The second notable property of the .rst plot is the notch on the right side of the alerting region. In cases where the intruder is close to co-altitude with the own aircraft, the logic will delay alerting. It waits until it is more certain whether the intruder will end up above or below the own aircraft before committing to an advisory.
In the second plot, the own aircraft is initially climbing at 1500ft/min while the intruder is initially level. The shape of the alerting region is more complex and lacks the symmetry of the .rst plot due to relative motion in the vertical plane. One notable property of this plot is that, in some situations, the system issues a climb when the intruder is above. In these situations, because the own aircraft is already climbing, there is insu.cient time for the own aircraft to accelerate downwards to pass below the intruder.
The third plot shows the alerting region when the own aircraft is climbing at 1500ft/min and the intruder is level, as in the second plot, but an initial descend advisory was issued two seconds previously. Unless the advisory is canceled, strengthened, or reversed, the pilot will begin descending in three seconds. The white region indicates where the system will discontinue the advisory, and the blue region shows where the system will continue with the advisory that has already been issued. In some situations, the logic will strengthen the advisory to a descend at 2500ft/min or reverse the advisory to a climb.

0 5 10152025303540
(a) h˙0 = 0ft/min,h˙1 = 0ft/min,sRA = COC
0 5 10152025303540
(b) h˙0 = 1500ft/min,h˙1 = 0ft/min,sRA = COC
0 5 10152025303540
(c) h˙0 = 1500ft/min,h˙1 = 0ft/min,sRA = DES1500-3
Figure 4. Optimal action plots. Horizontal axis indicates τ (s) and the vertical axis indicates h (ft).

.40 .30 .20 .100 10203040
Time (s)
Figure 5. Example encounter comparing the performance of the DP logic against the current TCAS logic. The own aircraft approaches from the left, and the intruder approaches from the right.

3.6 EXAMPLE ENCOUNTER
Figure
5
shows
an
example
head-on
encounter
comparing
the
behavior
of
the
DP
logic
and
the
current TCAS logic, Version 7.1. The DP logic, 15s into the encounter, issues a descend advisory to pass below the intruder as the intruder is climbing at approximately 1100 ft/min. The expected cost for issuing a descend advisory at this time is 0.012, smaller than the expected costs for not issuing an advisory (0.013) or issuing a climb advisory (0.020). Thepilotbeginsdescending5slater. As the intruder levels o. later in the encounter, the DP logic strengthens the descend advisory at 23s. Thepilotbeginstostrengthenthedescent3slater. Oncesafelyseparatedinaltitude,theDP logic issues a COC advisory. The vertical separation when τ = 0 is 396ft.
The performance of TCAS was evaluated using a constant 500ft/s horizontal closure rate and an initial altitude of 43,000ft,
which
puts
TCAS
into
its
highest
sensitivity
level
[38].
When
the own aircraft is 324ft above the intruder 4s into the encounter, TCAS issues a climb advisory because it anticipates, using straight-line projection, that by climbing it can safely pass above the intruder. Ten seconds later, when the own aircraft is only 141ft above the intruder, TCAS reverses the climb to a descend because it projects that maintaining the climb will not provide the required level of separation. As the intruder begins to level o. and then descend, the descend advisory becomes ine.ective. The vertical separation when τ = 0 is 94ft.

3.7 PERFORMANCE ASSESSMENT
The overall performance of the system can be estimated by generating a large collection of en-counters and running them in simulation. The results in this section use the (continuous) dynamic
　
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