=Paper=
{{Paper
|id=Vol-2300/Paper17
|storemode=property
|title=Simulation of optimal routes passenger transport
|pdfUrl=https://ceur-ws.org/Vol-2300/Paper17.pdf
|volume=Vol-2300
|authors=Oksana Bashutska,Nadiia Panchuk
|dblpUrl=https://dblp.org/rec/conf/acit4/BashutskaP18
}}
==Simulation of optimal routes passenger transport==
https://ceur-ws.org/Vol-2300/Paper17.pdf
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 2ππ β (ππ β 1),
place of residence to the place of work or training is 30-35 where n β 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 1,24Γ1027 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
ππΡ = = 17 ππππππππππ
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 π»π» = (ππ, ππ) with a set of vertices V and a
plurality of edges U. The vertex iβV, |ππ| = ππ, corresponds to
city stops. The vertices i and j form in the graph π»π» = (ππ, ππ)
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 β9
km.
The calculation of the duration of the flight is carried out
by the formula 1, which is presented below.
ππππ
ππππ = + πππ π β π‘π‘π π + π‘π‘ππππ (1)
π½π½βππππ
where ππππ β is the length of the route,
π½π½ β runway coefficient (for Ternopil city π½π½ = 0,9),
ππππ β technical velocity (average for Ternopil ππππ = 25 km/h),
πππ π β number of stops on the route,
π‘π‘π π β idle time at a stop (for the city of Ternopil π‘π‘π π = 0,02 β),
π‘π‘ππππ β idle time at the final stop (for the city of Ternopil π‘π‘ππππ =
0,11 β).
Calculate the duration of the voyage of the existing trolley
route No. 9 by the formula 1:
Fig. 2 Active bus route β7
21,795
ππππ = + 29 β 0,02 + 0,11 = 1,66 β. The need to build new optimal routes in the city of
0,9 β 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
ππππ = + 29 β 0,02 + 0,11 = 1 β. the fact that in the "Warsaw neighbourhood" will be built: a
0,9 β 25
Thus, the duration of the voyage of the existing trolleybus large sports complex and swimming pool, shopping and
route β9 is 1.66 hours, and the duration of the voyage of the entertainment centre, a new bus station, multi-level parking,
existing bus route β7 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
ππππ amount of 6008000 UAH. However, these costs will quickly
ππΡ = , (2) pay off.
ππππ
where ππππ β time on the route (for the city of Ternopil ππππ = Imagine a new trolleybus route β9A (see Figure 3) in the
17 βππππππππ), form of a graph. Having analyzed Figure 3, it can be argued
ππππ β the duration of the routes. that the new trolleybus route β9Π contains 29 stops, and its
Calculate the optimal number of routes for the existing length is 20,755 km.
trolley route β9 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
ππΡ = = 10 ππππππππππ 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): β9Π for (1):
ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic
69
20,755 43 284 β 12
ππππ = + 29 β 0,02 + 0,11 = 1,62β . ππππππππππππ = = 1 423 ππππππππ.
0,9 β 25 365
Determine the daily passenger traffic by the formula:
Π ππππππππππ = ππππππππππππ β ππππππππ , (4)
where ππππππππ β is the average distance over which the
passenger overcomes (for the city of Ternopil ππππππππ = 2 ππππ).
Π ππππππππππ = 1 423 β 2 = 2 846 ππππππππ. ππππ
The coefficient of variability of passengers is determined
by the formula:
ππππ
πππ£π£ = (5)
ππππππππ
Determine the coefficient of passenger variation for the
new trolley route No. 9A:
20,755
πππ£π£ = = 10,38
2
Determine the coefficient of variation of passengers for the
Fig. 3 New optimized trolleybus route β9Π
new bus number 7:
20,435
πππ£π£ = = 10,22
2
Determine the maximum daily productivity of vehicles:
ππππππππππ = ππ β ππππππππ β ππππ β πππ£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);
ππππππππ - coefficient of passenger capacity utilization (for the
city of Ternopil ππππππππ = 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 β9Π:
ππππππππππ = 100 β 0,5 β 11 β 10,38 = 5 709 ππππππππ.
Fig. 4 New optimized bus route β7 For trolleybus "15Tr" of the new trolley route β9Π:
Calculate the duration of the routes of the new bus route ππππππππππ = 172 β 0,5 β 11 β 10,38 = 9 820 ππππππππ.
number 7 for (1): For the bus "Etalon" of the new bus route number 7:
20,435 ππππππππππ = 42 β 0,5 β 11 β 10,22 = 2 361 ππππππππ.
ππππ = + 29 β 0,02 + 0,11 = 1,6 β.
0,9 β 25 Determine the required number of vehicles:
Thus, the duration of the route of the new trolley route ππππππππππππ
ΠΡΡ = (7)
β9Π is 1.66 hours, and the duration of the flight of the new ππππππππππ
bus route β7 is 1 hour. For trolleybus "14Tr" of the new trolley route β9Π:
Calculate the optimal number of routes for the new trolley 1 423
ΠΡΡ = β 1 trolleybus
route β9A for (2): 5 709
17 For trolleybus "15Tr" of the new trolley route β9Π:
ππΡ = = 11 ππππππππππ 1 423
1,62 ΠΡΡ = β 1 trolleybus
Calculate the optimal number of ππππππππππ for the new bus 9 820
route β7 for (2): For the bus "Etalon" of the new bus route number 7:
17 1 423
ππΡ = = 11 ππππππππππ ΠΡΡ = β 1 bus
1,6 2 361
So, for optimal operation of the transport in the "Warsaw
Thus, the required number of ππππππππππ for the new trolley
district" it is expedient to launch 1 bus "Etalon", 1 trolley bus
route β 9Π and the new bus route β7 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:
ππ for this multiply the maximum performance of the vehicle by
ππππππππππππ = Ρ , (3) the fare in it:
π·π·ππ
where ππΡ β is the volume of passengers transported per For trolleybus "14Tr" of the new trolley route β9Π:
year; Revenue = 5 709 β 3 = ππππππ 17 127 .
π·π·ππ β calendar number of days in a year. For trolleybus "15Tr" of the new trolley route β9Π:
Planned volume of passenger traffic per day with new Revenue = 9 820 β 3 = ππππππ 29 460
optimal routes: For the bus "Etalon" of the new bus route number 7:
Revenue = 2 361 β 4 = ππππππ 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 β9 [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, βNetwork design and
transpotation planning: models and algorithmsβ,
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[7] B.L. Geronimus and L.V. βChaparin Economic-
mathematical methods in planning on motor transportβ
Moscow: Transport, 1988. - 192 p. (in Russian)
Fig. 6. Interactive transport network of optimized bus route
β7
ACIT 2018, June 1-3, 2018, Ceske Budejovice, Czech Republic