Operational throughput parametrized by fleet mix

Having established that in the filtered dataset in saturation, the departure throughput is primarily a function of arrival throughput and prop departures, we estimate the departure throughput as a function of arrival throughput and prop departures using an approach similar to the one described in Section 2.2. Similarly to the other curve fitting problems, we exclude data points with extreme values of the variable P_Deps by filtering out datapoints, which exceed the top 1 percentile of the

measured values of P_Deps.

Given k triplets of measurements A(t), PDeps(t) and T (t), denoted by (v1, w1, y1), . . . , (vk, wk, yk), in the filtered dataset in saturation, we seek a function h_p : R² → R that estimates the mean T (t) = hp(A(t), PDeps(t)). Again, we only need to estimate the points hp(0, 0), hp(0, 1), . . . , hp(l, m), where l = max(A(t)) and m = max(P_Deps(t)). Thus, the function h_p is a piecewise linear function of A(t) and PDeps(t). The constraints are imposed only between neighboring points, as was done in the 2D case:

min

m

X

i=1

( ˆy_i− y_i)² (2.26)

subject to:

ˆ

yi= hp(vi, wi), i = 1, . . . , k (2.27)

hp(i + 1, j) ≤ hp(i, j), i = 0, . . . (l − 1), ∀j (2.28)

hp(i + 1, j) − hp(i, j) ≤ hp(i, j) − hp(i − 1, j), i = 1, . . . (l − 1), ∀j (2.29)

hp(i, j + 1) ≥ hp(i, j), j = 0, . . . (m − 1), ∀i (2.30)

hp(i, j + 1) − hp(i, j) ≤ hp(i, j) − hp(i, j − 1), j = 1, . . . (m − 1), ∀i (2.31) hp(i + 1, j + 1) − hp(i + 1, j) ≤ hp(i, j + 1) − hp(i, j), i = 0, . . . (l − 1), j = 0, . . . (m − 1) (2.32) hp(i, j + 1) − hp(i + 1, j + 1) ≥ hp(i, j) − hp(i + 1, j), i = 0, . . . (l − 1), j = 0, . . . (m − 1) (2.33)

Inequalities (2.28)-(2.29) are analogous to those in the case of the capacity envelope (Inequalities (2.23)-(2.24)). For a given fleet mix, the departure throughput is a monotonically non-increasing, concave function of the arrival throughput. Inequalities (2.30)-(2.31) ensure that for fixed arrival throughput, the departure throughput is a non-increasing, concave function of the number of prop departures. This constraint models the operational observation that increasing the number of props is expected to boost departure throughput. It is also expected to deliver diminishing gains as the number increases, because opportunities for dispersal headings decrease.

Similarly, Equation (2.32) ensures that the marginal gain in departure throughput from increas-ing the number of props by one unit decreases as the arrival throughput increases. The operational reason for this is that as the number of arrivals increases, there is more pressure to cross arriving aircraft on runway 22R, and this pressure can reduce the impact of dispersal headings. The runway is likely to be utilized for crossing arriving aircraft during inter-departure intervals independent of

the separation requirements.

Finally, Equation (2.33) ensures that the marginal gain in departure throughput from decreas-ing the arrival throughput by one unit increases as the number of prop departures increases. If decreasing the arrival throughput by one unit enables the airport to increase departure throughput by some amount, decreasing the arrival throughput by one unit and replacing one jet aircraft with one prop will lead to at least the same improvement in departure throughput.

The plot of the estimated function, h_p(A, P_Deps), can be seen in Figure 2-7 overlaid with the dashed curve of Figure 2-5b (average throughput). The comparison shows that the solid lines in Figure 2-7 are, in fact, the dashed line parameterized by the number of props departing in that 15-minute interval.

Average Fleet Mix Throughput 0 dep. props/15 min throughput

Figure 2-7: BOS parametrized operational throughput envelope in configuration (VMC; 22L, 27 | 22L, 22R).

We observe the following features in Figure 2-7:

• The average departure throughput curve lies between those corresponding to a fleet mix of 1 departing prop/15 min and 2 departing props/15 min, which is consistent with the number of props in the fleet mix at BOS (around 15% in 2007).

• The number of props has a significant impact on the departure throughput. During the most common operating scenarios in which the arrival throughput is 5-10 aircraft/15 min and the number of prop departures is 0-2/15 min, the departure throughput increases at a a rate of almost one aircraft for each additional prop.

• From this plot and the previous statistical analyses, we conclude that for this runway con-figuration at BOS, the fleet mix is a more significant explanatory variable for the departure throughput than the arrival throughput is. The departure throughput decreases with the arrival throughput by at most 2.6 AC/15 min, for an increase of arrival throughput from 0 to 14 AC/15 min. In contrast, increasing the number of props in the fleet mix from 0 to 5 increases the departure throughput by 4.4 AC/15 min.

For completeness, we provide the parametrized operational throughput envelopes for the other major runway configurations at BOS under VMC, 4R, 4L | 4R, 4L, 9 and 27, 32 | 33L, in Figures 2-8 and 2-9. We observe that the three runway configurations have similar characteristics: In all of them arriving traffic utilizes two arrival runways and has the same arrival priority capacity value, 14 AC/15 min. This is very close to the FAA airport arrival rates (AAR)⁴, which are 61 arrivals/hr and 59 arrivals/hr for the configurations 4R, 4L | 4R, 4L, 9 and 22L, 27 | 22L, 22R [39] correspondingly. There is a fraction of unutilized arrival capacity, since the empirical capacity is estimated at 14 AC/15 min (or 56 AC/hr), which is 3-5 aircraft fewer than the AAR . For configuration 27, 32 | 33L at VMC, the AAR is 44 arrivals/ hour, which is much smaller than the estimated arrival capacity (56 AC/hr). However, Runway 32 is exempt from Traffic Management Initiatives (TMI’s) in the published AAR for this configuration [39]. Its empirical arrival priority capacity can therefore be much higher, and is 56 AC/hr according to our analysis.

We also note that props increase the departure throughput in a similar fashion in all runway configurations: As the number of props increases from 0 to 3, the departure throughput increases by 2 AC/15 min. A policy implication of this observation is that the airport should incentivize the use of props as opposed to jets of similar size, as this increases overall passenger capacity. By the same rationale, the marginal external cost of a prop departure is much smaller than the marginal cost of a jet departure.

4the number of arrivals an airport is capable of accepting each hour

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

(a) Mean, median, and standard deviation of the departure throughput for all values of the arrival throughput.

6 dep. Props/15 min throughput 5 dep. Props/15 min throughput 4 dep. Props/15 min throughput 3 dep. Props/15 min throughput 2 dep. Props/15 min throughput 1 dep. Prop/15 min throughput 0 dep. Props/15 min throughput Average Fleet Mix Throughput

(b) Departure throughput as a function of arrival throughput and departing props.

Figure 2-8: BOS operational throughput envelope in configuration (VMC; 4R, 4L | 4R, 4L, 9).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

(a) Mean, median, and standard deviation of the departure throughput for all values of the arrival throughput.

(b) Departure throughput as a function of arrival throughput and departing props.

Figure 2-9: BOS operational throughput envelope in configuration (VMC; 27, 32 | 33L).