer showed that for a special category of games, namely games of identical interests, FP can converge
to equilibrium. Since virtually all at liberty distinct optimization issues are often described as games of identical interests,
this result has recently galvanized researchers in optimization to introduce FP as an optimization tool. During this paper,
when we model the light management drawback as a game of identical interests, we'll apply a variation of the FP
algorithmic program to search out an answer.
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Seema V. Lathkar & U. B. Jangam
SFP ALGORITHM FOR THE TRAFFIC SIGNAL CONTROL PROBLEM
As mentioned on top of, traffic signal management issues are sometimes solved by either limiting the area of
solutions by finding out parameters of planned cyclic patterns, or by limiting the amount of signals significantly. Instead,
our approach is to go looking for solutions to the total scale coordinated signal designing downside by using the SFP
formula. To solve a tangle with the SFP formula, we tend to should initial formulate it as a game. Within the following
sections, we'll describe a way to construct a game-theoretic model for the traffic signal improvement drawback. supported
this formulation, we will then specify the performance live accustomed value signal temporal arrangement plans and
describe the simplest reply subroutine using this performance measure.
The SFP algorithm, with sample size one, is described below:

Initialization: An initial joint strategy is chosen arbitrarily. It is then stored in the history.

Sample: A strategy is independently drawn from the history of each player (i.e., for each player, each past play is
selected with equal probability).

Best Reply: For every player, the best reply is computed by assuming that all other players play the strategies
drawn in step 2.

Update: The best replies obtained in step 3 are stored in the history.

Stop? Check if the stopping criterion is met; if not, go to step 2, otherwise stop.
Algorithm 1 Sampled Fictitious Play (sample size 1).
SFP ()
o
H (0; :) Ã INITIALSOLUTION()
o
kÃ0
o
while STOPCRITERION() is false do
o
D Ã SAMPLE(H; k)
o
B Ã BESTREPLY(D)
o
H (k + 1; :) Ã BT
o
kÃk+1
o
end while
D = SAMPLE (H; k)
o
for j = 1 to P do
o
u à DISCRETEUNIFORM(0; k ¡ 1)
o
D(j) Ã H(u; j)
o
end for
o
return D
Innovation in Air Traffic Strategy Using Game Theory
111
Formulating coordinated traffic signal control problem as a game:
With the same notation as defined in section II, we can formulate the problem as a game:
Player
Each tuple (i; n), i 2 I, n 2 N, is a player. Let Pbe the set of all players, and P = I ¢ N, be the number of players.
Strategy Space
For each player (i; n) 2 P, its strategyspace is the set Si. Player (i; n)’s decision is denoted by D ( i ; n).
Payoff Function
By collecting decisions D (i; n) from all players, a signal timing plan for the planning horizon isformed. By
sending this plan to the traffic simulator, we can find the average travel time experienced by all drivers, which is the payoff
function value for all players.
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