Article
citation information:
Azemsha, S., Kravchenya, I., Vovk,
Y., Lyashuk, O., Vovk, I. Scheduling technique of route vehicles on duplicating
stretches. Scientific Journal of Silesian
University of Technology. Series Transport. 2021, 113, 5-16. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2021.113.1.
Siarhei AZEMSHA[1],
Irina KRAVCHENYA[2],
Yuriy VOVK[3], Oleg LYASHUK[4], Iryna VOVK[5]
SCHEDULING
TECHNIQUE OF ROUTE VEHICLES ON DUPLICATING STRETCHES
Summary. Schedule optimization
is a proven strategy to improve service quality for public transport networks.
However, current research mostly optimizes schedule design using prior
knowledge of users’ routings, ignoring the optimization of public
transport schedules on duplicating stretches of route vehicles. This article
presents a new alignment technique of time intervals between consecutive
vehicles of different routes on duplicating stretches, considering existing
public transport networks in attaining optimization of public transport
schedule. Scheduling technique of route vehicles on duplicating stretches
includes some steps: analysis of public transport network and determining a lot
of duplicating stretches, calculation of the optimal time intervals among arrivals
of route vehicles and alignment of these intervals among consecutive route
vehicles on duplicating stretches, realization simulation model of urban
passenger transport within the simulation modeling system of GPSS World.
Furthermore, testing the optimization technique of route vehicle scheduling,
analysis of the quality of adjusted schedule with route vehicles of different
kinds included, and determining the optimization efficiency for duplicating
stretches. The adjusting technique of urban passenger transport schedule allows
to increase movement steadiness of consecutive vehicles of different routes on
duplicating stretches, adjust traffic intervals for each route, shorten the
traffic load on stations, reducing idle time and queue lengths of route vehicles
in front of transport stops and also minimize waiting time for route vehicle by
those passengers who can be transported along several routes. Improving the bus
schedule on duplicating stretches in Gomel is illustrated demonstrating the
technique developed. This scheduling technique can be used by carriers and
transport operators to improve the quality of services provided.
Keywords: scheduling technique, route vehicles,
duplicating stretches
1.
INTRODUCTION
Accessibility and quality of urban passenger
transport determine the real living standard and social climate, while reducing
its attractiveness leads to the use of personal vehicles by passengers, which
has a negative impact on the environmental situation of cities [1-7].
Therefore, the task of public transport efficiency improvement and development
of activities on improvement of public transport operation through qualitative
scheduling is an urgent challenge.
An efficient and rational schedule of urban
public transport could provide:
- regularity of the route vehicle traffic;
- high-quality public service for passengers
and travel with minimal waste of time;
- traffic of vehicles in accordance with
passenger traffic on routes;
- coordination of the route vehicle traffic
with the traffic of other types of passenger transport.
Several approaches and computer-aided software
packages have been dedicated to the scheduling methodology of passenger
transport. According to the different features, the approaches developed can be
categorized into three groups: (i) interactive graphical visualization and
optimization approach, (ii) mathematical programming and analytical modeling
approach, and (iii) heuristic and metaheuristic approaches (genetic algorithm,
simulated annealing, and ant colony optimization).
In the first group, interactive graphical
optimization techniques were proposed by a few researchers. Cao et al. [8, 9],
developed real-time schedule adjustments for autonomous public transport
vehicles The solution methodology proposed is based on time-space graphical
techniques using multi-criteria decision analysis to minimize schedule changes
as the primary objective, as well as to reduce travel time and active energy
consumption. Further, Krause et al. [10] proposed a visualization system, BusVis, that provides overviews of a transport system in
terms of distance and travel time, and comparisons between different routes.
The second approach widely found in the
literature adopts the mathematical programming models. Liu and Ceder [11]
developed a bi-objective, bi-level integer programming model, taking into
account the interests of public transport users and operators in attaining the
optimization of public transport timetable synchronization integrated with
vehicle scheduling and considering user demand assignment. Furthermore, Wu et
al. [12] proposed a bi-level programming model in which the schedule design and
passenger route choice are determined simultaneously via two travel strategies:
non-adaptive and adaptive routings. Additionally, Yin et al. [13] offered the
use of mixed-integer linear programming approaches for metro train scheduling.
The third group employs heuristic and
metaheuristic approaches: genetic algorithm, simulated annealing, and ant
colony optimization. Carosi et al. [14] proposed a multicommodity-flow type
model for integrated timetabling and vehicle scheduling and a diving-type
metaheuristic approach for the problem. While Naumov [15] provided a
genetic-based algorithm of the public transport lines synchronization in a
transfer node. The described approach is based on the simulations of the demand
for changing the public transport lines with a genetic algorithm. Subsequently,
Gorokhova [16] and Kochegurova et al. [17] developed an algorithm for
generating schedules of passenger transportation using the ant colony
optimization algorithm.
A series of follow-up studies related to the
optimization of public transport schedules (for example, Yakimov and Trofimenko
[18], Muller et al. [19], Leng et al. [20, 21], Ahmed et al. [22], Banerjee et al. [23], Shelton et
al. [24], Dike et al. [25]) have been conducted.
When developing a schedule for urban passenger
transport to improve the quality of passenger service, it is necessary to
consider the joint stretches of traffic on different routes. If there are
several routes servicing a particular stretch in a transport network, then it
is necessary to coordinate traffic schedules of different routes on the joint
(duplicating) stretches of their traffic by adjusting departure time for each
of them to avoid the formation of queues at transport stops.
Thus, a duplicating stretch is a compatible
stretch of vehicle traffic on different routes. The length of the stretch that
can be considered a duplicate depends on the size of the public transport
network. Servicing of duplicating stretches causes some problems: transport
queues at transport stops, irregular intervals of traffic vehicle, increasing
passengers’ waiting time leading to discomfort while traveling.
The problem of improving passenger service
quality and efficiency of urban public transport is the alignment of the
schedules of different routes on duplicating stretches, thereby contributing to
a more regular traffic interval and vehicle occupancy.
2. METHODOLOGY
Scheduling technique of route vehicles on duplicating stretches includes the following steps.
2.1. Analysis of
public transport network and duplicating stretches
Urban network is analyzed and its
characteristics are defined:
- a lot of routes M = {M1, M2, …, MNm};
- a lot of transport
stops S = {S1,
S2, …, SNs};
- frequency of movement on
different routes NM = {NM1, NM2, …,
NMm};
- route vehicle’s arrival / departure frequency of
different routes at each transport stop (according to the existing schedule) ST = {ST1, ST2,
…, STNst} [26, 27].
For different routes, it is necessary to determine:
· a lot of duplicating stretches D = {D1, D2, …, DNd},
· length of duplicating stretches LD = {LD 1, LD 2, …, LDNd},
·
frequency
of movement of different routes of duplicating stretches ND = {ND1, ND2,
…, NDd},
· route vehicles arrival / departure frequency of different routes at each transport stop of duplicating stretches SDT = {SDT1, SDT2, …, SDTNst},
· social value of service area KD = {KD1, KD2, …, KDNd}: railroad passenger and bus terminals, facilities of the attraction, large-scale enterprises, educational establishments, etc.
A lot of planned schedule optimization periods Т = {T1, T2, …, TNt} is defined, for example, every hour, rush hours or periods between rush hours.
Each transport stop Sj in the planned period
T is characterized by a vector (Sj, Mj, NMij, STij). Each duplicating stretch Dj in the planned period
T is characterized by a vector (Dj, KDj, LDj,
NDij, SDTij). The next steps are
performed for each planning period Т.
Duplicating stretches D = {D1, D2, …, DNd} are ranked in a descending
order of the transport stop amount and number of routes. Social
value of service area KD = {KD1,
KD2, …, KDNd} may also be considered. The
routes MD = {MD1,
MD2, …, MDNmd} with the largest duplicating
stretches are determined with the following ranking in an ascending order of
route vehicles amount.
The basic transport stop SBr is assigned for determined routes. The social value of a service area should be considered when choosing a basic transport stop, the stretch length in which routes are duplicated, and the route vehicle frequency of different routes along such stretches.
Compulsory arrival/departure frequency of route vehicles are defined pegging to: passenger service of railway and bus terminals; the beginning or the end of the enterprise performance; the beginning or the end of the working shift, lunch break of route vehicle drivers; the beginning or the end of the classes in the educational institutions.
2.2.
Alignment of time intervals among consecutive route vehicles on duplicating
stretches
The
optimal time interval among arrivals of route vehicles of all routes 
and duplicating
stretch routes 
at the transport
stop is calculated:
(1)
(2)
Where:
Т – planning period
NMk – number of runs carried
out on the route k at the time interval T,
NDri – number of runs carried
out on the duplicating stretch r at the time interval T,
n – number of
routes on the duplicating stretch r.
Boolean assignment matrix is formed [28]. It
shows the assignment of route j to time interval i for the basic transport stop
SBr of the duplicating stretch Dr (Table 1):
xij = 1, if route j is assigned to time
interval I,
xij = 0, if not,
xij = 1* – compulsory assignment.
Tab.
1
Assignment matrix for the duplicating stretch Dr for basic transport stops
|
Arrival time |
МD1 |
… |
МDk |
KD |
|
TW |
|
… |
|
|
t1 |
x11 |
… |
x1k |
KD1 |
|
TW1 |
|
… |
|
|
t2 |
x21 |
… |
x2k |
KD2 |
|
TW2 |
|
… |
|
|
… |
… |
… |
… |
… |
… |
… |
… |
… |
… |
|
ti |
xi1 |
… |
xik |
KDi |
|
TWi |
|
… |
|
|
… |
… |
… |
… |
… |
… |
… |
… |
… |
… |
|
tn |
xn1 |
… |
xnk |
KDn |
|
TWn |
|
… |
|
|
Sum |
|
… |
|
|
|
|
|
… |
|
For each time interval of assignment matrix, the next values are defined:
: load factor, equal to the number of vehicles arriving
at the transport stop on the duplicating stretch; 
: deviation value of intervals among consecutive route
vehicles from the optimal value of the duplicating stretch, 
: deviation value of intervals among consecutive route
vehicles from the optimal value of the route k, 
: passengers’ waiting time, where λi
is the intensity of incoming passenger traffic using vehicles of the
duplicating stretch.
Using the assignment matrix, route vehicle schedules are aligned with the following:
- intervals between vehicles on the duplicating stretch (ID1 ≈ … ≈ IDi ≈ … ≈ IDN) and between vehicles of the routes on this duplicating stretch (IMD1 ≈ … ≈ IMDi ≈ … ≈ IMDN) become equal,
- load factor KDi for arrival time ti is equal 1, this means that only one vehicle from the duplicating stretch is located at the transport stop,
- decreases the value of passengers’ waiting time TWi.
It is necessary to minimize the value of the objective function – the amount of intervals deviation Dr(I) between consecutive route vehicles from optimal value for the time interval T:
(3)
After the comparison assignment matrix and Dr(I) before and after the optimization, the decision on formation of the schedule of duplicating routes is adopted.
Then calculation of traveling time through the rest transport stops of the route regarding the basic stop and transition to the next duplicating stretch is performed.
2.3.
Simulation modeling of route vehicles on duplicating stretches
The next step is to realize the simulation model of duplicating stretches within the simulation modeling system of GPSS World [29, 30]. This makes it possible to test the scheduling technique of route vehicles on duplicating stretches.
A mathematical model of the movement of traffic flows going through a duplicating stretch can be represented as a queuing system. Its graphical representation is shown in Figure 1.
The proposed queuing model of duplicating stretches is developed in the GPSS World simulation automation package.
The properties of the simulation model of duplicating stretches have been tested and studied. The simulation model test includes two stages: verification and validity check. At the verification stage, the correctness of the operating algorithm of duplicating stretches simulation model using the model’s interactive single-step debugging properties was checked.
Because of the simulation experiment on the developed simulation model, transport stop load factors at route vehicle traffic on duplicating stretches and lengths of queues on the transport stops were obtained.
2.4.
Analysis of the quality of adjusted schedule with route vehicles of different
kinds included
For each basic stop, is formed a general assignment matrix, involving all duplicating stretches with routes MD1, MD2, etc. passing through chosen transport stops and other route vehicles M1, M2, etc. In addition, it includes information on route vehicles of all kinds (КDM) arriving at each transport stop.
For each type of route vehicle, the transport stop load factors are calculated, and subsequently, summarized to formulate the common load factor (KDO). Based on the values of the transport stop load factors, the lengths of queues on the transport stops are defined.
Comparison of statistical data (common transport stop load factor and average queue length on the transport stop), obtained through the simulation modeling in GPSS World, with results obtained during the implementation of the methodology proposed, is being conducted.
Then synchronization of the adjusted route vehicle schedules considering schedules at stops being used as transfer facilities for passengers is executed. When it is impossible to synchronize the obtained route vehicle schedules among each other, some steps must be repeated.
Fig. 1. Mathematical model of a duplicating stretch
2.5.
Determining the optimization efficiency for duplicating stretches
The efficiency of optimizing public transport schedules on duplicating stretches is calculated:
(4)
Where:
– deviation
between consecutive route vehicles from optimal value before optimization,
– deviation
between consecutive route vehicles from optimal value after optimization.
3.
APPLICATION
Scheduling
technique of route vehicles on duplicating stretches was tested in the public
transport network of Gomel. The city of Gomel with about 530,000
inhabitants is the administrative center and the second-most populous city in
Belarus. Currently,
transportation of passengers in Gomel is carried out on 81 regular bus routes.
There were defined six duplicating stretches provided
for buses movement of three or more routes (Table 2).
Tab. 2
Parameters of duplicating stretches
|
Duplicating stretch |
Bus routes |
Transport stop amount |
Sum of stops and routes |
Length of duplicating stretch (km) |
|
D1:
“Institute “Gomel project” – Ogorenko street” |
No 17, 18, 34 |
13 |
3 + 13 = 16 |
7,5 |
|
D2:
“Railway station – First school” |
No 35, 55, 58 |
12 |
3 + 12 = 15 |
8,47 |
|
D3:
“Railway station – “Gorelektrotransport” ” |
No 10, 19, 43 |
10 |
3 + 10 = 13 |
4,94 |
|
D4:
“Railway station – Cinema “October” ” |
No 20, 21, 40, 52 |
8 |
4 + 8 = 12 |
4,47 |
|
D5: “ “Medgorodok”
– Technical University named after P.O. Sukhoi” |
No 16, 17, 26, 33 |
8 |
4 + 8 = 12 |
3,39 |
|
D6:
“Railway station – Palace of culture “Gomselmash” ” |
No 6, 8, 8A, 9 |
7 |
4 + 7 = 11 |
3,93 |
Duplicating
stretches were ranked in a descending order of the sum of stops and routes on
the stretch, and also optimized
the main bus route schedules. Performance evaluation of the adjusted
schedule by six duplicating
stretches is presented in Tables 3-4.
Tab. 3
Optimization result
of the schedule by six duplicating
stretches
for the period between rush hours
|
Di |
Before optimization |
After optimization |
|
||||
|
|
|
|
|
|
|
||
|
D1 |
33 |
35 |
68 |
15 |
32 |
47 |
21 |
|
D2 |
24 |
34 |
58 |
6 |
18 |
24 |
34 |
|
D3 |
35 |
23 |
58 |
3 |
20 |
23 |
35 |
|
D4 |
26 |
32 |
58 |
9 |
17 |
26 |
32 |
|
D5 |
28 |
34 |
62 |
9 |
25 |
34 |
28 |
|
D6 |
20 |
31 |
51 |
5 |
28 |
33 |
18 |
|
Sum |
166 |
189 |
355 |
47 |
140 |
187 |
168 |
Tab. 4
Optimization result
of the schedule by six duplicating
stretches for rush hours
|
Di |
Before optimization |
After optimization |
|
||||
|
|
|
|
|
|
|
||
|
D1 |
32 |
20 |
52 |
11 |
17 |
28 |
24 |
|
D2 |
24 |
34 |
58 |
9 |
28 |
37 |
21 |
|
D3 |
34 |
38 |
72 |
9 |
33 |
42 |
30 |
|
D4 |
39 |
32 |
71 |
4 |
29 |
33 |
38 |
|
D5 |
31 |
44 |
75 |
13 |
45 |
58 |
17 |
|
D6 |
15 |
27 |
42 |
2 |
23 |
25 |
17 |
|
Sum |
175 |
195 |
370 |
48 |
175 |
223 |
147 |
The value
of the efficiency of optimizing public transport schedules for the six
duplicating stretches is equal to 168 minutes – for the period between
rush hours and 147 minutes – for rush hours.
Due to the
traffic schedule optimization on the six duplicating stretches,
·
the traffic intervals of buses for each route
separately were aligned, deviation value of intervals among consecutive buses
from the optimal value reduced by 26% for the period between rush hours, and
10% for rush hours;
·
in total deviation value of intervals among
consecutive buses from the optimal value by the six duplicating stretches
reduced by 47% for the period between rush hours, and 40% for rush hours;
·
waiting time for
route vehicles by passengers that can be transported along several route
options was reduced by 27% for the period between rush hours, and 28% for rush
hours.
The obtained
optimization results may be used by the Open Joint Stock Company,
Gomeloblavtotrans, for
improving the quality of public passenger transportation.
4. CONCLUSIONS
Using the
scheduling technique of route vehicles on duplicating stretches allows to:
·
determine the optimal vehicle traffic intervals for
each route, considering duplicating
stretches,
·
coordinate the movement of route vehicles on duplicating stretches,
·
determine the optimal number of vehicles on routes,
·
reduce waiting time for route vehicles for passengers
that can be transported using several route options,
·
increase uniformity of vehicle occupancy,
·
reduce the load
on transport stops.
While
optimizing the existent schedule, particular consideration was given to
reducing transport delays due to lack of forced idle time of route vehicles in
front of a transport stop (waiting for an opportunity to drive to it), and
subsequent accelerations, there is also the effect of reducing economic
(additional fuel consumption) and environmental (from emissions of air
pollutants) losses.
Improving the bus schedule on duplicating stretches in Gomel
was conducted to illustrate the effectiveness of the proposed technique.
Experimental
researches have shown the applicability of the developed technique in practice.
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Received 15.09.2021; accepted in revised form 29.10.2021
Scientific
Journal of Silesian University of Technology. Series Transport is licensed
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