
| Mean           | Std Dev   | Variance   | Min    | Med    | Max     |         |      |      |        |       |
|----------------|-----------|------------|--------|--------|---------|---------|------|------|--------|-------|
| Sliding window | before    | after      | before | after  | before  | after   | both | both | before | after |
| 08:00–09:00 pm | 9.442     | 7.692      | 15.538 | 10.200 | 241.416 | 104.030 | 0    | 3    | 133    | 40    |
| 08:12–09:12 pm | 8.792     | 7.114      | 14.412 | 9.355  | 207.692 | 87.519  | 0    | 3    | 121    | 40    |
| 08:24–09:24 pm | 8.204     | 6.735      | 13.566 | 8.941  | 184.042 | 79.940  | 0    | 3    | 123    | 40    |
| 08:36–09:36 pm | 7.535     | 6.515      | 12.525 | 8.879  | 156.867 | 78.844  | 0    | 3    | 117    | 40    |
| 08:48–09:48 pm | 6.842     | 6.344      | 11.525 | 9.104  | 132.826 | 82.884  | 0    | 3    | 108    | 40    |
| 09:00–10:00 pm | 6.233     | 6.271      | 10.765 | 9.526  | 115.888 | 90.752  | 0    | 2    | 106    | 40    |
| 04:00–05:00 pm | 12.393    | 8.386      | 22.404 | 10.417 | 501.919 | 108.51  | 0    | 4    | 235    | 40    |
| 04:12–05:12 pm | 12.144    | 7.994      | 22.042 | 9.609  | 485.863 | 92.332  | 0    | 4    | 235    | 40    |
| 04:24–05:24 pm | 11.992    | 7.853      | 22.084 | 9.445  | 487.710 | 89.216  | 0    | 4    | 257    | 40    |
| 04:36–05:36 pm | 11.754    | 7.860      | 21.783 | 9.514  | 474.478 | 90.513  | 0    | 4    | 243    | 40    |
| 04:48–05:48 pm | 11.513    | 8.129      | 21.580 | 10.128 | 465.707 | 102.570 | 0    | 4    | 245    | 40    |
| 05:00–06:00 pm | 11.353    | 8.705      | 21.375 | 11.485 | 456.874 | 131.900 | 0    | 4    | 245    | 40    |

Table 1: Statistics on the ECAC cell demands before and after minimisation of the total delay on two chosen time intervals (s = 9 pm to e = 10 pm, and s = 5 pm to e = 6 pm) that are 3 hours ahead, with capacity enforced within [s*,...,* e] every t = 12 minutes over a window of w = 60 minutes, with a maximum g = 120 minutes of ground holding, and with w 0 = 0 (no demand balancing in the objective function)

| Interval   | Run-time   | Iterations   | |RWF|   | |RAF|   | Total Delay   | Avg Delay   | Demand Dev   | Violations   |
|------------|------------|--------------|---------|---------|---------------|-------------|--------------|--------------|
| 9–10 pm    | 140 sec    | 8,000        | 4,295   | 463     | 65,457 min    | 13.76 min   | −35%         | 9,013        |
| 5–06 pm    | 620 sec    | 22,000       | 8,806   | 811     | 246,267 min   | 25.61 min   | −43%         | 45,985       |

Table 2: Statistics for the two chosen time intervals: run-times, numbers of iterations, numbers of relevant waiting and airborne flights, total and average delays of all relevant flights, changes in the standard deviations of the cell demands, and initial numbers of constraint violations show that it can only be lowered to about g = 100 minutes without losing the satisfiability of the capacity constraints, though without significant deterioration of the run-time or total delay.

Note that the trivial way to meet all the capacity constraints (namely by delaying a maximum of flights out of the time interval for re-planning, and thus exacerbating the situation for the next such interval) would be sub-optimal since we aim at minimising the total delay.

## 4 Conclusion

Summary. Constraint-based local search (CBLS) offers a very effective medium for *modelling* and efficiently *solving* the problem of optimally balancing the traffic demands on an airspace of adjacent cells, while ensuring that their capacity constraints are never violated. The demand on a cell is here defined as the hourly number of flights entering it. The currently only allowed form of re-planning is the changing of the take-off times of not yet airborne flights. Experiments with projected European flight plans of the year 2030 show that this can already lead to significant demand reductions and re-balancing at little cost.

Ultimately, we hope to show that EuroControl can gain from a tight integration of planning and