Internationales Verkehrswesen (70) 3 | 2018 84 TECHNOLOGIE Wissenschaft Public transport capacity limitations Means for a-prompt Occupancy Rate (O.R.) evaluation Public Transport, Capacity Assessment, Residual Capacity, Occupancy Rate This article provides with the adequate tools for a prompt and general assessment of public transport capacity limitations. It does so by retrofitting the notion of residual capacity with the adequate mechanisms to evaluate its most elusive variable; namely, the passenger transport demand (here contemplated as an Occupancy Rate factor). To assess this complex variable, the article carries out a mode-specific calibration of the Occupancy Rate of three different public transport modes (Buses, Light Rail, Subways) utilizing information from six different German networks across 25 different lines. Arturo Crespo, Andreas Oetting F or many years, public transport systems, have been pushed aside in favor of auto-mobility, however, they are once again being contemplated as key elements for the proficient development of metropolitan areas at large [1]. That said, with their patronage consistently growing across the board [2] and due to their tight coupling with other systems [3], they have become particularly vulnerable and prone to the occurrence of unusual and extreme operational situations. Public transport operations are planned such that passengers reach their destination in an appropriate timeframe (e.g. waiting time, travel time) through adequate structures (e.g. overall capacity, number of transfers) [4]. Nevertheless, unusual operational situations (e.g. disruptions, maintenance works) inherently undermine their overall service capabilities. If systems do not encompass the minimum coping aptitudes, their reliability and serviceability can not be upheld. Envisioning a public transport network with proficient coping mechanisms is a matter of resilience. Within the field of public transport research, resilience has been described as the system’s ability to adapt and maintain its serviceability during a disrupted situation, with redundancy and robustness as its two main features. In this context, redundancy is understood in terms of strong, preferably intermodal, integration and robustness as the systems’ overall residual capacity [5, 6]. While integration is an important feature of any public transportation system, it can not be considered in isolation. Residual capacity is critical to ensuring that systems can service unexpected shifts in demand regardless of the existing situation. In sum, placing the capacity limitations of public transportation under the spotlight sets the stage for a more holistic understanding of the system’s coping potentials. Related work As explained above, public transport capacity robustness is built over the system’s remaining passenger transport capabilities also described as its residual capacity. The residual capacity embodies the nonutilized capacity within a public transport vehicle during its operations, thus, highlights its ability to transport unexpected demand [7]. Abiding by this definition, the residual capacity of a public transport structure can be mathematically expressed as in (1) [8]. RC = C * (1 - OR) (1) where RC = Residual Capacity, C = Scheduled Capacity, OR = Occupancy Rate Equation (1) reflects two important elements in public transport capacity planning: the operative structure of the system (e.g. operating program, vehicle sizes, etc.) embodied by the scheduled capacity [4], and the passenger transport demand, condensed as an OR factor. The OR factor conveys the liaison between the scheduled ca- AUF EINEN BLICK Der Beitrag beschreibt einen geeigneten Ansatz zur schnellen, allgemeingültigen Abschätzung von Kapazitäts- Einschränkungen im ÖV. Er ergänzt dafür den Begriff der Rest-Kapazität um geeignete Mechanismen zur Erhebung einer schwer fassbaren Variablen: des Auslastungsgrad- Faktors (Occupancy Rate, OR) genannt. Um diese komplexe Variable ansetzen zu können, führt dieser Artikel auf Basis der Daten von sechs verschiedenen ÖV-Netzen und 25 Verkehrslinien in Deutschland aus, wie der OR-Faktor für die drei Verkehrsträger Bus, Tram und U-Bahn entfernungs- und tageszeitabhängig ermittelt werden kann. Internationales Verkehrswesen (70) 3 | 2018 85 Wissenschaft TECHNOLOGIE pacity and the actual passenger travel behavior in the system by stressing the shifts in net passenger vehicleoccupancy along a public transport route. Whereas the scheduled capacity of a line can be unequivocally asserted by observing its planned characteristics, evaluating its OR entails dealing with the complexity behind passengers’ travel behaviour. Passengers’ travel behaviour is understood as the result of the objective and subjective aspects that constitute the local urban mobility culture. The objective aspects range from the urban form, transport infrastructure to socioeconomics and may be unequivocally evaluated. However, the subjective aspects, comprised by people’s lifestyles, attitudes, and perceptions, are difficult to appraise due to their abstract nature [9]. The intricacy behind conducting a deep assessment of the residual capacity elements is also reflected in public transport scholarly inquiry. Some authors propose complex models to assess the degree and significance of the residual capacity within particular links and specific border conditions [5, 10]. Others expand propose ways in which the residual capacity can be fostered and efficiently located across a given network [7, 11]. However, mechanisms that allow practitioners and decision makers to promptly assess capacity limitation issues regardless of the boundary conditions (e.g. during real operations) are still lacking. In this regard, a model capable of assessing the residual capacity of public transportation for real-time passenger rerouting was put forward in [8]. Since a thorough and exact assessment of the OR is not compatible with a prompt valuation of its capacity limitations, the authors in [8] propose a modespecific calibration of the OR. What is more, they outline a framework to calibrate the OR as a holistic assessment tool. This article makes use of the analytical framework in [8], and assembles the necessary mechanisms for its appraisal across three public transport modes (i.e. buses, light rails and subways). To do so, the next section describes the OR assessment framework and calibration method. Then, the attributes of the gathered data and the necessary function-fitting process for the calibration are discussed. Finally, the article discusses the importance of the successfully calibrated OR functions as tools. Assessment framework Calibrating the OR implies rendering the specific shifts in net passenger vehicle-occupancy as mathematical relations. Yet, to guarantee their general application (i.e. not bound to the border conditions of any network) the assessment framework defines three spatiotemporal conditions (see Figure 1) [8]. At the outset, the mathematical relation depicts the changes in occupancy regarding the vehicle’s position within the network. To reference this position, the first condition points towards identifying a “gravity center” for all the trips generated across the network, which is usually located in the Central Business District (CBD) [12]. The second condition, which also focuses on the spatial aspect, stresses the need to manage the uncertainty across the length of public transport lines by normalizing their dimensions. Normalizing the lines’ lengths implies securing they have uniformed range, in this case equating their total length to one, and be comparable with one another. Lastly, to capture the trending changes in occupancy across the operational day, the third condition steers the OR functions towards acquiring a time-specific arrangement. Thus, the calibrated relations must distinguish the changes in occupancy between peak and off-peak hours. By and large, the OR function is believed to find its maximum value in the course of peak hours and comprise a negative slope while it decreases as it retreats from the proposed origin (i.e. city center). The explained provisions suggest that to isolate the changes in passenger trips within a given mode it is critical to retrieve actual operational data samples across multiple networks. For this, direct passenger counts represent plausible data sources, as they systematically record the number of passengers boarding and alighting from a line’s timetabled journey at every stop. Once the passenger counts for all the timetabled journeys during an entire operational day of a given set of lines are made available, the effective calibration of the OR function can be divided into six steps. First, to reference the route distances of all the scrutinized lines and networks their respective mobility gravity centers must be identified. In a second step, the network’s peak (HVZ) and offpeak hours (NVZ; SVZ: German abbreviations for normal and weak traffic times respectively) must be identified. For this, all timetabled journeys of a given line are combined into one-hour intervals and assigned to one of the three temporal categories on the basis of the net inflow and outflow of passengers from the acknowledged gravity-centers as well as the number of services. Third, with the passenger exchange information at every stop, the shift in the number of passengers along a single vehicle’s journey can be deduced. This information can be then transformed into an OR by placing it in relation to the vehicle capacity. Fourth, at each scheduled stop, an average OR can be determined for all the timetabled journeys assigned to a respective temporal category. Fifth, for the individual line length normalization the total length is defined as the distance between the city center and the line’s last stop. In the case of diametrical lines, these are considered as two radial lines separated at the identified center. The total line length is then divided by itself (d/ D) to secure the unitary range. Finally, Figure 1. Route base occupancy rate shift and spatiotemporal constraints Source: by author Internationales Verkehrswesen (70) 3 | 2018 86 TECHNOLOGIE Wissenschaft the averaged OR for all the lines belonging to the same mode (i.e. bus, tram or light rail & subway) and temporal category (HVZ, NVZ & SVZ) are isolated and plotted against their normalized distances. This allows for a function to be later fitted to the obtained scattered plots by means of a linear regression. Data sets and OR calibration Within the framework of this study, passenger counts from 6 different German cities and networks have been collected. The retrieved datasets record passenger exchange records for all the timetabled journeys corresponding to one entire day of operations (during the school season) along 25 different lines and three public transport modes. The 25 lines are distributed as shown in Table 1, where the specific line number per every mode can be appreciated. The lines were chosen on basis of their ability to connect the city center with the outskirts of their respective urban areas. In this case, lines with both radial and diametrical qualities were preferred over those with circular characteristics. It must be noted that all bout one dataset included the scheduled vehicle capacity for each journey. For the one network which only identified the vehicle types, the maximum vehicle capacities detailed in [17] were utilized. Abiding by the methodology described in the previous section, the averaged OR for all the lines belonging to the same mode and divided per temporal category are plotted against their normalized distances. These were fitted to a linear function of the form (y = a + x * -b) by means of a linear regression. The regression results for all three modes and temporal categories are displayed in Figure 2. As it can be appreciated the overall properties of the fitted functions remain uniform as they keep the same general pattern across modes and temporal intervals. Furthermore, the absolute fit of the regressed functions is compatible with the overall aim of securing a rough estimate towards a prompt capacity limitation assessment. For all modes, as anticipated in the assumptions (see Figure 1) the slope is the steepest during the HVZ and delivers an overall maximum at the city center. By the same token, a consistent inverse association between OR and distance to the center provides substantial evidence to corroborate the relevance of the utilized method and an effective calibration of the OR across diametrical and radial lines. From the calibrated results, it can also be observed that the maximum OR value never exceeds 50%, which is to be expected if contrasted with the acceptable value (i.e. 65 %) conveyed in the German transport quality standards [18]. This would indicate that in Germany a conventional bus or light-rail line would have the equivalent of 50 % of its total capacity as residual capacity all along its route; an additional 15 % more than the specified in [18]. This last percentage would be even higher (i.e. up to 25 %) for a subway line. Conclusions The presented results constitute the ground work for a prompt assessment of capacity limitation issues and robustness qualities across the three studied means of transport. Following the positive calibration of the OR functions and combined with Equation (1), decision makers can promptly identify the residual capacity of the assessed public transport lines throughout any point of their route independently of the border conditions of the network. Ultimately, this information enables to place the system’s robust potentials and the wellbeing of the users within the operational context. The calibrated OR functions provide vital information across many scenarios of the public transport operations. For example, for the development of proficient preparedness strategies during planned but extreme operational situations (e.g. construction works, city events, schedule modifications, etc.). With help of the OR functions, and an overall knowledge of the operational principles of a given network, it is possible to recognise criti- Figure 2. Calibrated OR functions for subway; bus and light rail lines Source: by author Urban Area Lines Assessed Mode Source Esslingen 101; 108 & 110 Bus [13] Frankfurt a.M. 2; 3; 4; 6; 7 & 8 Light Rail [14] Hamburg 1; 2 & 4 Subway [15] Ludwigsburg 421; 427 & 430 Bus [13] Stuttgart 4; 5; 7; 9 & 14 Light Rail [13] Wiesbaden 4; 5; 17; 22 & 48 Bus [16] Table 1. Assessed networks, lines, modes and sources Source: by author Internationales Verkehrswesen (70) 3 | 2018 87 Wissenschaft TECHNOLOGIE cal sections (e.g. bottlenecks) and adequately arrange (intermodal) transferences and replacement services. What’s more, the OR functions would convey special relevance during the occurrence of unexpected events (e.g. sudden disruptions in the network or in other transport systems). Under disrupted situations upholding the system’s serviceability and reliability implies balancing the residual capacity among different lines and modes in key locations of the network. Thus, a rapid capacity limitation assessment permits decision makers to envision measures that uphold the welfare of both the original and disrupted users. By relying on the same methodological structure, the OR functions can be expanded to include other public transport modes (e.g. commuter railway services). Moreover, a special inquiry can be made to elucidate the average OR during the 20 min peak and where the quality standards permit a maximum occupancy of 80%. All in all, it is not only through system qualities (e.g. enhanced robustness or redundancy), that the resilience of a public transport network is advanced, but it is also necessary to possess the adequate mechanisms for prompt access to key information (e.g. residual capacity). ■ REFERENCES [1] Newman P., Kosonen, L., Kenworthy J. (2016). Theory of urban fabrics: planning the walking, transit/ public transport and automobile/ motor car cities for reduced car dependency, TPR, 87 (4) 2016 doi: 10.3828/ tpr.2016.28 [2] Newman P., Kenworthy J. (2015). The End of Automobile Dependence. Island Press, USA [3] Rinaldi, S., Peerenboom, J.P., and Kelly, T.K. (2001). Identifying, understanding, and analyzing critical infrastructure interdependencies, IEEE Control Systems Magazine 21(6), 11-25 [4] Schnieder L. (2015). Betriebsplanung im öffentlichen Personennahverkehr. Springer- Verlag Berlin Heidelberg, Germany, DOI: 10.1007/ 978-3-662-46456-4 [5] Jin J., Tang L., Sun L., Lee D. (2014). Enhancing metro network resilience via localized integration with bus services. Transportation Research Part E: Logistics and Transportation Review, 63, 17-30. DOI: 10.1016/ j.tre.2014.01.002 [6] Mattsson, Lars-Göran; Jenelius, Erik (2015). Vulnerability and resilience of transport systems - A discussion of recent research. In Transportation Research Part A: Policy and Practice 81, pp. 16-34. DOI: 10.1016/ j.tra.2015.06.002 [7] Cats O., Jenelius E. (2015). Planning for the unexpected: The value of reserve capacity for public transport network robustness. Transportation Research Part A: Policy and Practice, 81, 47-61 [8] Crespo Arturo, Oetting Andreas (2018). Model for Estimating the Residual Transport Capacity During Passenger Deviation. Grenzenlos(er) Verkehr! ? In Fakultät für Verkehrswissenschaften (Ed.): 26. Verkehrswissenschaftliche Tage. Grenzenlos(er) Verkehr? ! (Verkehrswissenschaftliche Tage), 110-122 [9] Klinger T. Kenworthy J. Lanzendorf M. (2010) What shapes urban mobility cultures? A comparison of German cities. European Transport Conference, Glasgow, Oct. 8. 2010 [10] Xu X., Chen A., Jansuwan S., Heaslip K., Yang C. (2015). Modeling Transportation Network Redundancy. Transportation Research Procedia, 9, 283-302, DOI: 10.1016/ j.trpro.2015.07.016 [11] Chen, A., Kasikitwiwat, P., Yang, C. (2013). Alternate capacity reliability measures for transportation networks. Journal of Advanced Transportation 47(1), 79-104 [12] Lefèvre B. (2010). Urban Transport Energy Consumption: Determinants and Strategies for its Reduction. An analysis of the literature. Cities and Climate Change 2(3), 1-17 [13] Verkehrs- und Tarifverbund Stuttgart GmbH - VVS (2016). Verkehrsstromerhebungen 2010-2016 (Nachfrageniveau Herbst 2016) [Data file: Linienbelastung verschiedene Linien] [14] Lokale Nahverkehrsgesellschaft Frankfurt am Main mbH - traffiQ (2016). Fahrgaststromerhebungen (Nachfrageniveau Winter 2016) [Data file: Querschnittsbelastung pro Linie] [15] Hamburger Verkehrsverbund GmbH - HVV (2016). Fahrgastzahlen (Nachfrageniveau Frühling 2016) [Data file: Anzahl der ein- und aussteigenden Passagiere pro Linie] [16] Verkehrsgesellschaft mbH - ESWE (2016). Fahrgastzahlen (Nachfrageniveau 2016) [Data file: Anzahl der ein- und aussteigenden Passagiere pro Linie] [17] Dorbritz R., Anderhub G. (2007). How many passengers can public transport systems handle and how much do they handle-A new approach to capacity. 7 th Swiss Transport Research Conference Monte Verità / Ascona, Sept. 12-14 2007 [18] Verband Deutscher Verkehrsunternehmen. (2001) VDV-Schrift 4 - Verkehrserschließung und Verkehrsangebot im ÖPNV. Köln: Verband Deutscher Verkehrsunternehmen Andreas Oetting, Univ.-Prof. Dr.-Ing. Leitung Institut für Bahnsysteme und Bahntechnik, Fachbereich Bau- und Umweltingenieurwissenschaften, Technische Universität Darmstadt eisenbahn@verkehr.tu-darmstadt.de Arturo Crespo, M.Sc. Wissenschaftlicher Mitarbeiter, Institut für Bahnsysteme und Bahntechnik, Fachbereich Bau- und Umweltingenieurwissenschaften, Technische Universität Darmstadt eisenbahn@verkehr.tu-darmstadt.de Brief und Siegel für Wissenschafts-Beiträge Peer Review - sichtbares Qualitätsinstrument für Autoren und Leserschaft P eer-Review-Verfahren sind weltweit anerkannt als Instrument zur Qualitätssicherung: Sie dienen einer konstruktiv-kritischen Auseinandersetzung mit Forschungsergebnissen, wissenschaftlichen Argumentationen und technischen Entwicklungen des Faches und sollen sicherstellen, dass die Wissenschaftsbeiträge unserer Zeitschrift hohen Standards genügen. Herausgeber und Redaktion laden daher Forscher und Entwickler im Verkehrswesen, Wissenschaftler, Ingenieure und Studierende sehr herzlich dazu ein, geeignete Manuskripte für die Rubrik Wissenschaft mit entsprechendem Vermerk bei der Redaktion einzureichen. Die Beiträge müssen „Originalbeiträge“ sein, die in dieser Form und Zusammenstellung erstmals publiziert werden sollen. Sie durchlaufen nach formaler redaktioneller Prüfung ein standardisiertes Begutachtungsverfahren, bei dem ein Manuskript zwei, in besonderen Fällen weiteren Gutachtern (Referees) aus dem betreffenden Fachgebiet vorgelegt wird. Interessierte Autoren finden die Verfahrensregeln, die Autorenhinweise sowie das Formblatt für die Einreichung des Beitrages auf www.internationales-verkehrswesen.de/ autoren-service/ KONTAKT Eberhard Buhl, M.A. Redaktionsleiter Internationales Verkehrswesen Tel.: +49 7449 91386.44 eberhard.buhl@trialog.de