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Airspace configuration using_air_traffic_complexity_metrics

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Airspace configuration using_air_traffic_complexity_metrics

5. 5. we are necessarily in one of the above three cases, the Let us consider our three probabilities sorted by de-sum of the three probabilities y1 , y2 , and y3 is always 1. creasing values p1 , p2 , p3 . The new decision criterion, Let us note that, although these probabilities can that we will call D2, is expressed as follows, dependingbe used to determine if a sector is normally loaded, on which probability is the highest:overloaded, or under-loaded, they are not actually a • if p1 is the probability pmerge to merge the sector:numeric quantiﬁcation of the workload. the decision to recombine the sector is taken only if 1 − p1 < α and p1 − p2 > η, where α and η areIV. B UILDING AIRSPACE CONFIGURATIONS chosen parameters.A. General description of the process • if p1 is the probability psplit to split the sector: we decide to split only if 1 − p1 < β, where β is a Our aim is to compute at each time step of the day chosen parameter.a realistic airspace conﬁguration, so that each controlsector has the highest possible probability to be in its In the other cases, the sector remains unchanged.normal domain of operation. We choose different criteria for the ’split’ and ’merge’ To do so, we start at time t=0 with a conﬁgura- decisions, because we may need to be more reactivetion where all elementary sectors are assigned to a when the workload is increasing than when it is droppingsingle controller’s working position. The situation is down.then reconsidered every minute of the day. The current The decision criteria will provide us with a list of sec-conﬁguration is re-assessed by considering the status tors that need to be recombined. The decision criterionprediction of each control sector. D2, as described above, is bound to ﬁnd a smaller list Some of these sectors will remain unchanged: those of sectors than D1, which may reduce the choices whenfor which the status is manned with a high probability. recombining the sectors. A typical example is when onlyThe others – which need either to be split or merged one sector needs to be merged, or several sectors thataccording to the neural network’s prediction – will be are not neighbours. So we will use D2 to decide when aentirely recombined as follows. We build every possible conﬁguration must be recombined, and use D1 to buildpartition11 from the elementary sectors composing these the larger list of sectors that will be recombined.sectors. The best partition is then chosen (we shall see The algorithm described in the next section will uselater what criteria are used to assess the partitions), and this list as input, by building the subset of elementaryit replaces the initial set of sectors that needed to be sectors from which the initial control sectors are made,recombined. in order to compute all the possible partitions from these Let us now give a few details, ﬁrst on the decision sectors. Let us now describe how this is done.criteria which allows to decide when the airspace conﬁg- C. Searching sector conﬁgurationsuration must be changed, second on the algorithm usedto explore all the combinations of sectors that need to be The algorithm used to build all the valid sector con-reconﬁgured, and third on the evaluation criterion used ﬁgurations from an initial set of elementary sectors is ato select the best conﬁguration. classical tree search algorithm. Figure 2 shows how to build all the partitions of a set of 5 elements: startingB. Decision criteria with element 1 in a single group, we have the choice to add the second element in the same group, or create The decision to reconﬁgure sectors is driven by the a new group, and so on until all elements have beenprediction made by the neural network. The neural considered.network’s output is a triple (pmerge , pman , psplit ) ofprobabilities to belong to one of the classes (merged, {1}manned, or split), with pmerge + pman + psplit = 1 (seesection III). {1,2} {1} {2} The most straightforward decision criterion is tochoose the class with the highest probability. Let uscall D1 this decision criterion. This criterion may lead {1,2,3} {1,2} {3}to many sectors reconﬁgurations: the highest probability and so on...may be only slightly higher than the others, and for short {1,2,3,4} {1,2,3} {4}periods of time. The actual sector conﬁgurations exhibit few ﬂucta- {1,2,3,4,5} {1,2,3,4} {5} {1,2,3,5} {4} {1,2,3} {4,5} {1,2,3} {4} {5}tions in time. So we tried another decision criterion Fig. 2. Searching the partitions of a set of 5 elementsD2, considering how close the highest probability isfrom 1, and also the difference between the two high-est probabilities. For example, a triple of probabilities We can use this algorithm to build all the partitions(0.1, 0.1, 0.8) is a stronger incitation to split the sector of a set of sectors. However, many of these partitionsthan (0.1, 0.44, 0.46). contain groups of sectors which are not valid, from the operational point of view. For example, it is most 11 A partition is a mapping of the elementary sectors on a number unlikely that a controller will handle a group of sectorsof controller’s working positions. which does not form a contiguous portion of airspace. 5
7. 7. ... t= 258 [AOUS FZX RNG RQJ]conﬁguration is: t= 261 [AOUS RFX RNG RQJ Z] evalconf ig = 10k2 +k3 +k4 × N (k1 , C+ (t)) t= 265 [AOUS FZX RNG RQJ] t= 266 [AOUS RFX RNG RQJ Z] +10k3 +k4 × N (k2 , Nunits (t)) t= 281 [AOUS J Q RFX RNG Z] (4) +10k4 × N (k3 , C− (t)) t= 283 [AOUS FBRT J Q RNG RZX] +N (k4 , C(t)) t= 304 [AOUS FBRT J Q RNG X Z] t= 317 [AOUS J Q RFX RNG Z]where N is a function such that t= 324 [A FBRT J O Q RNG RZX] t= 328 [A FBRT J O Q RNG X Z] N (k, c) = max(0, (10k − 1) − c) t= 332 [AOUS FBRT J Q RNG X Z] t= 335 [AOUS FBRT G J N Q X Z]and the exponents k1 , k2 , k3 , and k4 are chosen so that t= 337 [AOUS J Q RFX RNG Z]the term (10k −1) is an upper bound of the corresponding t= 338 [AOUS FBRT G J N QS QU X Z]cost c. t= 342 [AOUS FBRT J QS QU RNG X Z] This criterion is designed so that the k1 digits of t= 343 [AOUS J QS QU RFX RNG Z] t= 344 [AOUS FBRT J QS QU RNG X Z]higher order represent the cost of overloads, the k2 t= 347 [AOUS FBRT J QS QU RNG ZXIU ZXS]next digits are related to the number of units in the t= 354 [AOUS FBRT J Q RNG ZXIU ZXS]conﬁgurations, the k3 next digits are assigned to the t= 356 [AOUS FBRT J Q RNG XIU ZIU ZXS]underloads cost, and the k4 digits of lower order are t= 360 [AOUS FBRT J Q RNG X ZIU ZS]related to the cost of normally loaded conﬁgurations. t= 363 [AOUS FBRT J Q RNG X Z] t= 370 [A FBRT J O Q RNG X Z]V. R ESULTS t= 381 [AOUS FBRT J Q RNG X Z] t= 394 [AOUS FBRT J Q RNG X ZIU ZS] Let us now present some results, and compare the t= 409 [A FBRT J O Q RNG X ZIU ZS]conﬁguration schedule computed with the complexity t= 426 [AOUS FBRT J Q RNG X ZIU ZSmetrics to the real conﬁgurations recorded by the ATCC ... and so onon the same day, and also to the FMP opening scheme. Fig. 4. Example of computed airspace conﬁgurations for Brest ATCC Note that the comparison with the FMP opening (2003, June 1st)scheme is not entirely fair: our conﬁguration schedule iscomputed using recorded radar tracks, whereas the FMP t= 254 [NGA ROQ RFJ RZX] t= 257 [NGA ROQ J FBRT RZX]scheme was built using the ﬁled ﬂight plans available t= 285 [N RGA ROQ J FBRT RZX]two or three days before D-day. Still, it gives a good t= 300 [N RGA ROQ J FBRT ZXU ZXSI]hint of the potential beneﬁts of the method we propose, t= 394 [N RGA ROQ J FBRT ZXU ZXI ZXS]and the comparison with the real conﬁgurations remains t= 419 [N A G ROQ J FBRT ZXU ZXI ZXS]fair: the actual merge/split decisions were taken with the Fig. 5. Example of real airspace conﬁgurations for Brest ATCC (2003,same radar data as input. June 1st)A. A full example As a ﬁrst example of the results provided by the At a more macroscopic level, we may compare thealgorithms proposed in section IV, let us consider Brest number of control units in the computed schedule and inAir Trafﬁc Control Centre, on the 1st june, 2003. The the real conﬁgurations. It is also interesting to comparedecision criterion is D2, with the following parameters these two schedules with the FMP opening scheme madevalues: α = 0.5, η = 0.2, and β = 0.5. two days before D-day. Figure 6 shows the evolution of Figure 4 shows an example of the ﬁnal ouput of our the number of control units for the three conﬁgurationalgorithm. The time t is given in minutes after 00h00. schedules. The horizontal axis shows the time, expressedOnly a short period of time is presented, roughly between in minutes after 00h00, and the vertical axis the number04h20 and 07h00. The airspace conﬁgurations actually of control units.used on the same day for the same period are shown on On this ﬁgure, we see that the prediction usingﬁgure 5. complexity metrics shows more variations in time than When comparing these two schedules, we observe the real conﬁgurations. The reason is that, with oursome differences in the choice of the control sectors algorithms, some overloads or under-loads lasting only acomposing the conﬁgurations. This is not a surprise. For few minutes will lead to conﬁguration changes, whereasa same trafﬁc situation, there are often several ways to in the real world, they are disregarded and the resultingsplit the airspace in order to balance the workload among curve is smoother. If we go a little further in thethe control sectors. And in a same situation, different explanation, it may be that, apart from the incomingcontrol room’s managers may make different arbitrary ﬂows which use an anticipation window of 15 or 60choices. So it is not surprising that we do not ﬁnd exactly minutes, most of the metrics used as input of our neuralthe same conﬁgurations. network give only a snapshot of the situation at time From the author’s past experience in Brest ATCC, the t. These metrics are subject to high variations in time,conﬁgurations of the computed schedule seem realistic, which may account for the many changes we observe inalthough this would have to be conﬁrmed by experienced the number of conﬁgurations. It may have been usefulFMP operators. to smooth the metrics values on a chosen time window 7
8. 8. 18 18 Prediction Prediction 16 Real 16 Real FMP prediction FMP prediction 14 14Nb. control units Nb. control units 12 12 10 10 8 8 6 6 4 4 2 2 0 0 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 Time (minutes) Time (minutes) Fig. 6. Number of control sectors (computed schedule, real conﬁgu- Fig. 7. Number of control sectors (computed schedule, real conﬁgu- rations, and FMP opening scheme) for Brest ATCC (2003, June 1st), rations, and FMP opening scheme) for Reims ATCC (2003, June 2nd), with decision criterion D2 with decision criterion D1 B. Inﬂuence of the decision criterion before using them as input, or to use the anticipated Figure 7 shows the evolution of the number of control values of these metrics, predicted for a short period units for Reims ATCC, on june the 2nd, 2003, using the ahead the current time t. decision criterion D1. Another and more simple way to get a more realistic airspace conﬁguration schedule would be to introduce 18 an anticipation window in the process described in IV. Prediction 16 Real This would allow to detect and discard the conﬁguration FMP prediction changes that last only a few minutes. 14 Nb. control units 12 Despite these variations, our prediction stays fairly close to the real conﬁgurations. There is however an 10 exception between 1110 minutes (18h30) and 1240 min- 8 utes (20h40), where our computation shows between two 6 and three more control sectors than what was actually manned. The detailed outputs of our algorithms showed 4 several consecutive conﬁgurations where two or three 2 non-adjacent sectors (Q, ZX, and GS for example) were 0 given a "merge" decision by the neural network, and the 0 200 400 600 800 1000 1200 1400 others had a "no change" decision. The list of sectors Time (minutes) to recombine was only made of sectors that were not Fig. 8. Number of control sectors (computed schedule, real conﬁgu- neighbours, so it was not possible to merge them, and rations, and FMP opening scheme) for Reims ATCC (2003, June 2nd), with decision criterion D2 (α = 0.5, η = 0.2, and β = 0.5) they remained opened. We tried to avoid this problem when designing the Figure 8 shows the results for the same day and the decision criterion D2 but it seems this was not enough, same center, but using criterion D2 with α = 0.5, and we will have to improve our algorithm by extending η = 0.2, and β = 0.5. The curve of the computed the recombination to neighbouring sectors, even if it was conﬁgurations is slightly different from ﬁgure 7. This is not initially decided to merge or split them. not surprising, as the sequence of merge/split decisions Although there remains a few points that need to be is different. However, the curve still exhibits many varia- improved, the results shown on ﬁgure 6 are already fairly tions. The use of criterion D2 with the chosen values of good, especially if we compare with the FMP opening α, η and β does not succeed in smoothing the variations scheme. Of course, in order to be in the same context as in the number of control sectors. the FMP, we should use the ﬂight plans of the ﬁnal trafﬁc We tried different values of these parameters. Figure 9 demand as input instead of the recorded radar tracks. shows the best compromise that we found, with α = We could then check if our prediction would remain 0.10, η = 0.2, and β = 0.3. These values were chosen so so close to reality. The work presented here was only that our algorithms is more reactive when the workload intended to show that the use of complexity metrics increases than when it drops down. This seems to reﬂect allows to simulate how a control’s room is operated, the actual controllers behaviour. with a high degree of realism. This is a necessary step The results may again be improved through more towards realistic predictions that could be used in the extensive parametric tests to tune the criterion D2, by FMP/CFMU ﬂow regulation process. minimizing the quantiﬁed difference between the com- 8