Aerospace and Electronic Systems Magazine April 2018 - 40
Simulation Modelling of Traffic Collision Avoidance System
complex operations. To overcome the above-mentioned shortcomings of the TIMSPAT and CPN Tools and combine their advantages,
the GMAS has been developed. It is a powerful graphical and mathematical modelling tool that is extensively used to model, simulate, and analyze DESs characterized by concurrency, parallelism,
causal dependency, resource sharing, and synchronization.
MODEL FORMALISM
The graphical components of the GMAS model include a start
component, data component, function component, nested function
component, link component, and end component.
Definition 1 A GMAS model can be defined as the following
nine-tuple:
GM = ( S , D, H , H ′, F , E , FW , M , M 0 )
(19)
where
S = {s} represents the set of start component, and the element is
unique.
D = {d1 , d 2 ,, d a } represents the set of data components, and a is
the amount.
H = {h1 , h2 ,, hm } represents the set of function components, and
m is the amount.
H ′ = {h1′, h2′ ,, hn′ } represents the set of nested function components, and n is the amount.
F = { f1 , f 2 ,, f u } represents the set of link components, and u is
the amount.
E = {e} represents the set of end component, and the element is
unique.
FW : F f1,w , f 2, w ,, f u ,w is the set of functions on each link
component.
M : S ∪ E ∪ D → {s, e, d1 , d 2 ,, d a } is the set of state identifications, which are the state data of start component, end
component and data components during the model operation.
M 0 : S ∪ D → {s1,0 , d1,0 , d 2,0 ,, d a ,0 } is the set of initial identifications, which are the initial state data of start component
and data components before the model operation.
D ∩ ( H ∪ H ′ ) = ∅ (set D does not intersect with the union of set
H and H′), and D ∪ ( H ∪ H ′ ) = ∅ (set D and the union of
set H and H′ are not empty at the same time).
F ⊆ ( S ∪ D ∪ E ) × ( H ∪ H ′ ) ∪ ( H ∪ H ′ ) × ( S ∪ D ∪ E ) indicates that link component connects start component,
data component or end component with function component or nested function component, and it is the set of
directed arcs.
40
STATE EVOLUTION
The state space concept is introduced to represent the system evolution process, i.e., a global perspective on scenario dynamics and
a better understanding of the system principles. The state space
analysis enhances a quantitative approach, relying on computational tools to explore the different states that DES could reach,
starting from a particular initial state. The system state is characterized by the entities with its attributes distributed in the different
data storage units. The state space is generated quantitatively by
firing all the enabled data computing units at any system state, calculating the new states.
State identification M(S|E|D) is the timing state data of the start
component s, end component e and data component di(i = 1, 2,
..., a). Then the state identification M of the model is defined as
a row vector: M(S|E|D) = {M(s), M(e), M(d1), ..., M(da)}. Initial
state identification M0(S|D) is the initial M setting, including the
start component s and data component di(i = 1, 2, ..., a). Then the
initial state identification M0 of the model is defined as a row vector: M0(S|D) = {M0(s1), M0(d1), ..., M(da)}. After the activation of
the function component node h, the state identification M(S|E|D)
of the data component d will change to the new state identification
M′(S|E|D):
M ( s ) − W ( s, h ) ,
if s ∈ I ( h )
M
e
+
W
h
,
e
,
if e ∈ O ( h )
(
)
(
)
M ( d ) − W ( d , h ) ,
if d ∈ I ( h ) , d ∉ O ( h )
M′ S E D =
if d ∈ O ( h ) , d ∉ I ( h )
M ( d ) + W ( h, d ) ,
M ( d ) − W ( d , h ) + W ( h, d ) , if d ∈ I ( h ) ∩ O ( h )
else
M ( s ) , M ( e ) , M ( d ) ,
(
)
(20)
among which, W(s, h) and W(d, h) are separately the weight of the
directed arc from the start component s or the data component d to
the function component h; W(h, e) and W(h, d) are the weight of the
directed arc from the function component h to the end component
e or the data component d.
DEVELOPMENT OF A GMAS-BASED TCAS MODEL
In this work, TCAS operations are modelled using the GMAS formalism. The main reasons for using GMAS are the possibility of
modelling interactions between different sociotechnical system
elements (e.g. crew, procedures) of the TCAS operations and the
support of the powerful mathematical basis for simulations.
Figure 2 represents the developed model, which should be informed with the initial aircraft states involved in the same scenario.
The aircraft trajectories are discrete to be a sequence of 4-dimensional (3D track + timestamp) waypoints that the corresponding
aircraft will follow, with the sequence containing the state information (i.e., positions and speeds). It tries to detect and resolve the
threat based on the TCAS logic, and determines whether a secondary threat occurs in the collision avoidance process of the previous multiple aircraft scenario. The following four agents model
for the improved TCAS operations: Agent wind disturbance, Agent
aircraft TCAS, Agent pilot response, and Agent multi-threat esti-
IEEE A&E SYSTEMS MAGAZINE
APRIL 2018
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