67 Simulation of Optimal Routes Passenger Transport Oksana Bashutska1, Nadiia Panchuk2 1. Department of Economic Cybernetics and Informatics, Ternopil National Economic University, UKRAINE, Ternopil, 3 Peremoga sguare, email: o.bashutska@gmail.com 2. Department of Economic Cybernetics and Informatics, Ternopil National Economic University, UKRAINE, Ternopil, 3 Peremoga sguare, email: nadiapanchuk95@gmail.com Abstract: The purpose of the study is to create an and long 20-23 km. The total length of bus routes is economic and mathematical model for improving the approximately 500 km. The average length of the bus route is performance of urban passenger transport and to make 16.5 km. effective management decisions for planning and We found that in the city of Ternopil, the longest bus route redevelopment of city routes. The research takes into is the route number 18. In one direction, it travels about 15 account the current plans for the development of the city km and it takes about 55 minutes. The longest trolleybus of Ternopil and the trends of urban passenger route is the route number 8. In one direction, it travels about transportation. 11 km and it takes about 52 minutes. In Ternopil, city Keywords: passenger transport, route, passenger passenger transportation provides 55 trolleybuses of large and transportation, optimal route, network, graph. especially large passenger capacity, as well as 210 buses of low passenger capacity, which are designed for 42 I. INTRODUCTION passengers. The main task of urban passenger transport is the provision The Trolley Park of Ternopil city contains 32 trolleybuses of passenger transportation services. This topic is relevant as with a total passenger capacity of 100 passengers (TP14) and there is a need to create new routes and increase the 23 trolleybuses with a passenger capacity of 150 passengers competitiveness of existing urban passenger traffic through (TP15). However, in most of them the term of normative the provision of quality transport services. It is possible to exploitation has expired and needs to be replaced. In order to improve their quality by improving technological and fully update the trolleybus park, you need a lot of money, organizational transportation provision. because new trolleybuses are very expensive (the new short The theme of the study becomes particularly relevant, Lviv or Lutsk trolleybus costs about 2 million UAH, and the given the current plans for the development of the city of big one - not less than 4 million UAH). Ternopil and the trends of urban passenger transport. The The bus fleet of the city consists of three types of buses: optimal organization of urban passenger transport to date is IVAN, Bogdan and Etalon. Most of these buses also need an not sufficiently explored. That is why we set ourselves the update[2-5]. task of improving the organization of urban passenger In Ternopil, motor transport complements electric transport transport, improving the quality of transport services for the due to duplication of routes. In peak hours, buses take up a city's residents, reducing transport tensions on the roads, significant number of passengers, and in the period when the improving the ecological situation and ensuring the economic number of passengers is small - contribute to reducing the efficiency of transport enterprises. number of trolleybuses on the line to save energy. The following scientists worked on improving the efficiency of urban passenger transport: Afanasyev LL, II. THE METHOD OF OBTAINING OF THE OPTIMAL Braylovsky MO, Butko T.V., Vorkut AI, Gavrilov EV, ROUTE Geronimus B.L., Granovsky B. I., Dmitrichenko MF, Dolya The terms of each routing task include a description of the V.K., Zablotsky G.A., O.S. Ignatenko, V. V. Kobozev, A. network of communications, which determine the set of Kotsyuk, P. Levkovets, P. Lopatin, L. P. Magnanti, T.L. Mun, possible ways of following one or more moving objects. V. V. Polischuk, A. Petrashevsky, Samoilov DS, Safronov Typically, the structural parameters of the network remain Ye.A., Khabutdinov RA, MS Fiscsells, Hasselstroem D., unchanged from the beginning and until the end of the Mandl C., Nebelung H., Sonntag H. et al. process of solving the problem. The city of Ternopil does not belong to large cities (more The task of finding the optimal route in urban transport than 250 thousand people), nor to secondary (up to 250 networks can only be solved by a complete overview of all thousand people), it is on the border between large and possible options [7]. It is worth noting that the number of medium. For such a city, the time spent traveling from the possible variants of route schemes is equal to 2𝑛𝑛 βˆ™ (𝑛𝑛 βˆ’ 1), place of residence to the place of work or training is 30-35 where n – the number of public transport stops. With minutes, and for those who live in remote districts - 60-70 increasing n this value is rapidly increasing, and already at minutes. For this period in Ternopil 40% of passengers n=10 it is approximately 1,24Γ—1027 variants. transport electric transport and 60% - bus. The total length of It is clear that the complete overview of such an amount the contact network is more than 60 km, and the total length of options takes a lot of time and requires very powerful of trolleybus routes is approximately 150 km. The length of computing [6]. That is why we came up to solve this problem short trolleybus routes is 10-14 km, the average 15-19 km, ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 68 from the expert point of view, that is, built the routes in order 17 𝑛𝑛р = = 17 π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ to cover as much territory as possible and at the same time 1 minimize overlap with one transport route of another. Thus, the required number of routs for the existing It is known that the base model for constructing an trolleybus route number 9 is 10, and the required number of optimal transport network in the routing problem is a routs for the existing bus route number 7 is 17. weighted graph 𝐻𝐻 = (𝑉𝑉, π‘ˆπ‘ˆ) with a set of vertices V and a plurality of edges U. The vertex i∈V, |𝑉𝑉| = 𝑛𝑛, corresponds to city stops. The vertices i and j form in the graph 𝐻𝐻 = (𝑉𝑉, π‘ˆπ‘ˆ) the edge {i, j} if they are represented by stops, directly connected segments of the road (trails), adjacent street crossings on a city map, etc[6]. Imagine an existing trolleybus route No. 9 (see Fig. 1) in the form of a graph. The vertices of this graph are the stops of the route, and the edges are the distance between the stops. Having analysed Figure 1, it can be argued that the current trolleybus route No. 9 has 29 stops, and its length is 21,795 km. Imagine an existing bus route No. 7 (see Fig. 2) in the form of a graph. The vertices of this graph are the stops of the route, and the edges are the distance between the stops. Having analysed Figure 2, it can be argued that the current trolleybus route No. 7 contains 25 stops, and its length is 6.95 Fig. 1 Active trolleybus route β„–9 km. The calculation of the duration of the flight is carried out by the formula 1, which is presented below. 𝑙𝑙𝑙𝑙 𝑇𝑇𝑇𝑇 = + 𝑛𝑛𝑠𝑠 βˆ™ 𝑑𝑑𝑠𝑠 + 𝑑𝑑𝑓𝑓𝑓𝑓 (1) π›½π›½βˆ™π‘‰π‘‰π‘‰π‘‰ where 𝑙𝑙𝑙𝑙 – is the length of the route, 𝛽𝛽 – runway coefficient (for Ternopil city 𝛽𝛽 = 0,9), 𝑉𝑉𝑉𝑉 – technical velocity (average for Ternopil 𝑉𝑉𝑉𝑉 = 25 km/h), 𝑛𝑛𝑠𝑠 – number of stops on the route, 𝑑𝑑𝑠𝑠 – idle time at a stop (for the city of Ternopil 𝑑𝑑𝑠𝑠 = 0,02 β„Ž), 𝑑𝑑𝑓𝑓𝑓𝑓 – idle time at the final stop (for the city of Ternopil 𝑑𝑑𝑓𝑓𝑓𝑓 = 0,11 β„Ž). Calculate the duration of the voyage of the existing trolley route No. 9 by the formula 1: Fig. 2 Active bus route β„–7 21,795 𝑇𝑇𝑇𝑇 = + 29 βˆ™ 0,02 + 0,11 = 1,66 β„Ž. The need to build new optimal routes in the city of 0,9 βˆ™ 25 Calculate the duration of the voyage of the existing bus Ternopil is due to the fact that a new micro district is being route number 7 by the formula 1: built, which will provide the city with a large passenger 6,95 traffic (approximately 43 284 people/month). This is due to 𝑇𝑇𝑇𝑇 = + 29 βˆ™ 0,02 + 0,11 = 1 β„Ž. the fact that in the "Warsaw neighbourhood" will be built: a 0,9 βˆ™ 25 Thus, the duration of the voyage of the existing trolleybus large sports complex and swimming pool, shopping and route β„–9 is 1.66 hours, and the duration of the voyage of the entertainment centre, a new bus station, multi-level parking, existing bus route β„–7 is 1 hour. houses, school and kindergarten. The number of flights that is required for the smooth It should be emphasized that for the laying of routes in the operation of urban passenger transport is calculated by the area, it is necessary first to lay 750 m road and 1850 m formula 2: contact network. It will bring the city's expenses in the 𝑇𝑇𝑇𝑇 amount of 6008000 UAH. However, these costs will quickly 𝑛𝑛р = , (2) pay off. 𝑇𝑇𝑇𝑇 where 𝑇𝑇𝑇𝑇 – time on the route (for the city of Ternopil 𝑇𝑇𝑇𝑇 = Imagine a new trolleybus route β„–9A (see Figure 3) in the 17 β„Žπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œπ‘œ), form of a graph. Having analyzed Figure 3, it can be argued 𝑇𝑇𝑇𝑇 – the duration of the routes. that the new trolleybus route β„–9А contains 29 stops, and its Calculate the optimal number of routes for the existing length is 20,755 km. trolley route β„–9 for (2): Imagine a new bus number 7 (see Figure 4) in the form of 17 a graph. After analyzing Figure 4, it can be argued that the 𝑛𝑛р = = 10 π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ new bus β„– 7 has 27 stops, and its length is 20,435 km. 1,66 Calculate the optimal number of routes for the existing bus Calculate the duration of the route of the new trolley route route number 7 for (2): β„–9А for (1): ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 69 20,755 43 284 βˆ™ 12 𝑇𝑇𝑇𝑇 = + 29 βˆ™ 0,02 + 0,11 = 1,62β„Ž . 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = = 1 423 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝. 0,9 βˆ™ 25 365 Determine the daily passenger traffic by the formula: Р𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 βˆ™ π‘™π‘™π‘šπ‘šπ‘šπ‘šπ‘šπ‘š , (4) where π‘™π‘™π‘šπ‘šπ‘šπ‘šπ‘šπ‘š – is the average distance over which the passenger overcomes (for the city of Ternopil π‘™π‘™π‘šπ‘šπ‘šπ‘šπ‘šπ‘š = 2 π‘˜π‘˜π‘˜π‘˜). Р𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 1 423 βˆ™ 2 = 2 846 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝. π‘˜π‘˜π‘˜π‘˜ The coefficient of variability of passengers is determined by the formula: 𝑙𝑙𝑙𝑙 πœ‚πœ‚π‘£π‘£ = (5) π‘™π‘™π‘šπ‘šπ‘šπ‘šπ‘šπ‘š Determine the coefficient of passenger variation for the new trolley route No. 9A: 20,755 πœ‚πœ‚π‘£π‘£ = = 10,38 2 Determine the coefficient of variation of passengers for the Fig. 3 New optimized trolleybus route β„–9А new bus number 7: 20,435 πœ‚πœ‚π‘£π‘£ = = 10,22 2 Determine the maximum daily productivity of vehicles: π‘Šπ‘Šπ‘„π‘„π‘šπ‘šπ‘šπ‘šπ‘šπ‘š = π‘žπ‘ž βˆ™ π‘Œπ‘Œπ‘šπ‘šπ‘šπ‘šπ‘šπ‘š βˆ™ 𝑛𝑛𝑝𝑝 βˆ™ πœ‚πœ‚π‘£π‘£ , where q is the nominal capacity of the vehicle (the "Etalon" bus is 42; the trolleybus "14Tr" is 100; the trolleybus "15Tr" is 172); π‘Œπ‘Œπ‘šπ‘šπ‘šπ‘šπ‘šπ‘š - coefficient of passenger capacity utilization (for the city of Ternopil π‘Œπ‘Œπ‘šπ‘šπ‘šπ‘šπ‘šπ‘š = 0,5). Since, in Ternopil there are two types of trolleybuses with different passenger capacity, we will determine the maximum daily productivity for each of them with the help of (6). For trolleybus "14Tr" of the new trolley route β„–9А: π‘Šπ‘Šπ‘„π‘„π‘šπ‘šπ‘šπ‘šπ‘šπ‘š = 100 βˆ™ 0,5 βˆ™ 11 βˆ™ 10,38 = 5 709 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝. Fig. 4 New optimized bus route β„–7 For trolleybus "15Tr" of the new trolley route β„–9А: Calculate the duration of the routes of the new bus route π‘Šπ‘Šπ‘„π‘„π‘šπ‘šπ‘šπ‘šπ‘šπ‘š = 172 βˆ™ 0,5 βˆ™ 11 βˆ™ 10,38 = 9 820 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝. number 7 for (1): For the bus "Etalon" of the new bus route number 7: 20,435 π‘Šπ‘Šπ‘„π‘„π‘šπ‘šπ‘šπ‘šπ‘šπ‘š = 42 βˆ™ 0,5 βˆ™ 11 βˆ™ 10,22 = 2 361 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝. 𝑇𝑇𝑇𝑇 = + 29 βˆ™ 0,02 + 0,11 = 1,6 β„Ž. 0,9 βˆ™ 25 Determine the required number of vehicles: Thus, the duration of the route of the new trolley route 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 Арс = (7) β„–9А is 1.66 hours, and the duration of the flight of the new π‘Šπ‘Šπ‘„π‘„π‘šπ‘šπ‘šπ‘šπ‘šπ‘š bus route β„–7 is 1 hour. For trolleybus "14Tr" of the new trolley route β„–9А: Calculate the optimal number of routes for the new trolley 1 423 Арс = β‰ˆ 1 trolleybus route β„–9A for (2): 5 709 17 For trolleybus "15Tr" of the new trolley route β„–9А: 𝑛𝑛р = = 11 π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ 1 423 1,62 Арс = β‰ˆ 1 trolleybus Calculate the optimal number of π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ for the new bus 9 820 route β„–7 for (2): For the bus "Etalon" of the new bus route number 7: 17 1 423 𝑛𝑛р = = 11 π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ Арс = β‰ˆ 1 bus 1,6 2 361 So, for optimal operation of the transport in the "Warsaw Thus, the required number of π‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿπ‘Ÿ for the new trolley district" it is expedient to launch 1 bus "Etalon", 1 trolley bus route β„– 9А and the new bus route β„–7 is 11. "14Tr" and 1 trolley "15Tr". Determine the planned volume of passenger transportation We will calculate what revenue will get vehicles per day per day: 𝑄𝑄 for this multiply the maximum performance of the vehicle by 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = Ρ€ , (3) the fare in it: 𝐷𝐷𝑐𝑐 where 𝑄𝑄р – is the volume of passengers transported per For trolleybus "14Tr" of the new trolley route β„–9А: year; Revenue = 5 709 βˆ™ 3 = π‘ˆπ‘ˆπ‘ˆπ‘ˆπ‘ˆπ‘ˆ 17 127 . 𝐷𝐷𝑐𝑐 – calendar number of days in a year. For trolleybus "15Tr" of the new trolley route β„–9А: Planned volume of passenger traffic per day with new Revenue = 9 820 βˆ™ 3 = π‘ˆπ‘ˆπ‘ˆπ‘ˆπ‘ˆπ‘ˆ 29 460 optimal routes: For the bus "Etalon" of the new bus route number 7: Revenue = 2 361 βˆ™ 4 = π‘ˆπ‘ˆπ‘ˆπ‘ˆπ‘ˆπ‘ˆ 9 444 The total revenue that vehicles will receive per day is UAH ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic 70 56030. However, taking into account the privileged travel, it The constructed model of the interactive transport network will amount to UAH 47626. can be used as a tool for developing new and improving Develop a visualization of the transport system and existing urban passenger transport routes. It allows you to interactive surveillance, which will allow you to see the predict the number of vehicles on the route, the length of traffic of vehicles on the route in real time from stop to stop. routes, the intervals between vehicles. It also allows you to This interactive model will, unlike the existing ones, take into account speed mode and change of traffic rules (for automatically take into account the location of the vehicle on example, the appearance of new road signs on routes). the route, and will also provide instant detection of deviations from normal traffic. III. CONCLUSION The interactive transport network, constructed taking into As a result of the research carried out, the visualization of account the adjusted routes for the new "Warsaw" district in the transport system and interactive surveillance, which the city of Ternopil, is presented in Figures 5 and 6. allows you to see the movement of vehicles on the route in real time from stop to stop. This interactive model will, unlike the existing ones, automatically take into account the location of the vehicle on the route, and will also provide instant detection of deviations from normal traffic. An interactive transport network, built on tailored routes for a new micro district in the city of Ternopil. The constructed model of an interactive transport network can be used as a tool for developing new and improving existing urban passenger transport routes. It allows you to predict the number of vehicles on the route, the length of routes, the intervals between vehicles. It also allows you to take into account speed mode and change of traffic rules (for example, the appearance of new road signs on routes). REFERENCES [1] Grigorkiv V. S. Economic cybernetics: Teaching. manual - Fig. 5 Interactive transport network of optimized trolleybus Chernivtsi: Ruta, 2006. - 9 p. route β„–9 [2] Classification and system properties [Electronic resource]: - Access mode: http://buklib.net/books/22350/ [3] Law of Ukraine "On Transport" [Electronic resource]: - Mode of access: http://zakon3.rada.gov.ua/laws/show/232/94- %D0%B2%D1%80 [4]. Internet article "Trolley-bus fleet of Ternopil plan to update in 2 years" [Electronic resource]: - Access mode: http://www.0352.ua/y article / 277181 [5] News of the official site of the Municipal Enterprise "Ternopillectrotrans" [Electronic resource]: - Access mode: http://elektrotrans.te.ua/routes/ [6] T.L. Magnanti, R.T. Wong, β€œNetwork design and transpotation planning: models and algorithms”, Transportation Science. - 1984. - No. 18 (1), pp. 1-55. [7] B.L. Geronimus and L.V. β€œChaparin Economic- mathematical methods in planning on motor transport” Moscow: Transport, 1988. - 192 p. (in Russian) Fig. 6. Interactive transport network of optimized bus route β„–7 ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic