By Frank Geraets, Leo Kroon, Anita Schoebel, Dorothea Wagner, Christos Zaroliagiis
This cutting-edge survey constitutes papers that have been chosen after an open name that the overseas Dagstuhl-Seminar on Algorithmic tools for Railway Optimization, held in Dagstuhl fort, Germany, in June 2004. the second one a part of the quantity constitutes the refereed court cases of the 4th foreign Workshop on Algorithmic tools and versions for Optimization of Railways, ATMOS 2004, held in Bergen, Norway, in September 2004 within the context of the mixed convention ALGO 2004.
The quantity covers algorithmic equipment for reading and fixing difficulties bobbing up in railway optimization with unique specialise in the interaction among railway and different public delivery structures. Beside algorithmics and mathematical optimization, the relevance of formal types and the impression of applicational facets for challenge modeling are regarded as good. The papers additionally handle experimental stories and or helpful prototype implementations.
The 17 revised complete papers offered have been conscientiously reviewed and chosen from a variety of submissions and are prepared in topical sections on community and line making plans, timetabling and timetable details, rolling inventory and group scheduling, and real-time operations.
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Extra resources for Algorithmic Methods for Railway Optimization: International Dagstuhl Workshop, Railway Optimization 2004, Dagstuhl Castle, Germany, June 20-25, 2004, ... Computer Science and General Issues)
17) In fact, this condition is quite similar to the symmetry constraints (6). What makes things more complicated is the fact that we must not predict in advance The Modeling Power of the PESP: Railway Timetables — and Beyond 35 Table 4. Asymmetric service of line S2 (Berlin) Blankenfelde Lichtenrade Buch Bernau dep dep arr arr | ↓ o o 10:09 | 10:15 10:25 11:06 11:16 11:21 | arr arr dep dep o 11:14 | o 11:05 11:15 ↑ 10:14 10:24 | | 10:10 for which pairs (i, j) requirement (17) has to hold, and for which pairs it may be violated.
Together, these constraints (13) and (14) yield (πdj − πai ) mod T ∈ [0, h] ∪˙ [d, T − d + h]. (15) Trivially, 0 ≤ h < d is necessary for every feasible timetable π to be alternating at S. Theorem 3. Let π be a timetable respecting constraints (11) to (14). Then for every departure event dj , there exists a unique arrival event ai satisfying πdj − πai ∈ [0, h]T , if and only if h < (n + 1)d − T . (16) The Modeling Power of the PESP: Railway Timetables — and Beyond Since 0 ≤ h, from h < (n + 1)d − T we conclude T n+1 33 < d.
As usual, we assume the period time to be 60 minutes. Remark 2. There are of course alternating periodic timetables in the case d ≤ T n+1 . PESP solvers are able to detect even those, if we were able to pre-deﬁne suﬃciently many empty slots. By an “empty slot” we understand an artiﬁcial line which we have to schedule in the same way as the original lines, hereby separating the lines before and after the empty slot. In more detail, let us assume that n∗T+1 < d ≤ nT∗ for some n∗ > n, and that h satisﬁes the assumptions of Theorem 3 for n∗ .
Algorithmic Methods for Railway Optimization: International Dagstuhl Workshop, Railway Optimization 2004, Dagstuhl Castle, Germany, June 20-25, 2004, ... Computer Science and General Issues) by Frank Geraets, Leo Kroon, Anita Schoebel, Dorothea Wagner, Christos Zaroliagiis