@unpublished{Liebchen2021, author = {Liebchen, Christian}, title = {Maximizing Bidirectional Green Waves for Major Road Axes}, doi = {10.15771/2827}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-15449}, pages = {1 -- 20}, year = {2021}, abstract = {Both, from an environmental perspective and with respect to road traffic flow quality, planning so-called green waves along major road axes is a well-established target for traffic engineers. For one-way road axes (e.g. the Avenues in Manhattan), this is a trivial downstream task. For bidirectional arterials, the well-known necessary condition for establishing a green wave in both direction is that the driving times between two subsequent crossings must be an integer multiple of half of the cycle time of the signal programs at the nodes. In this paper, we propose an integer linear optimization model to establish fixed-time green waves in both directions that are as long and as wide as possible, even in the situation where the driving time condition is not fulfilled. In particular, we are considering an arterial along whose nodes separate left-turn signal groups are realized. In our computational results, we provide examples which illustrate that allowing for selecting among different strategies for the left-turn phases is beneficial. Moreover, we show that there is always a solution with green waves in both directions that are as long and as wide as possible, where absolute priority is put on just one direction. Only when considering prioritized parts of a green band (e.g. some first few seconds), then an ideal green wave into one direction can provide suboptimal quality compared to optimizing both directions together.}, language = {en} } @inproceedings{LindnerLiebchenMasing2021, author = {Lindner, Niels and Liebchen, Christian and Masing, Berenike}, title = {Forward Cycle Bases and Periodic Timetabling}, series = {21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)}, booktitle = {21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-15408}, pages = {2:1 -- 2:14}, year = {2021}, abstract = {Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance R1L1 of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds.}, language = {en} } @unpublished{LiebchenDutschJinetal.2021, author = {Liebchen, Christian and Dutsch, Steffen and Jin, Shiguang and Tomii, Norio and Wang, Yihui}, title = {The Ring Never Relieves}, doi = {10.15771/1479}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-14790}, pages = {1 -- 23}, year = {2021}, abstract = {Regarding the disposition of metro lines in order to recover from delays, in the literature there can be found two branches of contributions: On the one hand, there are descriptions of response rules such as expressing (also referred to as skip stop), holding and short-turning together with studies in what situation to apply which of them. On the other hand, there are fully-automated optimization models which make use of any possible driving and routing options, according to some specified objective function. To the best of our knowledge, we are not aware of any study that puts its focus specifically on ring lines (also known as circle or loop lines). Yet, in the absence in particular of more or less 'natural' time buffers in turnaround activities in the endpoints, the operation of a circle line is particularly challenging. In this spirit, we are collecting response rules that are applicable especially for circle lines. We sketch their impacts on the passengers' travel experience as well as on the resource schedules for the rolling stock and staff (train drivers). For selected response rules, we provide illustrative drawings. Moreover, we present the answers that experts of eleven metro networks that are operating circle lines were pointing to us during interviews. It turns out that despite the limited possibilities along circle lines there is a broad repertoire of response action that is taken on a regular basis - but also that some standard general response rule (expressing) is almost never applied in practice.}, language = {en} }