Public Transport Prioritization and Descriptive Criteria-Based Urban Sections Classification on Arterial Streets

Abstract

The present paper is aimed at improving minimization methods in traffic flows, particularly reducing the costs of civil transportation through sections of the transport network by giving priority to public transport in densely developed areas. In cities with a radial and radial–circular planning scheme of the road network, where arterial traffic flows converge in the central part, the challenge of street congestion with traffic often arises. As a result, delays of all types of vehicles increase, which causes excessive travel time for users of private and public transport. In this regard, it is proposed to divide the sections of the transport network into eight types based on their geometric parameters and traffic conditions. This differentiation of sections improves the existing methods for determining the spatial delay of traffic flows on sections of the transport network with different parameters. It was achieved by considering the duration of vehicles passing signalized intersections and pedestrian crosswalks and the sections of streets between them, while simultaneously recording the duration of public transport movement, as well as the time they spend at stopping points, using GPS receivers. The results of onsite monitoring and further computations revealed that there are particular urban sections with specific, different distances between adjacent stop lines that are critical for public transport operation. Furthermore, based on the delay criterion, there were three different passage modes proposed to improve the efficiency of the traffic.

1. Introduction

When planning their travel, commuters consider the economic and social impacts of the connections network related to time loss, cost, and comfort. Although most metropolitan areas are developing their public transport systems towards rail on the ground and underground systems, the non-rail means of transport in big cities are still very much in use. This means of public transport presents a number of inherent features as it participates in general traffic flow, still using the same lanes as private transport. Thus, this type of public transport directly impacts the dynamics of urban traffic flow in general. Congestion of the road network is a major challenge, considering the modern tendencies of the development towards the increase of urbanization levels.

This phenomenon causes a significant increase in the amount of time spent by commuters in traffic. To face that challenge and reduce the congestion of the road network both in theory and practice, several well-established solutions are available [1,2,3,4,5], and these are mainly:

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Optimization of network parameters (building of new or the reconstruction of existing streets and roads; design of arterial directions; parking restrictions, etc.);

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Optimization of functional and transport zoning (reduction of the share of transit motion; changes of city services; development of new functional or transport zones, etc.);

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Establishing regulation and policies in the field of transportation (restriction of transport allowance in certain zones; regulation of vehicles taxation; tariff policy management, etc.);

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Traffic flow management (traffic routing; implementation of automated traffic control systems; speed limits optimization, etc.);

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Increasing the attractiveness of public transport (provision of priority in movement; improvement of rolling stock; provision of social funding, etc.).

Taking into account the specifics of each city’s development, unorganized residential areas planning, diversity in road network parameters, and simultaneous implementation of activities in all directions are challenging tasks. This is observed especially in cities with old infrastructure, where transport districts were formed according to various engineering practices in urban planning. To avoid severe consequences associated with congestion of the road network, the most often researched and implemented methods here are related to the reconstruction of intersections and sections of streets between them: improvement of operation of automated traffic control systems and prioritization of particular types of transport. Although every city tries to take a balanced approach to develop all means of transport, the highest priority is given to public transport. This is due to its ability to provide large volumes of transportation. However, giving priority to this type of transport indicates a change in efficiency (according to the criterion of time losses) for different transport areas of the city or road networks with different geometric parameters. It is essential that, when implementing prioritization, time factors are taken into account based on the number of passengers using transport, not the number of private or public transport vehicles.

Nowadays, a variety of methods and techniques are used to improve city transport services for residents. Mostly all of them are grouped based on efficiency criteria: volume of transportation, minimization of traffic delay, time spent on movement, economic costs, ecological impact on the environment, etc. The present study pays attention to minimizing traffic delays in traffic flows on the road network with a significant share of public transport.

In studies [1,2], the authors admit that the determining criteria for the operation of the road network are travel time and the reliability of this network for users of private and public transport. Such a rather general formulation confirms that road traffic needs to meet two major requirements and provide efficient communication without decreasing users’ safety. Along with this, the travel time for private and public transport passengers on the same street is different in terms of duration and level of comfort. The authors in the research [3,4] determined that the main factors of impact on the peculiarities of traffic flow movement in cities are traffic flow volume, expressed through the volume–capacity ratio, traffic light control, and geometric parameters of the street. They significantly influence the amount of traffic delay of the entire traffic flow, which is formed by both private and public transport. For the latter, additional delays occur at regulated stopping points and are also associated with the dynamic characteristics of the rolling stock. It is about the existence of common and distinctive features of different groups of vehicles in traffic flows and their mutual influence.

The results of monitoring the operation of public transport on routes using GPS trackers, given in the paper [5], show the significant impact of the volume–capacity ratio of the roadway on the average speed of rolling stock of public transport, even in conditions of its prioritization at traffic light systems. Such an impact is the largest in sections with no allocated public transport lanes. It was determined that if they were available, the connection speed could be increased up to 16%. A greater increase in connection speed is more difficult to achieve due to the impact of stopping points. In addition, prioritization at traffic lights is a difficult task without dedicated lanes, as traffic coordination is disrupted due to the influence of stopping points, as well as under the influence of conditions and regulations implemented for road users. Without additional lanes, when public transport is in a queue at a considerable distance from the intersection, the detector is not able to recognize it and provide priority. The influence of these conditions is analyzed in papers [6,7]. These issues are mainly related to the length of time pedestrians have to wait for crossing, the geometric differences of the roadway in the transverse and longitudinal profiles, and the established modes of operation of the traffic lights.

Researchers [1,2,3,4,5] have tried to minimize the delay of public transport in heavy traffic flows and compare the efficiency of signalized (by traffic light) sections of city arterial streets based on their planning features and traffic safety conditions. By applying methods of traffic flow management, it is possible to achieve a reduction in the number of private and public transport vehicles standing before the stop lines of signalized intersections or the maximum queue length, etc. Such methods emphasize the general traffic flow. More attention needs to be paid to the passengers in the vehicles, as there are much more passengers in one bus than in one car. Based on this, it is necessary to analyze in more detail other approaches to prioritize public transport, which is used to reduce traffic delays per passenger.

Authors [8,9,10] have determined such types of prioritizations for public transport in a zone of operation of signalized intersections:

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Active and passive priority. The first provides traffic control in real-time movement mode, and the second provides balanced redistribution of the permissive signal between control phases with finite optimization of the duration of the traffic light cycle. Active priority is best used at isolated intersections and passive priority at both isolated intersections and in coordination systems;

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Full, partial, and relative priority. During the full priority, efforts are made to achieve zero delays for public transport. With partial priority, the time limits for the duration of the permissive signal in the control phases are changed (switched early on or extended). According to the relative priority, preference can be given to both public transport and private transport, based on the length of delays and the traffic volume;

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Unconditional and conditional priority. With unconditional priority, non-stop travel is provided to each unit of rolling stock of public transport. During conditional priority, such non-stop travel is provided only if public transport is behind schedule.

So, in addition to differences in the roadway geometry, drivers’ behaviour, traffic flow indicators, and the specifics of transport planning, there are also differences in the principles of the application of traffic light signal algorithms. Already, at this stage of the analysis, it is clear that it is only possible to achieve better public transport efficiency in the case of a combination of time-based and spatial prioritization. Spatial prioritization allows structuring the traffic flow both at the approaches to signalized intersections and along the entire street length.

In the research of [11,12], the flow of private transport is stopped at some distance before the signalized intersection. A so-called preliminary traffic light with an intermediate stop line is set up. This allows public transport to occupy any traffic lane before the intersection. A mandatory condition for such traffic management is the presence of a dedicated lane for public transport. Under such control, it is quite easy to change traffic light signals on all lanes of the main stop line, using any method of giving priority described in papers [8,9,10]. In the study [13], the combination of spatial and time-based prioritization is achieved with the use of eight possible traffic light signalling control scenarios, taking into account the random nature of the arrival of public transport at the intersection. Taking into account the results of the research [11,12], any scenario predicted in the study [13] can be reached on the main stop line, but there must be sufficient distance between signalized intersections, which can accumulate the traffic of private vehicles. Therefore, it is difficult to apply such a prioritization method to a road network with a high density. In addition, it is necessary to pay attention to the peculiarities of arranging stopping points for public transport. In papers [13,14,15], to take into account the geometric features of the roadway, the requirements for the location of stopping points, and the configuration and density of the road network, it is recommended to arrange the allocated lanes in different ways relative to the axis of the street, that is, the emphasis is made on allocation and planning and only then when giving priority using various traffic signal control algorithms can be considered.

In general, the location of bus stops requires special attention when justifying the method of public transport prioritization. Depending on their location relative to intersections and the sections of streets between them, the regularities of delays in the movement of both public and private transport may change [16,17,18]. Based on the analysis of these studies, the location of a stopping point before the intersection is a better solution than after it but only for distances within 70–200 m. Along with this, in the studies [16,17], it is noted that with such a solution the number of delays at the stopping point will be relatively insignificant when the volume of public transport traffic is up to 200 p.c.u./h. With its larger values, public transport will more often enter the lanes for private transport, increasing the traffic delays there caused by lane-change manoeuvres [18]. At a traffic volume of more than 200 p.c.u./h, buses (trolleybuses) will spend most of their downtime at the stop due to waiting for the opportunity to enter or depart.

Based on research results [19,20,21,22], it is necessary to consider the condition that a significant reduction in traffic delay values is achieved mainly for public transport. At the same time, the reduction of traffic delay for private transport is insignificant, where no allocated lanes are provided for public transport [19,20], and when lanes for public transport are provided, traffic delay increases [21,22]. This phenomenon is connected to the fact that the available lanes are mostly allocated within the existing roadway width.

Given analysis shows that the application of the same methods of time-based and spatial prioritization of public transport on different roadways (by planning and the value of traffic indicators) can have different efficiency based on the criterion of minimization of traffic delays and time losses.

Bearing all those challenges in mind, the aim of this study is to provide a solution for giving priority to public transport on urban arterial streets of controlled motion, depending on the changes in traffic indicators and planning parameters of the roadway.

To achieve this aim, the following tasks were formulated and completed:

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Analyses of the peculiarities of public transport prioritization on urban streets;

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Performing transport flow analyses using the method of field measurements at fixed stations and by using geoinformation systems (GPS trackers);

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Simulations of traffic flow conditions at signalized sections of urban arterial streets with different ways of passage for private and public transport;

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Providing recommendations on decision-making processes aimed at giving priority to public means of transport.

2. Materials and Methods

For all the vehicles in the traffic flow, spatial delay can be determined by comparing time losses in the period of the most intensive and low traffic conditions. The low traffic conditions are considered as a qualitative state of traffic flow that corresponds to the level of convenience. At this level of convenience, there is practically no interaction between vehicles. One of the best indicators showing the travel time change is the speed of movement. When measuring the spatial speed of movement of the entire traffic flow in urban conditions, it is necessary to single out public transport. This is because its speed is affected not only by road conditions and the peculiarities of the movement of private vehicles but also by regulations related to the monitoring of traffic schedules and the arrangement of stopping points. In the public transport sector, this speed is called operating speed. In the present research, the collection of information from GPS trackers about the movement of buses that operate on city public transport routes took place throughout the work shifts on weekdays and weekends. The research was carried out for one year. Data were first systematized and grouped according to separate routes. In the next stage, data were superimposed from different routes for the same sections. Such grouping made it possible to establish information about whether the speed indicator is related to the traffic characteristics inherent in only one route or whether such common (for all routes on the section) indicators indicate the characteristics of the transport service of the section.

The measurement of the operating speed of public transport within the area of an entire city or distinguished transport zones is performed using GPS tracker data [23,24]. For the purpose of the present study, we used the database of server geoinformation software MicroGIS for public transport in Lviv city (Ukraine). The database contains information on the movement of public transport between stopping points. Such information available for each means of transport (bus, trolleybus, or tram) can be conveniently presented in the form of a table (

Table 1. A section of an analytical report generated from the program MisroGIZ on the execution of schedules for buses on selected urban public transport routes.

The Number Plate of the Bus: Is AA-6201-TX
Route No. А03 (King Cross Leopolis Shopping Centre–Rizni Sq.) 05/12/2021 07:00
Schedule Number: 08–12
Name (Number) of Ozone	Planning Time of Bus Arrival in the Geozone (Schedule)	The Actual Time of Bus Arrival in the Geozone	Notes
King Cross Leopolis Shopping Centre (320)	05/12/2021 19:44	05/12/2021 19:28	Movement ahead of the set schedule 1
Ipodrom (434)	05/12/2021 19:46	05/12/2021 19:31
Sokilnytska (435)	05/12/2021 19:48	05/12/2021 19:33
Autovokzal (433)	05/12/2021 19:53	05/12/2021 19:36
Maksymovycha (432)	05/12/2021 19:56	05/12/2021 19:38
Teatralna (40)	05/12/2021 20:31	05/12/2021 20:33	Movement according to the schedule 2
onfirmedRizni Sq. (62)	05/12/2021 20:39	05/12/2021 20:39
Svobody Av. (67)	05/12/2021 20:49	05/12/2021 20:58	Movement behind the schedule 3
Kniaza Romana (39)	05/12/2021 20:53	05/12/2021 21:01
Shota Rustaveli (291)	05/12/2021 20:57	05/12/2021 21:04
Sokilnytska (564)	05/12/2021 21:29	05/12/2021 21:24	Movement ahead of the set schedule 1
Shopping centre King Cross Leopolis (320)	05/12/2021 21:32	05/12/2021 21:26

Conditions: ¹: the arrival of the bus at the stop is considered to be ahead of schedule by 5 min or more; ²: less than 4 min delay is considered to be moving according to the schedule; ³: the arrival of the bus at the stop 5 min or more later than the set time is considered to be behind schedule.

).

In Table 1, column 1, the name and the number of the stopping point are given with respect to their city-wide numbering. In column 2, there are schedules set for every bus on the route. These schedules are embedded in the software environment MicroGIS, which is used in the centre of traffic management of public transportation to monitor the operation of public transport. Column 3 contains information about the real-time arrival of buses at every specific stopping point. This arrival time is recorded by a GPS tracker, information from which is transferred to the monitoring program. After every working shift, a final report on compliance with traffic schedules on all routes of the public transport network is formed.

While processing the data from these tables, it is necessary to remember that the program software records the time of arrival of the rolling stock at the stopping point. It is needed to subtract the average value of the duration of downtime at a stopping point from the speed of public transport to compare the spatial speed of public and private transport on the same street sections. Only this value of the speed of public transport can be compared with the spatial speed of private transport.

To systematize data obtained from GPS trackers (Table 1) about the speed of public transport movement ($v_i^{pt}$) at i section of the route network without considering the downtime of buses at stopping points, the following equality is derived:

$$v_i^{pt}=\frac{S_{se{c}_i}}{t_{se{c}_i}-t_{s{p}_i}}$$

(1)

where $S_{se{c}_i}$ denotes the length of the section (m);

$t_{se{c}_i}$ is time spent on the movement in the section, which is determined as the difference between the actual arrival time at adjacent stopping points (s);

$t_{s{p}_i}$ is duration of downtime at stopping points (s).

The duration of the downtime at stopping points ($t_{s{p}_i}$) is determined using monitoring. This delay component includes the following time losses by the rolling stock: arrival at a stopping point, passengers boarding and dropping off, and departure from the stopping point. In cases when public transport lines are available, arriving at the stopping point may take some time if there are other buses (trolleybuses) occupying the lane. If no such lanes are allocated, entry time losses may be caused by traffic of vehicles before the intersection near the stopping point.

Spatial speed for private transport ($v_i^{prt}$) can be determined using video surveillance. For this purpose, appropriate control points (video cameras) are installed along the investigated street at the approaches to the stopping points. Private vehicles are monitored by recording their registration plates and time of arrival at the checkpoint. Another way to obtain data about the speed of private transport $v_i^{prt}$ is a simulation (PTV VISSIM) [25,26,27,28]. Here, by having the data about the traffic volume and time parameters of the traffic light control system, the duration of the passage to the checkpoints by private transport can be determined. Its advantage is the possibility of entering any values of traffic volume, including forecasted ones, to determine the value $v_i^{prt}$.

The method allows the comparison of values of $v_i^{pt}$ and $v_i^{prt}$ on different sections of urban streets. The differences and similarities in their values will allow us to determine the variety of typical sections by way of prioritizing public transport and minimizing the delay in the entire traffic flow.

3. Results

The present research was performed on a local scale in Lviv city, which has the radial–circular configuration of an arterial road network. Features of traffic conditions in cities with such arrangements use the city centre approach, which is the increase of the network density and volume–capacity ratio.

The processing of decrypted data from GPS trackers (according to the example in Table 1) was carried out for all the routes of public transport, which pass by radial arterial streets, for four days (Wednesday) during one month (October), recorded in 2021. For each route, the connection speed was determined from the morning (from 07:30 to 10:00) and afternoon (from 16:30 to 19:00) peak hours. Such time intervals of the peak period are specific for the city of Lviv, although they may differ from other cities based on the habits of the residents’ life activities. A graphical presentation of the connection speed changes for one of the selected routes is shown in Figure 1.

Further analyses were focused on measuring the average delay at the stopping points. During the measurements, all stopping points were grouped based on the planning peculiarities of the roadway and the method of their arrangement. Based on such criteria, five groups were established: group 1—without stopping point bays, with one lane per direction; group 2—without bays with two lanes per direction; group 3—with bays with one lane per direction; group 4—with bays with two lanes per direction; group 5—allocated lanes for public transport with bays. The spatial priority was assumed to be a single traffic lane, and separate distributions of directions with two and three traffic lanes were not considered in the analyses. A total of 100 measurements were performed for each group. The results of the measurements are given in

Table 2. Numerical characteristics of public transport delay distribution at stopping points.

Stopping Points Group	Off-Peak Period		Peak Period
	$\mathbf{Mathematical} \mathbf{Expectations},\mathit{M}[\mathit{t}]$	$\mathbf{Dispersion}, \mathit{D}[\mathit{t}]$	$\mathbf{Mathematical} \mathbf{Expectations},\mathit{M}[\mathit{t}]$	$\mathbf{Dispersion}, \mathit{D}[\mathit{t}]$
1	18	36	29	58
2	24	55	33	107
3	40	165	46	214
4	34	74	48	152
5	31	99	41	140

.

Table 2 shows that for groups 1 and 2, the delay time was the shortest; as for the stopping with no delays, the public transport vehicle did not spend too much time on the arrival and departure. This means that separate distribution of directions with two and three lanes were not considered provided and that spatial priority was given to public transport in the form of a dedicated lane. Moreover, it does not depend on the flow of private transport. The only factor which has the most significant influence on these groups are the intersections equipped with traffic light systems, located after the stopping point. The operating regime in such cases can cause traffic jams of private and public transport and block the approach to the stopping point. In groups 3 and 4, delays at the stopping point zones were more extensive. This is related to the insufficient length of the bus bay. This is due to the significant volume of public transport, so not all the vehicles can enter the bay immediately after arrival. Besides the impact of the control regime, there is also an issue with the effectiveness of private transport operations. At the stopping points of group 5, delays are directly related to the volume of public transport itself and, to a minor extent, to the control regime.

Next, subtracting from the values $t_{se{c}_i}$ (results of measurement of operating speed using GPS trackers), the value $t_{s{p}_i}$ (results from Table 2) and speeds $v_i^{pt}$ at known fixed values $S_{se{c}_i}$ were determined. Provided that there are two or more stopping points on the section between intersections, the computations of ${{\displaystyle \sum }}_{i=1}^n{t}_{s{p}_i}$ were performed, where n is the number of stopping points.

The final computations were performed for different types of sections of arterial radial streets. Such a distribution of these areas, where public transport can pass, was based on planning features and the volume and speed of the vehicles. The measurement results are given in

Table 3. Summarized results of measurements of the volume and speed of private and public transport on different sections of arterial radial streets.

Type of the Section	Planning Features of the Section	Indicators of Private Transport Movement				Indicators of Public Transport Movement in Peak Hours
		Off-Peak Hours		Peak Hours
		Traffic Volume Per Lane, auto/h	Speed of Movement, km/h	Traffic Volume Per Lane, auto/h	Speed of Movement, km/h	Traffic Volume, p.c.u./h	Speed of Movement, km/h
1	Three lanes in one direction without spatial priority 1	400–450	40–55	520–550	30–40	50–55	25–30
2	Three lanes in one direction with spatial priority (with bus bays)	400–450	40–55	520–550	30–40	50–55	25–30
3	Three lanes in one direction with spatial priority (without bus bays)	300–350	30–35	470–550	25–30	110–115	20–25
4	Two lanes in one direction without spatial priority	300–350	35–40	470–520	25–30	95–100	20–25
5	Two lanes in one direction with spatial priority (with bus bays)	350–400	30–35	470–520	25–30	95–100	20–25
6	Three lanes in one direction with spatial priority (without bus bays)	300–350	30–35	470–520	20–25	110–115	15–20
7	With one lane per direction (without bus bays)	300–350	25–30	350–400	15–25	95–100	15–25
8	With one lane per direction (with bus bays)	300–350	25–30	350–400	5–15	120–125	5–10

¹ Spatial priority—allocation of the right lane only for public transport movement.

.

In addition to planning differences in the cross-section (number of traffic lanes), the sections of the studied streets differed in the distance between stopping lines. Based on that, three important indicators should be determined that characterize the traffic delay: the maximum length of a queue of vehicles that can form between adjacent signalized intersections; critical traffic volume, which causes a maximum queue; change in speed depending on the distance between signalized intersections.

Traffic simulation using the software PTV VISSIM [5] was carried out to determine the delay. During the simulation, the existing time parameters of the traffic light control cycles were preserved in all sections, where the duration of the restrictive signal in the main direction is less than 20s. The traffic volume is based on the results from Table 3. Three modes of vehicle passage were created for sections with three, two, and one lane(s). (Figure 2).

The length of segments in PTV VISSIM was set discretely and was: 200 m, 600 m, and 1000 m for three-lane sections; 200 m, 600 m, and 800 m for two-lane and one-lane sections. The segment here is considered to be the distance from the stop line to a vehicle located in the section between the intersections (or on the adjacent stop line). The simulation procedure considered the traffic volume increase in intervals of 10%, compared to the existing values, until it reached the maximum length of the queue of vehicles that reached the length of the segment or the limit value of the capacity under ideal traffic conditions (1200 p.c.u./h per one lane).

It should be noted that during the simulation, the allocation of a separate lane for public transport was achieved by reducing the number of lanes for private transport, not by expanding the roadway. Therefore, in the case where there is only one lane in a direction, the simulation of mode B was not carried out.

The results of the delay simulation are given in

Table 4. Summarized results of traffic delay simulation for different modes of sections of arterial streets passage.

Indicator of Traffic Delay, Determined during the Simulation	Segment Length (m)	The Largest Values of the Indicator for the Mode of Passage			Critical Values of Traffic Volume for the Mode of Passage (p.c.u./h)
		А	B	C	А	B	C
Three lanes in the direction
Maximal queue length of private transport flow on the segment (m)	200	122.9	197.1	70.39	–	1680	–
	600	136.9	222.1	96.19	–	1440	–
	1000	104.4	222.9	70.71	–	1440	–
Delay per one vehicle from the flow of private transport on the segment (s)	200	81.6	185.6	49.15	–	1680	–
	600	89.3	206.3	71.36	–	1440	–
	1000	71.2	197.7	51.36	–	1440	–
Two lanes in the direction
Maximal queue length of private transport flow on the segment (m)	200	258.1	256.0	278.2	900	900	1170
	600	483.6	512.3	442.6	990	990	1080
	800	498.4	515.9	405.5	900	990	990
Delay per one vehicle from the flow of private transport on the segment (s)	200	296.8	273.1	298.3	900	900	1170
	600	467.5	509.3	444.9	990	990	1080
	800	481.7	495.5	405.8	900	990	990
One lane in the direction
Maximal queue length of private transport flow on the segment (m)	200	208.3	–	201.1	495	–	675
	600	455.2	–	407.4	585	–	585
	800	512.6	–	449.3	–	–	–
Delay per one vehicle from the flow of private transport on the segment (s)	200	207.3	–	177.9	495	–	675
	600	437.7	–	375.2	585	–	585
	800	459.3	–	399.2	–	–	–

.

In general, for sections with three lanes of traffic in one direction, the lowest values of the investigated delay indicators are observed for the mode of passage C and the largest for mode B. For method B, queues and delays are the largest for all sections since the lane is extracted from the flow of private transport and moved to public transport. For two lanes in the direction of modes A and C, some similarity in results is observed since public transport is in the general flow for a significant part of the segment. On sections with one lane, the increase in delay is proportional to the increase in traffic volume, since there are few alternative options to speed up the public transport movements or management of queues, except for increasing the permissive signal in the control phase. It is important to note that with an increase in the number of traffic lanes, the critical value of the traffic volume per one lane decreases, which can be explained by frequent lane change manoeuvres between intersections. Information about the queue length, based on the traffic volume values, is essential when calculating the time parameters of the traffic light cycle. In addition, when organizing the passage according to mode C, it is possible to solve an engineering problem by determining the rational length of the expansion before the intersection. Such an expansion of sufficient length may also be provided by the arrangement of a stopping point. Table 4 also shows the homogeneity property of incoming data to the traffic simulation. It takes into account the number of lanes, length of sections, and traffic volume. Homogeneity dictates the number of lanes and lengths of observed sections.

Next step was to simulate the distance between stop lines influencing private and public transport speeds for peak hours, with each mode of passage, and to compare them with the results obtained from GPS trackers. Simulation results are given in Figure 3, Figure 4 and Figure 5.

To the data from Figure 3, the values of the speed of private vehicles on sections with the C and A modes of passage do not differ significantly from each other (the difference is 2–4 km/h). As for method B, the motion speeds are lower, and their difference from method A is 4–8 km/h. The speed of public transport was simulated only for mode C because in mode A it moves in the general flow. With method B, its speed is affected only by the volume of buses and their traffic schedules. Therefore, the speed of public transport decreases, and after reaching a distance of 250–300 m, it increases to a value of about 27 km/h. Referring to the results of modelling and the maximum queue length and delay per vehicle typical for sections 1 and 3, it can be noted that on sections 200 m long (typical section 3) the value of the maximum queue length is reached at the volume of 1560 p.c.u./h in method B. In sections 600 and 1000 m long (typical section 1), critical values of the maximum queue length are not observed, so in these typical sections, it is not expected to give spatial priority to public transport.

In the case presented in Figure 4, the values of the speed of private transport flow are similar for modes A and B. However, the speed difference is more significant up to a distance of 250–300 m. As for mode B, the speed of motion is lower (by 5–10 km/h) compared to methods A and C. The speed of public transport changes in the same way as for the case of three traffic lanes: it decreases down to 300 m, after which the speed increases to a value of 21 km/h. As for the typical sections, on the 200 m long segments, it is advised to implement the expansion of the roadway since the values of the maximum queue length and delay per vehicle are quite high here. In a typical section 4, the value of the maximum queue length increases uniformly for methods A and B, while the values of the indicators for method C differ insignificantly from those for method A, so there is no need to implement spatial priority here. In the simulation results shown in Figure 5, the same trend is observed as in the case of two traffic lanes: up to a length of 250 m, the speed values for mode C are higher than for mode A. After this distance, the speed difference is not high—1–3 km/h. The speed of public transport is lower but differs from the same speed on sections with a length of about 250 m up to 6 km/h and on other sections up to 4 km/h. The value of the maximum queue length on a typical section reaches 200 m. Therefore, it is advised to implement the roadway extension or allocate a separate direction for the passage of public transport. In a typical section, the values of the maximum queue length and delay per vehicle differ slightly but increase sharply after reaching a traffic volume of 540 p.c.u./h. Based on this, it is advised to implement a spatial priority in the form of expansion of the roadway in such areas. So, here a certain “critical” distance of 250–300 m is established, where it is necessary to give priority to public transport since private transport will cause delays.

Table 5. Changes in the speed of the traffic flow depending on the distance between the stop lines for different modes of passage.

Number of Lanes	Mode of Section Passage	Approximation Equation	$\mathbf{Coefficient} \mathbf{of} \mathbf{Determination}, {\mathit{R}}^2$	Number of Formula
3	А	$V_{prt}=0.00001L^2+0.0035L+23.468$	0.9526	2
	B	$V_{prt}=-0.0000003L^2+0.0122L+18.555$	0.9267	3
	C	$V_{prt}=0.00001L^2+0.0025L+25.321$	0.9496	4
	C (PT 1)	$V_{pt}=0.00002L^2-0.003L+12.432$	0.8957	5
2	А	$V_{prt}=-0.000003L^2+0.017L+18.755$	0.9364	6
	B	$V_{prt}=0.0000003L^2+0.009L+14.059$	0.891	7
	C	$V_{prt}=-0.000003L^2+0.0076L+22.675$	0.8667	8
	C (PT1)	$V_{pt}=0.00001L^2-0.0037L+13.144$	0.7866	9
1	А	$V_{prt}=0.000002L^2+0.0061L+13.268$	0.8262	10
	C	$V_{prt}=0.000005L^2+0.0017L+15.598$	0.8391	11
	C (PT 1)	$V_{pt}=0.000005L^2+0.0027L+1.089$	0.7518	12

¹ PT—public transport.

shows the approximation equations and coefficients of determination for the graphs shown in Figure 3, Figure 4 and Figure 5. In summary, it can be stated that when there are three lanes in one direction, it should be verified whether the speed of public transport is lower than the speed of private transport. If it is lower, no priority to public transport is given. If it is not, the condition is checked for whether the speed of public transport is equal to the speed of the traffic flow. Here, again, if the condition is fulfilled, the lane is allocated for public transport; if not, the priority passage is not given. When a separate lane is allocated for public transport, the condition is rechecked for whether the public transport is behind the schedule. If it is, conditional active priority is considered to be implemented; if it is not, no additional priority is given.

When there are two lanes in the same direction, it is verified whether the distance between signalized intersections is less than 200 m. If it is, a lane with active time-based priority is allocated for public transport. If it is not, the critical volume is checked: if it is less than those given in Table 3, the time-based priority without the roadway extension is given to public transport. If it is, more time-based active priority and appropriate extension up to the distance of 250 m from the stop line are given to the public transport.

In the case when there is one lane in a direction, the condition, of whether the distance between signalized intersections is less than 200 m, is verified. If it is, the allocation of a direction exclusively for public transport with active time-based priority is considered. If it is not, the condition of whether the critical volume reaches the values given in Table 3 is verified again. If it is, the time-based priority of public transport without the roadway extension is checked. If the critical volume is smaller, the extension with an active time-based priority is given for public transport.

4. Discussion

Based on the research results, it can be stated that the implementation of spatial or time-based priority for public transport has different efficiency for road network sections, which are different due to their planning parameters. The most important task is to achieve a reduction in the time losses for commuters while travelling, regardless of which mode is chosen. Since priority is given to public transport in the plans of sustainable urban mobility and spatial development, it is necessary to increase its attractiveness [29]. Although, this cannot be achieved by reducing alternative means of transportation, as a result of limiting the duration and the comfort of transportation [30].

The practical value of the present research is the development of recommendations for implementing modes of the passage of signalized sections of the arterial road network of different types. Such recommendations are given in

Table 6. Recommendations on the implementation of modes of the passage of signalized sections of the arterial road network, taking into account the priority for public transport.

Type of Section	Mode of the Passage of Section	Recommendations on Giving Priority to Public Transport
1	А	To give time-based conditional priority at traffic light systems sections when public transport is behind schedule; no spatial priority is given
2	А	To give time-based conditional priority at traffic light systems sections when public transport is behind schedule; no spatial priority is given
3	B	To give time-based active priority and spatial priority in the form of an allocated lane
4	А	To give time-based conditional priority at traffic light system sections when public transport is behind schedule; no spatial priority is given
5	А	To give time-based conditional priority at traffic light system sections when public transport is behind schedule; no spatial priority is given
6	C	To give time-based active priority and spatial priority in the form of extension of the roadway before the intersection in the length of up to 250 m with a volume of private transport of more than 900 auto/h and public transport of more than 110 auto/h
7	C	To give time-based active priority and spatial priority in the form of extension of the roadway before the intersection in the length of up to 250 m with a volume of private transport of more than 540 auto/h and public transport of more than 95 auto/h
8	B	To give time-based active priority and spatial priority in the form of allocated direction for public transport movement

. The authors are fully aware that stopping delays do not only depend on the type of stopping area. The other causes could be the number of passengers boarding and alighting or simply the bus occupancy level. However, when processing data directly from GPS trackers, it was not possible to detect the duration of the delay at the stopping points. Respectively, separate studies of traffic delays at stopping points were conducted, which were previously divided into five groups, based on the method of their arrangement and the geometric parameters of the roadway. With known values of the duration of this delay, we can determine quite accurately the speed of buses on the route sections and the duration of the traffic delay caused by the method of its regulation.

5. Conclusions

• When determining the method of public transport prioritization, it is expedient to divide sections of arterial streets into eight types, depending on the number of traffic lanes, the volume of traffic flow (including public transport), and the level of convenience.
• The results of field studies and simulation modelling established that “critical” (from the point of view of time spent on movement) on the arterial road network are sections with a distance between adjacent stop lines of 250–300 m and a volume of 540 p.c.u./h per one lane and more for typical sections 4–6 and with a traffic volume of 450 p.c.u./h per one lane for typical sections.
• Based on the criterion of minimizing the delay in the movement of one vehicle, three rational modes of organizing the passage of signalized sections of the arterial road network by public transport have been established: mode A (with the provision of conditional time-based priority)—on typical sections 1, 2, 4, and 5; mode B (with the provision of active time-based priority)—on typical section 3; mode C (with the provision of active time-based priority)—on typical sections 7 and 8.
• Due to the high value of the density of the road network, which is observed in cities with a radial–ring configuration, when approaching the city centre, it is advisable to introduce separate streets exclusively for the movement of urban public transport.