Article
citation information:
Kurganov, V., Gryaznov, M.,
Davydov, K., Polyakova, L. Increased efficiency and reliability of maintanance of
mass passenger flow with the regular route network of city transport. Scientific Journal of Silesian University of
Technology. Series Transport. 2020, 108,
107-119. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2020.108.10.
Valery KURGANOV[1],
Mikhail GRYAZNOV[2],
Kirill DAVYDOV[3],
Liliya POLYAKOVA[4]
INCREASED
EFFICIENCY AND RELIABILITY OF MAINTANANCE OF MASS PASSENGER FLOW WITH THE
REGULAR ROUTE NETWORK OF CITY TRANSPORT
Summary. This study is aimed at improving the methods of
carriage of passengers by urban transport to improve its reliability and
efficiency. It can be achieved by forming back-up bus routes within the
existing regular route network for servicing mass passenger-flows. This study
theoretically substantiates the impact of back-up bus routes in the current
regular route network on the reliability and efficiency of the transport
process. Mathematical models of reservation of regular route network and the
assessment of the reliability of passenger transport using different
reservation schemes are suggested. Methodological recommendations on the
formation of passenger traffic on back-up bus routes and cost reduction on its
maintenance, by managing the route speed depending on the loading of the city
road network, have been developed. Technical and economic evaluation was
conducted to the developed methodological toolkit.
Keywords: urban transport, route network, bus
transportation, reliability of transport process, efficiency of transportation,
back-up bus routes
1. INTRODUCTION
Passenger traffic is the
movement of passengers in the direction of the routes of the regular route
network of urban transport. The sign of mass passenger flows or the flows with
a great concentration of passengers is the presence of large centres of their
attraction in the city. Such a centre can be an industrial zone, which houses
several large enterprises, residential areas, trade and entertainment
complexes, and sports and leisure facilities popular with the citizens. An
example of a large centre of passenger traffic attraction is the city’s
core enterprise, located in the urban area, which is a workplace for the majority
of the city's residents.
The presence of mass
passenger flows in the city determines the pendulum principle of their
formation on several directions of the regular route network at certain periods
of the day, depending on the time of operation of these centres of attraction. Priority in the maintenance of mass passenger traffic significantly reduces
the efficiency of the regular route network of urban transport. Consequently,
the population loses interest in urban transport as a reliable and affordable
means of transportation. Consequently, the city's residents choose personal
transport for their trips, which causes a decrease in the volume of traffic on
the regular route network and loss of commercial appeal of urban transport for
business.
Modern scientific literature
proposes some ways of improving the efficiency of passenger traffic in cities,
mostly at the expense of addressing sustainable urban transport [1, 2], increasing the level of
informatisation of transport processes [3, 4, 5], surveys on the population's preferences in the choice of urban
transport [6, 7], the formation of urban transport network [8, 9], the analysis
of road transport companies operation [10, 11]. Despite the existence of a
theoretical framework, the proposed method of improving the efficiency of
passenger transport, including bus transport, does not entirely consider the
aspects of ensuring the reliability of the transport process.
The problem of
ensuring reliable transport processes and systems is studied by contemporary
researchers, the examples of these researches are the following works [12, 13, 14]. Reducing the cost
of transport work, without prejudice to the volume and reliability of transport
is achieved by reducing the number of structural elements in the transportation
process. Within the
current regular route network, this effect is achieved through a reservation,
which involves the formation of backup channels for the delivery of passengers
to compensate for the losses of productivity of the basic mode of urban
transport, caused by a decline in passenger traffic or congestion.
Currently, the impact of backup
delivery channels on the reliability and efficiency of transport process has
not been investigated. Moreover, the existing methods for coordinating regular
transport routes do not consider the additional costs, associated with the
formation of standby delivery channels within the existing regular route
network, as well as the consequences of their malfunctioning. In this respect,
the subject of our study is relevant.
2. METHOD OF RESEARCH AND
VERIFICATION
Theoretical studies were based on
the analysis of scientific literature, regulatory and technical documentation,
legal framework, the concepts of the theory of reliability of technical and
transport systems, and the systemic analysis of transport processes. The
analysis of scientific, regulatory and technical and legal literature has
allowed determining the depth of the problem of improving the efficiency and
reliability of passenger transport in cities, as well as to define the purpose
of this study.
The study of the main concepts of
the theory of reliability of technical and transport systems, as well as the
system analysis of transport processes, allowed us to justify the impact of
reserve regular bus routes on the reliability and efficiency of passenger
transport.
Pilot studies were carried out in
laboratory and road conditions using economic-mathematical modelling, the
methods of probability theory and mathematical statistics, computer modelling,
the feasibility study, the analysis of passenger flows, and the field data.
Through these research methods, the authors obtained the mathematical models of
reservation of the regular route network and the assessment of the reliability
of passenger transport using different reservation schemes. The adequacy of the
proposed mathematical models has also been assessed. Moreover, via
computer-aided simulation, we have established the dependence of traffic flow
on its density, as well as the dependence of the technical speed of the bus on
the additional roads on the density of the flow of vehicles.
The raw data for computer-aided simulation were obtained by the in situ observations of the traffic
flows on urban highways, as well as by direct counting of passenger traffic
correspondence on regular routes of urban transport.
The feasibility study made it possible to justify the value of the
practical implementation of the proposed tools and materials.
The reliability of the obtained results is confirmed by the validity of
accepted assumptions in the development of mathematical models, by the
coincidence of the results of our theoretical and experimental research with
the data of well-known academic works of other authors.
3. MODELLING
The justification for the impact of
the reserve bus routes in the current regular route network on the reliability
and efficiency of the transport process requires the analysis and understanding
of these concepts. According to the theory of reliability, a reservation is a
way of improving the reliability of processes and systems by the inclusion of
backup elements during the development or operational phases. The reservation
scheme of a regular route network, which determines the operational costs and
reliability of the transport process, is a way of connecting its core and
duplicating (reserve) structural elements and their connections, called
delivery channels. The operational costs and the reliability of the transport
process, determine its efficiency; first, as a measure of total costs; second,
as the indicator of the number of failures in the transport process and the
cost of their elimination.
The analysis of the concepts under consideration makes it possible to determine their hierarchy of relationship as represented by the Euler diagram (Fig. 1).
The reservation scheme of a regular
route network depends on the mode of resource consumption (Tab. 1).
The back-up regular bus routes are
characterised by the following features: the coincidence of the part of the
length and the synchronisation of traffic schedules with the main routes of
urban transport; the arranging of drop-off/pick-up of passengers in any place
not prohibited by traffic regulations; the ability to control the route speed
by redirecting the flow of route vehicles on additional roads of the city road
network during its loading.
We believe that the choice of the reservation scheme of a regular route network should be based on mathematical modelling.
|
|
|
Fig. 1.
Euler Diagram illustrating the hierarchy and relationship of the concepts
under consideration |
Tab. 1
Reservation regimes for the regular urban transport route network
|
Features |
Resource consumption scheme |
|
|
Regular |
Resource-efficient |
|
|
Reservation principle |
Build-up of rolling stock on the line in the absence of back-up bus
routes |
The organisation of back-up bus routes |
|
Reservation regimes |
Schemes with a series-parallel arrangement of elements |
Majority replacement
schemes |
The target function of the model is
to minimise the total cost (Ctotal), which is defined as the amount of cost spent on building transport
infrastructure to organise the bus traffic on reserve routes (Cbilding), operating costs for transportation (C) and the cost of eliminating failures
when operating on contingency routes (Cfailure):
|
|
(1) |
|
where D – the length
of the period under review [days]; CI
– the overall cost of infrastructure, necessary to organise
the movement of buses on back-up routes, [rub.]; K - the useful life of infrastructure for depreciation
groups [years]; к – the number of
depreciation groups under consideration; Ewages,
Econtribution, Efuel, Eoil servise, Etires,
Erepair, Eshock absorption, Eother costs –
the expenses, respectively, for the wages of drivers and conductors, extrabudgetary
contributions, fuel costs, oil service, wear of tires, shock absorption,
other costs in the amount of indirect costs for the vehicle fleet, [rub./km];
S – bus mileage for the
period, [km]; FΣ – the total amount of fines or compensations for violations in
the transport process through the fault of the carrier, [% from the traffic
fare]; T – traffic fare and
baggage charges, [rub.]; |
|
The system of restrictions enforces compliance with the quality of
transport services of the urban population in terms of conformity with the
transport interval, as well as the performance of contractual obligations on
the volume of traffic, the cost and the number of buses on back-up routes:
|
|
|
(2) |
|
|
||
|
|
||
|
where I, Is –
the suggested and specified interval of movement, [min.]; R – transportation
profitability, [%]; А – the number of vehicles required to service
a passenger flow, [pcs.]; Аh – the number of
vehicles on major routes, [pcs.]; Аl-h – the number of
buses on back-up routes, [pcs.]; h
– the number of main routes, [pcs.]; (l – h) – the number of back-up routes, [pcs.]; l – the amount of basic and
reserve routes, [pcs.]. |
||
The failure probability
in the transport process Q(t) is
determined by the reliability of passenger transport. When there are no back-up
routes, the regular route network has a consistent parallel structure. We
believe that evaluation of reliability for the carriage of passengers if there
are contingency routes in the regular route network, should be based on the
calculation of the reliability of the majority replacement schemes (Fig. 2) based
on the rule of total probability of compatible events.
|
|
|
|
а) |
b) |
|
Fig. 2. The structure of a regular route network in the aspect of
ensuring the reliability of passenger transport: (а) without back-up routes; (b) with back-up routes |
|
Thus, we offer to assess
the reliability of passenger transport using a mathematical model:
- a regular route
network without contingency routes:
|
|
(3) |
|
where Pi –
the probability of a fail-free operation of a bus on the main route. |
|
- a regular route
network with contingency routes:
|
|
(4) |
|
where Pj – the
probability of a fail-free operation of a bus on the back-up route. |
|
Positive results of verification of the proposed model of quantitative
evaluation of the reliability of passenger transport based on Fisher's
criterion prove its appropriateness.
4. PASSENGER FLOW
FORMATION ALGORITHM ON BACK-UP BUS ROUTES
The formation of
ridership on back-up bus routes is based on the analysis of the compatibility
of existing urban transport route network with the needs of the population in
their labour movements. Passenger traffic is not mastered by the main regular
routes, after its detail on the periods of the day, can be potentially mastered
on back-up routes.
Reducing the cost of
servicing the passenger traffic on contingency bus routes is achieved by
maintaining a specified interval of traffic with fewer buses. This is achieved
by increasing the average traffic speed resulting in the direction of buses on
additional roads during road loading.
The procedures are
implemented according to the algorithm (Fig. 3).
In the first stage of
the proposed algorithm, analysis of the compliance of the urban transport route
network to the needs of the population in their labour movements is carried
out. Based on the results of the performed analysis, on the second stage, is
determined the passenger flow, which is not mastered by the main regular
routes. Its detail is defined on the periods of the day and the trace of the
back-up bus routes is conducted within the framework of the current route
network. The third stage provides the mode of resource-saving passenger
services on back-up routes by controlling the route speed of buses. The result
of the algorithm is the development of the passenger schedule for the bus
traffic on back-up routes.
The conformity
assessment of the major urban transport routes to the needs of the population
in their labour movements is made by the coefficient:
|
|
(5) |
|
where
Qcomf. – the
number of people who have passed through the checkpoints of the enterprises,
and whose waiting time of the vehicle at the stops of the regular route
network does not exceed the time of comfortable waiting, person/24 hours; n – the total number of
transactions of entrances and exits through the checkpoints per day. |
|
The waiting time for the
passengers of the vehicle at the stop (t)
is determined on the basis of the survey of the passenger flows. The time of
comfortable waiting (tcomf.)
is set by the survey of the citizens' public opinion conducted by the
specialists of the municipality. The value (φ) is smaller than 1,0 and shows the
inconsistency of the urban transport network with the needs of the population
in their labour movements and the importance to organise the back-up bus
routes. The resource-saving mode of passenger traffic on back-up routes is
achieved by the direction of buses on additional roads of the city road network
during the periods of its loading. This allows for avoiding the need to
increase the number of buses for maintaining a predetermined traffic interval
by increasing the route speed.
|
|
|
Fig. 3. Passenger flow formation algorithm on
back-up bus routes |
The speed of the traffic
flow, considering the traffic density, is determined by the dependence obtained
by mathematical modelling of the three situations that characterise the
congestion of the road network when the vehicle overcomes the congestion at the
signal-controlled intersection at one, two or three cycles of traffic lights,
respectively (Fig. 4).
We propose to determine
the technical speed of the buses on the additional road network, when it is
loaded with the traffic flow of route vehicles, in accordance with the
dependency given in Fig. 5.
|
|
|
Fig. 4. Dependence of
speed of the traffic flow from the density of the flow of vehicles |
|
|
|
Fig. 5. Dependence of
technical speed of the bus on additional roads from the density of the flow
of route vehicles |
Furthermore, the planning decisions of the city
road network depend on route speed, the availability of additional roads on the
road, which duplicate the main highways. The planning
decisions of the road network are individual for each town area. The direction
of buses to additional roads, duplicating the main transport routes, allows
accelerating the traffic flow significantly. On the example of Magnitogorsk, we
have established that the through speed, when implementing such opportunities,
increases on average by 4 km/h (Fig. 6).
Thus, increasing the route speed, by directing buses on contingency
routes to additional roads of the municipal road network during its loading
makes it possible to reduce costs of ridership maintenance.
|
|
|
Fig. 6. Modification
of the average through the speed of buses when they are directed to the
additional road network (on the example of Magnitogorsk) |
5. TECHNICAL AND
ECONOMIC ASSESSMENT OF THE FINDINGS
The technical and
economic assessment of the findings was carried out on the example of public
transport routes in Magnitogorsk. The route network of Magnitogorsk is
characterised by the presence of departure lines to the industrial site of the
Magnitogorsk Iron and Steel Works (MMK), located on the left-bank part of the
city. The workflow of MMK units determines the pendulum principle of ridership
formation: heading to the east in the morning and to the west in the evening.
Checkpoints of MMK are
the places of generation and reducing of mass ridership; that is the reason
regular routes of urban transport run along the transport arteries, skirting
the boundaries of the industrial site, which cause the coincidence of
long-distance sections for majority of the regular routes.
The results were used to
form a backup delivery channel for MMK workers on the regular bus route No 33.
The larger part of the route is the same as route No 3 (Fig. 7), which is the
main route in our calculations.
Conformity assessment of the reserved route No 3 to the needs of the
population in their labour movements is made by f-le (5).
The calculations consider the present traffic schedule, as well as the
need to move the employee on foot between the checkpoint or residence and the
nearest stop. The results of the evaluation are shown in Tab. 2.
Passenger flow, in which the waiting time for the vehicle at the stop
exceeds 15 minutes (tcomf), accepted in the calculations, is
not transported by the main route. The presence of a common section of the
route makes it possible to service this passenger flow by the reserve regular
bus route No 33.
Knowing the time of the workers' passage through the checkpoints No 1,
2, 10, 16, the detailisation of the potential passenger flow on the reserve
route on the periods of the day is done.
|
|
|
Fig. 5. The location
of MMK’s checkpoints on the general section of the highway of routes
under consideration |
Tab. 2
Conformity assessment
results of the main route No 3 to the needs of the population in their labour
movements
|
Station |
No checkpoint |
Potential ridership,
person/a day |
|||||
|
total |
Waiting time is less than
15 min. |
Waiting time is more than
15 min. |
Another route is more convenient |
The desired route is missing |
φ |
||
|
Kirova |
10 |
1591 |
303 |
118 |
614 |
556 |
0,19 |
|
Kirova 70 |
2 |
4143 |
995 |
261 |
1917 |
970 |
0,24 |
|
Komsomol'skaya
ploshchad' |
1 |
12415 |
1837 |
1061 |
3979 |
5538 |
0,15 |
|
Lugovaya |
3 |
2991 |
518 |
165 |
1241 |
1067 |
0,17 |
|
pos. Bruskovyj |
13 |
631 |
112 |
51 |
239 |
229 |
0,18 |
|
Prokatmontazh |
9 |
1000 |
173 |
69 |
453 |
305 |
0,17 |
|
TEC |
16 |
446 |
69 |
13 |
222 |
142 |
0,15 |
|
On average: |
0,18 |
||||||
The accumulation level
of potential passengers at the nearest point to the checkpoints stops allows to
set the interval of bus traffic on the back-up bus route (Is), and the route speed allows to calculate the time of
turnover and the required number of buses (Аl-h).
The analysis of
congestion of the road network’s sections during the day, through which
the track of the back-up bus route No 33 runs, allowed determining the critical
section along Karl Marx Prospect (Starevarov Str. and Truda Str.), where at
peak hours of the day, from 15:00 to 18:00, the average traffic speed reduces
to 11 km/h, thus, leads to congestion at intersections and increases the
delivery time of passengers by fixed routes.
We suggest redistributing route vehicles on this section of the road
network to the additional road parallel to Karl Marx Prospect during this
period. Given these dependencies (Fig. 6), we have established that the
proposed redistribution would increase the route speed of buses to 18 km/h.
This would ensure the predetermined interval with fewer buses during the
loading of the road network and avoid the need to increase the number of buses
on the line.
Having calculated the
total cost of the infrastructure required to organise the movement of buses (CI), using the proposed
mathematical model, we have selected the optimal reservation scheme based on
the minimum cost of total costs (Ctotal)),
for which the passenger information schedule of traffic is being developed.
Based on the
calculations, we have proved that it is inappropriate to use the reservation
scheme to improve the efficiency and reliability of the labour movements of the
population of Magnitogorsk, which involves increasing the number of rolling
stock on route No 3. It has been established that the formation of a
contingency delivery channel based on the regular bus route No 33 will provide
an additional volume of transport equal to 178,000 passengers per year, by
submitting buses to the stops of the route during periods of lack of vehicles
on the main route. The direction of the buses of contingency route on the
additional road during the loading periods of the road network will increase
their route speed by 7 km/h.
Using the proposed
results will reduce the cost of transporting one passenger by 7%, increasing its
reliability by 1,14 times and the service of additional ridership without
increasing the costs of urban transport.
6. CONCLUSIONS
Based on the studies
carried out, we propose to solve the urgent scientific and practical problem of
improving the methods of transporting passengers by urban transport to enhance
its reliability and efficiency, by forming contingency bus routes within the
existing regular route network to service mass ridership.
The main findings and
results of this study are as follows:
1.
We
have proposed a mathematical model of a regular route network reservation, the
target function of which is to reduce the amount of costs for the formation of
transport infrastructure for the organisation of bus traffic on the back-up
routes, operating costs for transportation, and the costs of eliminating
malfunctions at work. The system of restrictions provides for compliance with
the interval of traffic, as well as contractual obligations on the volume of
traffic, their cost and the number of buses on contingency routes.
2. The
offered mathematical model of assessing the reliability of passenger traffic on
regular bus routes taking into account the scheme of reservation of the regular
route network, is built on:
- for
reservation schemes with a consistent location of elements - it is based on the
production of probabilities of fail-free operation of buses on the route,
- for
majoritarian reservation regimes with substitution - it is based on the use of
the formula of overall probability of joint events.
3. The value of ridership on
back-up bus routes is determined by the analysis of the compliance of the
existing urban transport route network with the needs of the population for
their labour movements. The ridership, being not mastered by the main regular routes,
after its detail on the periods of the day, can be potentially mastered on
back-up routes.
4. Reduced costs of servicing
ridership on contingency bus routes are achieved by maintaining the
predetermined interval of traffic by fewer buses. It is achieved by increasing
the route speed of traffic as a result of the direction of buses on additional
roads during its loading.
5. We have proved
the feasibility of the proposed results established on the example of public
transport routes in Magnitogorsk. The formation of a back-up delivery channel based on a
regular bus route will provide an additional volume of transportation by
submitting buses to stops during the periods of lack of transportation on the
main route. This will reduce the cost of transporting of one passenger by 7%,
increase its reliability by 1.14 times and acquire the additional passenger
flow without increasing the cost of urban transport.
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Received 20.02.2020; accepted in revised form 17.06.2020
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