INTERNATIONAL European Friedrich-List-Award 2022 Internationales Verkehrswesen (74) 2 | 2022 38 Models for optimizing parallel public transport services Between and within parallel domestic (long-distance and regional) public transport services Parallel public transport systems, optimization models, long-distance transport, regional transport One of the international problems of public transport system is that domestic (long-distance, regional) links are served both by buses and trains in parallel, furthermore it also appears in road systems connecting hamlets, as flexible systems have been operated besides traditional public transport services. This situation can result in a competition, generating a non-sustainable system. This mainly exists in countries, where the interurban public transport is based on a public service contract. The created models for optimizing the parallel public transport systems can be applied generally. András Lakatos B ased on the mentioned issues in the abstract, three topic areas have been identified: 1. Analytical and user preference-based modelling of long-distance public transportation 2. Modelling of parallel public transport services at the regional level 3. Modelling of parallel services concerning interurban bus services The various optimization models are interrelated, and if all of them are applied, the whole system of parallel transport services can be transformed into a sustainable and efficient network. The existing and recurring international problem [1] of parallel bus and train links in long-distance (within the border of each country) public transport has been addressed here. The aim of examining longdistance parallel public transport systems is to determine which transport mode or modes, or may be parallel links can ensure that public transport would be sustainable and efficient. The factors taken into consideration are user and operator parameters, and travel distance. In order to achieve this, a mathematical method, regression analysis [2] was applied to analyze the changes of temporal and cost values with respect to distance. An internationally applicable 5-step model was defined to solve this problem (Figure 1, top). In addition to this analytical approach, this study also aims to explore preferences of passengers for choosing transport modes. In order to achieve this and to be able to reach the highest possible level of services, the correlations between analytical aspects and passenger preferences concerning the quality of services depending on distance have been identified. Passengers take into consideration several parameters when deciding on the mode of transport. [3, 4, 5] Travel time, travel costs, comfort and motivation were examined as the influencing factors of mode choice. The complex correlations behind their mode choice have been explored and a model for user behavior has been set up based on revealed and stated preference types of questionnaires containing equal to reality parameters in order to determine the user preferences with respect to travel distance and passenger motivation in the case of parallel public transport links. The importance of each parameter in the decision-making process of users has been determined based on the answers to the questionnaires. The aim of examining regional parallel public transport systems is to create a complex, compact and generally applicable service quality index in order to evaluate and optimize regional parallel links (Figure 1, bottom). Moreover, to identify each value of the service quality index, some traffic organization measures (in some cases based on European best practices) result in an increase in the level of transport services, while costs are decreased. A mathematical method, the logit model [6] is used to explore the correlations between the values of the service quality index and the number of passengers, analyzing the extrema of utility functions [7]. The value of a quality index (M) has been calculated (Equation 1) based on some comprehensive parameters (travel time, available services, number of inhabitants) (Table 1). M n t p n t p daily travel j daily travel i,j,b = ⋅ ⋅ − ⋅ ⋅ 1 1 jj j n     = ∑ 1 i,j,b i,j,v i,j,v Based on objective functions [8] (Equations 2 and 3), interval boundaries for the values of quality parameters have been defined. These were validated by the logit model-based evaluation of the following values: number of passengers using parallel bus and train links, offered travel times, offered travel costs. M → max (2) K invest. i,j,k → min. (3) Traffic organization measures to maximize the M value have been defined for each interval, while minimizing investment costs (K invest. i,j,k ). In such rarely populated areas, the integration of the already existing traditional and demand-responsive transport systems [9] is suggested in order to create an economically sustainable system with the increasing of the service levels, i.e. ensuring that the hamlets are served at a higher level. European Friedrich-List-Award 2022 INTERNATIONAL Internationales Verkehrswesen (74) 2 | 2022 39 A generally applicable, demographical and public transport service level data based 7-step complex and compact model is created for optimization, which allows for the reorganization of transport performance in a way that operational costs do not rise (Equation 5), but the level of service is increased (Equation 4). Z → max (4) C day → min. (5) The model allows for replacing the traditional public transport network with a flexible system. Results To implement the long-distance parallel model into practice, a Hungarian case study was chosen. In Hungary, there are several parallel long-distance links, most of them are Budapest-centered. Based on this, travel chains between Budapest and 15 county seats or towns with county rights have been determined. During the evaluation, polynomial regression has been fit to the value pairs, i.e. travel time, as user parameter and travel distance; and unit cost per place in the vehicle, as operator parameter and distance. The optimization possibilities of long-distance public transport modes have been divided into 3 sections according to the relative position of the functions and deviation values (Figure 2, top). The competitiveness of buses even for long distances can be enhanced if Tempo1 00 (the allowed maximum speed is 100 km/ h on motorways) quality buses are applied. It has been demonstrated that the deviation of unit costs per seat in the vehicle is inversely proportional to distance. Based on revealed and stated questionnaires, user preferences change depending on travel distance. Three distance intervals have been defined, according to which user expectations concerning travel time, comfort and costs change. It has been proven that the distance intervals corresponding to mode choice are in harmony with the suggestions for traffic organization measures defined analytically. For shorter travels (under 150 kilometers) the users choose the bus service because of its reliability and the travel time, while in case of longer domestic mobility needs (above 180 kilometers) passengers pays extra money for the comfort (travel time is not so important) which can be guaranteed by railway service. Between 150 to 180 kilometers travel time and comfort affects in a same level regarding mode choice. The applicability of the regional model has been proven through a case study, which includes the optimization for all of the 7 regions of Hungary, handling all the parallel bus and train links of the country. It has been declared that calculating the quality index values for each parallel links and travel time and travel cost based utility functions, interventions can be suggested (Figure-2, bottom). The level of service can be increased solely by traffic organization measures, without the need for considerable investments. Regarding parallelism within the (bus) transport mode, a case study for an area in Hungary (Borsod-Abaúj-Zemplén county) was conducted, based on the 7-step model. The public transport service for ‘dead-end’ villages with a diminishing population can be improved by replacing traditional service in case of detours - as a feeder system to traditional main traffic - with demand responsive transport and the effective distribution of the present resources, without extra costs, which is beneficial both for users and operators. That replacing the traditional service with DRT service can decrease the Variable Description Dimension i departure (settlement) - j arrival (settlement) - k transport mode (b - bus, v - train) - t travel i,j,k total time required for covering the distance between the centres of i and j settlements, by k mode of transport min n daily i,j,k number of vehicles per day running between i and j settlements, by k mode of transport piece p j the proportion of the number of inhabitants of the given settlement and the total number of inhabitants of the settlements served by the given service - Table 1: Legend for Equation (1) Figure 1: 5-step model for optimizing parallel long-distance public transport (top); the optimization model for regional parallel public transport links (bottom) All figures: Author 01 Selection of parallel longdistance public transport links 03 04 DEFINITION OF TRAVEL CHAINS User parameters: 𝑡𝑡 ������ �𝑥�𝑥� � ∑𝑡𝑡 ����������������� �𝑥�𝑥� � 𝑡𝑡 ������� �𝑥�𝑥� ∑𝑡𝑡 ����������������� �𝑥�𝑥� � 𝑡𝑡 ������ �𝑥�𝑥� � 𝑡𝑡 ������ �𝑥�𝑥� 𝑡𝑡 ������ �𝑥�𝑥� � 𝑡𝑡 ��������������𝑥�� �𝑥�𝑥� � 𝑡𝑡 ���������������� �𝑥� 𝑡𝑡 ������ �𝑥�𝑥� � 𝑡𝑡 ��������������𝑥�� �𝑥�𝑥� � 𝑡𝑡 ���������������� �𝑥� 𝑠𝑠 ������ �𝑥�𝑥� � 𝑠𝑠 ������ �𝑥�𝑥� � 𝑠𝑠 ��������𝑥�𝑥� � 𝑠𝑠 ������ �𝑥�𝑥� 𝑠𝑠 ������ �𝑥�𝑥� � 𝑠𝑠 ��������������𝑥�� �𝑥� 𝑠𝑠 ������ �𝑥�𝑥� � 𝑠𝑠 ��������������𝑥�� �𝑥� 𝑡𝑡 ������𝑥����𝑥�𝑥� � ∑𝑡𝑡 ����������������� �𝑥�𝑥� � 𝑡𝑡 �������𝑥����𝑥�𝑥� Operator parameters: 𝐶𝐶 ������𝑥�𝑥� � � ��������𝑥�𝑥�𝑥��������������𝑥� ����������𝑥� CALCULATION OF USER AND OPERATOR PARAMETERS Modelling of correlations between parameter values 𝑓𝑓 𝑥𝑥𝑥 𝑥𝑥 � � 𝑥𝑥 � � � 𝑥𝑥 � 𝑥𝑥 � � � � 𝑥𝑥 � 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 � ��� � � ��𝑥𝑥 ��� 𝑥𝑥 � 𝑀𝑀 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 �� � 𝑥𝑥 � 𝑥𝑥 �� � 𝑀𝑀�𝑦𝑦 � � 𝑀𝑀 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 �� � 𝑥𝑥 � 𝑥𝑥 �� 𝑥𝑥 � � 𝑀𝑀 𝑦𝑦 � 𝑥𝑥 � 𝑀𝑀 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 �� � 𝑥𝑥 � 𝑥𝑥 �� 𝑥𝑥 �� � 𝑀𝑀 𝑦𝑦 � 𝑥𝑥 �� 𝑀𝑀 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 � � 𝑥𝑥 � 𝑥𝑥 �� � 𝑥𝑥 � 𝑥𝑥 �� 𝑥𝑥 �� � 𝑀𝑀�𝑦𝑦 � 𝑥𝑥 �� � Correlation variable: 𝑟𝑟 �� � � ∑ �� � ��̅ ���� � ���� ���� � � �� � ������ REGRESSION ANALYSIS From user and operator perspectives DETERMINATION OF THEORETICAL DISTANCE-BASED BOUNDARIES 05 Analysis of the possibilities of developing the model DEVELOPING 02 Selection of-parallel- public transport lines Collecting service-quality data Calculation of-quality parameters Defining the interval boundaries for the values of- quality parameters Validating the interval boundaries for the values of- quality parameters Defining the traffic organization measures Optimized public transport network National-Bus Timetable STATISTICAL-OFFICE Changes of-timetables National-Railway Timetable Travel time Frequency Local-public transport timetable Route planning software Local-public transport timetable Route planning sotfware Access-and- egress time Access-and- egress time Population register Travel time Frequency Access-and- egress time Access-and- egress time AB AB Fares LOGIT-MODELL Defining the interval boundaries for the values of-quality parameters Feeder service- within the city Feeder service- within the city Domestic travel VALIDATION OPTIMIZATION National-Bus Timetable ‐ Database Access-and- egress time ‐ Data LOGIT-MODEL ‐ Mathematical calculation or activity ‐ First step of-the optimization Selection of- parallel-public transport lines Route planning software ‐ Software LEGEND INTERNATIONAL European Friedrich-List-Award 2022 Internationales Verkehrswesen (74) 2 | 2022 40 costs by more than 50 EUR in the morning off-peak period, 228 EUR daily. Conclusions One of the international (especially in Middleand East-Europe) problems of public transport system is that domestic long-distance links are served both by buses and trains, in a parallel manner. Furthermore, there are parallel bus and train services in all regions of the countries, and several cross-country parallel links are also existing. This situation can result in a competition between the two modes, generating a system that is not sustainable. Parallel services are present not only between modes, but also within branches. This is characteristic of road systems connecting hamlets, as in these regions demand-responsive social transport systems have been maintained by local governments for closed communities in the past 20 years, while the state-ordered parallel traditional public transport services have also been operated. This means that both human resource management and vehicle management work suboptimally, in total in a wasteful manner. Generally applicable, complex, mathematical-based models for the optimization of the mentioned parallel public transport systems were developed. The complexity of the models is represented by the parameters considered (both from user and operator perspective). The practical applicability of the models is demonstrated through Hungarian case studies. The developed models can have a decision support function in the rationalization of parallel public transport systems. Adapting to the transport strategy and concept of each country, the parallel links/ systems exist between and within the different modes of transport can be optimized in time, either simultaneously or sequentially, according to the models. Regarding future research, the evaluation of the factors examined in the model developed for the optimization of parallel services between modes of transport. Within road public transport, the external effects (environmental and accident costs) can be quantified with a CBA based on guide document. Furthermore, the analysis of user preference and parameter-based long-distance models can be extended to parallel international public transport in order to optimize the division of labor in transport. ■ REFERENCES [1] Fleischer, T. (2005): Fenntartható fejlődés-fenntartható közlekedés. University Library of Munich, Germany. www.vki.hu/ ~tfleisch/ PDF/ pdf05/ fleischer_fe-fejl-fe-kozl_kmszle05-12.pdf (Access: 10.06.2016) [2] Buis, M. L. (2019): Logistic regression: When can we do what we think we can do? www.maartenbuis.nl/ wp/ odds_ratio_3.1.pdf (Access: 29.05.2016) [3] Kosztyó, Á.; Török, Á. (2007): Döntésmodellezés a közúti közlekedési módválasztásban. In: Marketing & Menedzsment 41(1), 48-51. http: / / real.mtak.hu/ 5258/ (Access: 09.10.2018) [4] Kövesné Gilicze, É.; Debreczeni, G.; Csiszár, Cs. 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In: Közlekedéstudományi Szemle 56(7), pp. 263-268. http: / / real-j.mtak. hu/ 10810/ 7/ Kozlekedestudomanyi_2006_07.pdf (Access: 02.01.2020) András Lakatos, PhD Research Fellow, Budapest University of Technology and Economics (BME), Budapest (HU) lakatos.andras@kjk.bme.hu Figure 2: Theoretical boundaries in Hungary, determined by regression functions (top); suggested measures, depending on the precise values of the quality index (bottom) Competition of railway and coach in distances under 150 kilometers parallel lines between 150-180 kilometers Optimizing Above 180 kilometers coach has a complementary role No-interventions needed Proper reconstruction or major- intervention needed The-vechicles should stop-in- towns with lower number of- inhabitants,-and- connect them with the local- centre Using DRT The-vechicles should stop- only in-towns with higher number of- inhabitants Increasing the quality of- service Increasing the quality of-service Carrying from and-to the railway by bus,- connections needed in-the timetable Using DRT The-vechicles should stop- only in-towns with higher number of- inhabitants The-role of- the bus service-in-the public transport network should be- revised No-interventions needed BUS-SERVICE RAILWAY-SERVICE ‐5 ‐2 +2 +5 M Business- politically reduced fare Businesspolitically reduced fare The-vechicles should stop-in-towns with lower number of- inhabitants,-and- connect them with the local-centre