Influence of the Parameters of the Bus Lane and the Bus Stop on The

sustainability

Article Inﬂuence of the Parameters of the Bus Lane and the Bus Stop on the Delays of Private and Public Transport

Fadyushin Alexey and Zakharov Dmitrii *

Department of Road Transport Operation, Industrial University of Tyumen, 625000 Tyumen, Russia; [email protected] * Correspondence: [email protected]; Tel.: +7-908-874-6252

Received: 28 September 2020; Accepted: 16 November 2020; Published: 18 November 2020

Abstract: The article deals with the influence of the infrastructure for public transport on the delay time of private and public transport in the city. The study employed the methods of simulation, mathematical modeling and field research. Imitation microscopic modeling determined the parameters of mathematical models of the delay time of private and public transport for various parameters of the bus lane, the length of the bus stop loading area, and its distance from the signalized intersection. Calculations determined the total delay time, taking into account the number of passengers in public and private transport on the section of the main street of regulated traffic. Determining the optimum parameters of the public transport infrastructure requires considering not only public transport passengers, but also drivers and passengers of private vehicles. Over-improving parameters of the bus lane has no effect on public transport, but traffic parameters for all other road users degrade. At high traffic intensity, the dependences of the total delay time on the length of the marking lines 1.11 and 1.5 are described by the parabola equation. The values for a road with three lanes have been determined, marking lines 1.11 and 1.5 at which the total delay time is minimal. For a highway with a high intensity, minimum bus stop parameters lead to significant increases in delay time.

Keywords: transport planning and modeling; urban transport system; public transport; private transport; bus lanes; bus stop; travel time; delay time

1. Introduction It is hard to imagine a modern city without sustainable population mobility. Despite a significant decrease in population mobility in 2020 during the period of restrictions due to coronavirus/COVID-19 [1,2], experts predict a gradual recovery in transport demand. For a long time, the policy in the field of transport in Russian cities was of a catch-up nature and consisted of the construction of new highways, transport interchanges, tunnels, underground or elevated pedestrian crossings [3]. At the same time, the quality of transport services increased for users of private and public transport and deteriorated for pedestrians. The trend of recent decades is urbanization, population growth in cities and their territories. In large cities of the world, sustainable mobility is achieved through the development of infrastructure and rolling stock of public transport, car and bicycle rental services, the creation of bike lanes and infrastructure for pedestrians [4,5]. To ensure sustainable urban mobility, priority conditions are created for public transport and cyclists in comparison with the use of a private car [6,7]. The authors in [8,9] show that in different cities the share of movements by different types of transport can differ significantly. At the same time, in most of the cities mentioned in [10],

Sustainability 2020, 12, 9593; doi:10.3390/su12229593 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 9593 2 of 18 residents prefer public transport. Both the development of public transport and ensuring the need for movement by public transport provide social justice for citizens [11,12]. When developing public transport in cities, it is important to form an efficient bus network that depends on transport demand [13]. The development of public transport, including its infrastructure, affects the economic performance of transport and the economy of the region [14,15]. The authors of [16] show that public transport affects the psychological state of people, and the development of infrastructure for public transport is one of the mechanisms for promoting health. Some of the most important factors determining the choice of public transport by people for movement in cities is the travel time [17]. To reduce travel time, active and passive priorities are created for the movement of public transport [18–21]. To create an active priority for the movement of public transport when passing through signal intersections, three strategies are used: bus speed control, traffic signal control, or a combination of these [22]. Using an active priority reduces the travel time, the delay time, and the average queue length. Limiting the capacity of a stop affects the performance and efficiency of buses. The results of the study show the need for a comprehensive account of the active priority when crossing intersections for public transport and the throughput of bus stops. In addition, it is necessary to pay attention to ensuring the necessary throughput of intermediate and final bus stops [23–25]. Optimization of road infrastructure for public transport is an urgent scientific and practical task. Models of traffic on a road near a bus stop and methods of its placement were considered in the works [26–32]. For example, in [33], of the four types of bus stop considered, one of them includes the presence of an entrance pocket outside the traffic lane. When using stops of this type, the best road traffic parameters are achieved. However, the authors of [26–33] do not consider the effect of the length of the loading area on the traffic parameters with different transport demand. In the paper [34], the influence of the location of the bus stop and distance from the intersection on the vehicle delay was established. With respect to the volume, the downstream bus stop is greatly superior to the upstream one when the distance is less than 70 m, and slightly inferior to the upstream one when the distance ranges from 70 m to 200 m. With regard to the vehicle delay, the upstream bus stop is better than the downstream one. However, the study uses constant values of traffic intensity and length of the loading area bus stop. Much attention in the research is paid to the location of the bus stop on the route of public transport [35]. This is done to strike a balance between the speed of communication and the availability of the bus stop for pedestrians. Increasing the average speed when creating bus lanes improves the operating conditions of electric buses which require stops to charge batteries with electric energy [36]. The creation of dedicated lanes for buses allows for organizing the movement of buses of different routes [37], which is important for large cities with a lack of highways and no off-street transport. However, even under such conditions, it is important to find the optimal parameters of the infrastructure for public transport which reduce the loss of time for people traveling by other modes of transport [38]. The aim of the work is to improve the efficiency of traffic management by establishing patterns of influence of the parameters of the infrastructure for public transport on the traffic delay time.

2. Materials and Methods In this work, transport modeling at the microscopic level was used to assess the change in traffic parameters [39]. Microscopic modeling has become widespread in the optimization of traffic flows, design of road transport infrastructure facilities, optimization of traffic light facilities, simulation of the movement of unmanned vehicles as part of intelligent transport systems of cooperative control, taking into account fuel consumption of cars and emissions of harmful substances with car exhaust gases and when solving other problems [40–45]. Modeling allows you to simulate conditions that cannot be implemented in actual practice without significant financial and material inputs. Simulation modeling at the microscopic level requires calibrating the models used, taking into account real traffic conditions Sustainability 2020, 12, 9593 3 of 18 and parameters [46]. To assess the effectiveness of traffic management, the delay time was selected. The work evaluated the average and total time delays in traffic. The average delay time of the i-th mode of transport is the delay time for one vehicle of the i-th mode of transport moving along the studied section. Further in the work, the delay time of the i-th mode of transport is used. Ratings of cities by the level of service traffic congestion commonly use a coefficient that characterizes how many times the travel time during peak hours ttrav increases in comparison with free traffic t0 [47]. The difference between ttrav and t0 will be the time delays td created during the movement. In the opinion of the authors of the article, it is not enough to take into account the parameters of traffic in relation to vehicles only. It is necessary to take into account the passenger capacity of vehicles and the number of passengers carried. On average, one passenger car accounts for 1.5 trips, and the simultaneous loading of buses can reach up to 100–120 passengers. Therefore, to take into account the time spent on movement, in this paper, the total delay time is used which is calculated by the equation:

n X t Q tdi qi Ni T = T = di· di = · · (1) d di 3600 3600 i=1 where Td—total delay time per hour of academic time, h/1 h; Tdi—total delay time of the i-th mode of transport, h; tdi—average delay time of the i-th mode of transport, s/person; Qi—number of passengers carried by the i-th mode of transport on a section of the road network, persons/1h; qi—average number of passengers in one vehicle of the i-th mode of transport, persons/vehicle; Ni—traﬃc intensity of the i-th type of transport, vehicle/1 h: i—serial number on the general list of modes of transport; n—the number of modes of transport on the general list. The total delay time of the i-th mode of transport is the delay time of all users of the i-th mode of transport and drivers of private transport moving around the area under study. The time spent on daily commuting to work and returning home can be a signiﬁcant fraction of a day. Reducing this timing improves the quality of human life and the competitiveness of the city. In this work, the objective function has the form:

T min (2) d → where Td—total delay time, h/1 h. The object of research is a system shown in Figure1. Transport modeling was carried out in the PTV Vissim 11 software program. The strengths and weaknesses of the PTV Vissim software for modeling traffic flows are described in [48]. An important advantage is its good accuracy for busy traffic flows and large intersections. In PTV Vissim, the simulation is performed with stochastic incoming flows, i.e., the time of vehicle arrival at the beginning of the segment is random. To improve the accuracy of the simulation results, 6 calculations of the average delay time were carried out during 10 min simulation time intervals and the average value of the delay time was calculated. These values are used in the article to check the adequacy of the mathematical models and the graphics. The average delay time calculation starts at 1200 s of simulation and continues for 3600 s. In the period from 0 to 1200 s, the road network model is filled with vehicles. When level of service LoS > 1, at the moment of the start of determining the traffic parameters (from 1200 s), traffic jams are formed at the traffic lights in the simulation model. It gives an opportunity to achieve the correspondence of the parameters of the simulation model to real traffic conditions at a specific point in the simulation time. The simulation model consists of a road, an approach to a regulated intersection and an intersection with traffic lights. The microscopic transport model of the city’s traffic includes 1000 m long sections; traffic lights with a four-phase operation mode. Due to traffic light regulation, traffic flows at the intersection are separated in time, and each direction moves in a separate phase. The phase coefficient for the forward and right-hand traffic direction of the vehicle is 0.37, for the left-hand turning flow, Sustainability 2020, 12, x FOR PEER REVIEW 3 of 18

account real traffic conditions and parameters [46]. To assess the effectiveness of traffic management, the delay time was selected. The work evaluated the average and total time delays in traffic. The average delay time of the i-th mode of transport is the delay time for one vehicle of the i-th mode of transport moving along the studied section. Further in the work, the delay time of the i-th mode of transport is used. Ratings of cities by the level of service traffic congestion commonly use a coefficient that characterizes how many times the travel time during peak hours ttrav increases in comparison with free traffic t0 [47]. The difference between ttrav and t0 will be the time delays td created during the movement. In the opinion of the authors of the article, it is not enough to take into account the parameters of traffic in relation to vehicles only. It is necessary to take into account the passenger capacity of vehicles and the number of passengers carried. On average, one passenger car accounts for 1.5 trips, and the simultaneous loading of buses can reach up to 100–120 passengers. Therefore, to take into account the time spent on movement, in this paper, the total delay time is used which is calculated by the equation: 𝑡 ∙𝑄 𝑡 ∙𝑞 ∙𝑁 𝑇 =𝑇 = = (1) 3600 3600

where Td—total delay time per hour of academic time, h/1 h; Tdi—total delay time of the i-th mode of transport, h; tdi—average delay time of the i-th mode of transport, s/person; Qi—number of passengers carried by the i-th mode of transport on a section of the road network, persons/1h; qi— average number of passengers in one vehicle of the i-th mode of transport, persons/vehicle; Ni—traffic intensity of the i-th type of transport, vehicle/1 h: i—serial number on the general list of modes of Sustainabilitytransport; 2020n—the, 12, 9593number of modes of transport on the general list. 4 of 18 The total delay time of the i-th mode of transport is the delay time of all users of the i-th mode of transport and drivers of private transport moving around the area under study. 0.11. ModelingThe time spent was carried on daily out commuting with the settings to work of and the programreturning corresponding home can be toa significant the optimal fraction weather, of climatic,a day. Reducing and road this conditions timing improves of vehicle the operation. quality of Simulation human life models and the were competitiveness calibrated with of the respect city. toIn changesthis work, in the maximum objective and function desired has acceleration the form: and deceleration functions, the Wiedemann’s car following model (look ahead distance, look back distance, average standstill distance, additive and multiplicative parts of safety distance), lane change𝑇 →𝑚𝑖𝑛 and lateral (general behavior, active cooperative(2) lanewhere change, Td—total desired delay position time, h/1 at free h. flow), etc. Delay time was determined for a traffic flow moving in one direction.The object of research is a system shown in Figure 1.

Figure 1. The structure of the system under study. Figure 1. The structure of the system under study.

The experimental part of the study is carried out in several stages:

Stage 1 involves the creation of simulation models of the movement of private and public transport • in PTV Vissim 11 with parameters corresponding to the real conditions of movement of road transport on the road network; Stage 2 envisages field studies and determination of traffic flow parameters to calibrate traffic • simulation models to match the actual traffic flow parameters; Stage 3 involves experimental research with the establishment of dependencies using • simulation modeling; Stage 4 involves field research and measurement of the traffic delay time and the establishment of • dependencies based on field research; Stage 5 provides for the analysis of research results and assessment of the adequacy of mathematical • models to the results obtained in field research.

The article presents the intermediate results of the research on the ﬁrst three stages using simulation modeling. According to experts’ forecasts, the number of residents in Tyumen will increase to 1 million by 2028–2029 and will reach 1.2 million by 2040. In 2016, in Tyumen, the average trip time for work purposes was 35 min. To maintain this parameter at a given level, the program for the integrated development of transport infrastructure plans to change the structure of population mobility and to increase the share of trips by public transport from 40 to 55% by 2040 (Figure2). SustainabilitySustainability2020 2020, ,12 12,, 9593 x FOR PEER REVIEW 55 ofof 1818

Structure of urban mobility , 2016 Structure of urban mobility , 2040

14% 16% 44% 31% Private Private transport transport Public transport Public transport Pedestrian 40% 55% and Bike Pedestrian and Bike

(a) (b)

FigureFigure 2.2. StructureStructure ofof urbanurban mobilitymobility accordingaccording toto thethe ProgramProgram forfor thethe IntegratedIntegrated DevelopmentDevelopment ofof TransportTransport Infrastructure Infrastructure in in Tyumen: Tyumen: ( a()a) in in 2016; 2016; ( b(b)) forecast forecast for for 2040. 2040.

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One However, way to improve the built-up the effi ciencydensity of and public the transport limited right-of-way is to increase in the most average Russian speed. cities This allow will reducefor creating the need a bus for lane rolling only stock by reducing while maintaining the number headways of lanes for or provideprivate vehicles. shorter headways At the same without time, changingthere willthe be an number improvement of buses. in It traffic is possible conditions to increase for public the average transport, tra butffic speeda deterioration by creating in private active andones. passive The lane tra ffiloadc priorities level for for buses public decreases, transport. and The for passiveindividual priority vehicles, of public increases. transport traffic is the creationThe of location bus lanes. of a bus stop relative to the signalized intersection can also affect the parameters of publicThe and greatest private effect transport. of their With creation high is traffic achieved intens whenity creatingof public a transport, separate lane the for length buses. of Atthe the bus same stop time,loading the parametersarea becomes of public significant. transport In trafficthe aggregate, are improved the andformation do not deteriorateof optimal for parameters private transport. of the However,infrastructure the built-up for public density transport and thecan limitedreduce right-of-waythe time spent in on most travel. Russian cities allow for creating a bus laneAs part only of by the reducing transport the planning number ofdocuments, lanes for privateby 2040, vehicles. the city plans At the for same the time,organization there will of beabout an improvement100 km of new in trafficbus lanes conditions and 500 for bus public stops. transport, If the butbus alane deterioration parameters in privateare selected ones. Theincorrectly, lane load a levelsignificant for buses increase decreases, in the and delay for individualtime on both vehicles, private increases. and public transport is possible. Conversely, by choosingThe location the optimal of a bus lane stop parameters, relative to the it is signalized possible to intersection reduce the canloss alsoof time affect for theall road parameters users. of publicThe andwork private considered transport. the following With high parameters traffic intensity of infrastructure of public transport, for public the transport: length of the bus stop• loadingThe length area of becomes the 1.11 significant.continuous-dashed In the aggregate, marking line the formationbefore the signalized of optimal intersection; parameters of the infrastructure• The length for of public the cancellation transport can of reduce the action the time of the spent bus on lane travel. (hereinafter—the 1.5 broken line Asmarking) part of thebefore transport the signalized planning intersection; documents, by 2040, the city plans for the organization of about 100• kmThe of newlength bus of lanes the bus and stop 500 busloading stops. area; If the bus lane parameters are selected incorrectly, a significant increase• The in removal the delay distance time on of both the privatebus stop and from public the transportsignalized is intersection. possible. Conversely, by choosing the optimal bus lane parameters, it is possible to reduce the loss of time for all road users. TheThe workrange considered of the factor the values following of the parameters variables under of infrastructure consideration for includes: public transport: • The length of the 1.11 marking line was varied from 20 to 60 m; The length of the 1.11 continuous-dashed marking line before the signalized intersection; •• The length of the 1.5 marking line was varied from 50 to 250 m; The length of the cancellation of the action of the bus lane (hereinafter—the 1.5 broken line •• The lengths of loading area and removal distance of the bus stop were varied from 20 to 60 m; marking) before the signalized intersection; • The traffic intensity of the private transport varied from 1000 to 2500 vehicle/h; The length of the bus stop loading area; •• The traffic intensity of the public transport varied from 60 to 240 bus/h; The removal distance of the bus stop from the signalized intersection. •• The average number of passengers in one bus varied from 20 to 80 persons/bus. The range of the factor values of the variables under consideration includes: 3. Results and Discussion The length of the 1.11 marking line was varied from 20 to 60 m; • 3.1. InfluenceThe length of the of theLength 1.5 markingof the 1.11 line Bus was Lane varied Marking from Line 50 on to 250the Traffic m; Delay Time • The lengths of loading area and removal distance of the bus stop were varied from 20 to 60 m; • When creating a bus lane on highways, it is usually placed in the far-right lane and separated from the second lane by a 1.1 solid marking line (Figure 3a). For the general motor vehicles to change Sustainability 2020, 12, 9593 6 of 18

The traﬃc intensity of the private transport varied from 1000 to 2500 vehicle/h; • The traﬃc intensity of the public transport varied from 60 to 240 bus/h; • The average number of passengers in one bus varied from 20 to 80 persons/bus. • 3.Sustainability Results and2020, Discussion12, x FOR PEER REVIEW 6 of 18

3.1.to the Influence far-right of lane the Length and make of the a 1.11 right Bus turn Lane before Marking the intersection, Line on the Tra theffic 1.1 Delay markings Time are replaced with 1.11. The bus lane marking parameters before the signalized intersection are regulated by the state standardWhen GOST creating R a52289-2004 bus lane on “Technical highways, itmeans is usually of traffic placed management”. in the far-right laneThe andlength separated of the from1.11 themarking second line lane before by a 1.1 the solid intersection marking line cannot (Figure exceed3a). For 80 the m generaland ends motor 20 vehiclesm or more to change before to thethe far-rightintersection. lane In and practice, make athe right length turn of before the 1.11 the marking intersection, line may the 1.1 be markings10 m. This are situation replaced is withobserved 1.11. Thein the bus central lane marking parts ofparameters cities with beforea high the densit signalizedy of the intersection road network are regulatedand a small by thedistance state standardbetween GOSTintersections, R 52289-2004 where “Technicala large number means of public of traffi transportc management”. routes can The pass. length of the 1.11 marking line beforeIf thethe intersection1.11 marking cannot line exceedis long, 80 am queue and ends of 14–15 20 m orcars more can before form thein the intersection. bus lane Inbefore practice, the thesignalized length ofintersection the 1.11 marking (Figure line 3b). may In this be 10case, m. th Thise bus situation may not is observedhave time in to the pass central the intersection parts of cities in withone traffic a high light density cycle, of which the road will network lead to an and increase a small in distance the delay between time. intersections, where a large number of public transport routes can pass.

(a) (b)

Figure 3. (a) Standardization of bus lane parameters before the intersection in accordance with GOST R 52289-2004. ( b) Scheme of tratrafficﬃc on a road with aa busbus lanelane beforebefore aa signalizedsignalized intersection.intersection.

IfThe the hypothesis 1.11 marking of linethe isstudy long, is a queuethat if ofthe 14–15 leng carsth of can the form 1.11 in marking the bus laneline beforebefore the a signalized intersection (Figureincreases,3b). the In delay this case, time the increases bus may for not public have transport time to pass (hereinafter—PuT) the intersection and in one decreases tra ﬃc lightfor private cycle, transport which will (hereinafter—PrT). lead to an increase in the delay time. The hypothesisinfluence of of the the length study of is the that 1.11 if the marking length line of the before 1.11 the marking signalized line beforeintersection a signalized on the intersectionaverage delay increases, time of thePrT delay and PuT time is increases described for by public linear transport mathematical (hereinafter—PuT) models (Equations and decreases (3) and for(4)): private transport (hereinafter—PrT). The inﬂuence of the length of the 1.11 marking line before the signalized intersection on the 𝑡 =𝑡 −𝑆 ∙𝐿. (3) average delay time of PrT and PuT is described by linear mathematical models (Equations (3) and (4)): 𝑡 =𝑡 +𝑆 ∙𝐿. (4) tdPrT = tdPrT0 SL L1.11 (3) where tdPrT—average PrT delay time, s; tdPrT0—average− PrT· delay time at the minimum value length of the 1.11 marking line, s; Sj—parameter of sensitivity to changes in the length of the 1.11 marking tdPuT = tdPuT0 + SL L1.11 (4) line; L1.11—length of the 1.11 marking line before the signalized· intersection, m; tdPuT—average PuT wheredelay time,tdPrT—average s; tdPuT0—average PrT delay PuT time, delay s; timetdPrT 0at—average the minimum PrT delay value time length at theof the minimum 1.11 marking value lengthline, s. of theFigure 1.11 marking 4 shows line, the graph s; SL—parameter of the dependence of sensitivity of the to average changes delay in the time length of PrT of the and 1.11 PuT marking on the line;lengthL1.11 of —lengththe 1.11 marking of the 1.11 line marking before the line signalized before the intersection. signalized intersection, m; tdPuT—average PuT delayIf time, the length s; tdPuT of0—average the 1.11 marking PuT delay line time increases at the minimumfrom 20 to value 80 m lengthbefore ofa signalized the 1.11 marking intersection, line, s. the averageFigure4 delay shows time the for graph PrT ofdecreases the dependence by 47%, and of the for average PuT it increases delay time by of140%. PrT and PuT on the lengthThe of thestudy 1.11 hypothesis marking line is that before with the a signalizedhigh number intersection. of passengers on public transport, with an increase in length of the 1.11 marking line, the total delay time increases; with a low number, it decreases. Sustainability 2020, 12, 9593 7 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 7 of 18

Figure 4.4. InﬂuenceInfluence lengthlength ofof the the 1.11 1.11 marking marking line line before before a signalizeda signalized intersection intersection on aon road a road with with a bus a lanebus lane on the on averagethe average delay delay time time of private of privat transporte transport (PrT) (PrT) and publicand pu transportblic transport (PuT). (PuT).

IfThe the linear length one-factor of the 1.11 model marking (Equation line increases (5)) descri frombes 20the to effect 80 m of before the length a signalized of the 1.11 intersection, marking thelineaverage before the delay signalized time for intersection PrT decreases on by the 47%, tota andl PrT for delay PuT time. it increases The model by 140%. is one-factor because, on average,The study 1.5 passengers hypothesis per is thattrip travel with ain high a private number car. ofA multiplicative passengers on two-factor public transport, model that with takes an increaseinto account in length the length of the 1.11 of the marking 1.11 marking line, the totalline delayand the time number increases; of passengers with a low number,in public it decreases.transport (EquationThe linear (6)) describes one-factor the model total delay (Equation time (5))for PuT describes passengers. the eﬀect of the length of the 1.11 marking line before the signalized intersection on the total PrT delay time. The model is one-factor because, 𝑇 =𝑇 −𝑆 ∙𝐿 (5) on average, 1.5 passengers per trip travel in a private car. A multiplicative. two-factor model that takes into account the length of the 1.11 marking(𝑇 +𝑆 line ∙𝐿 and.)∙𝑞 the number 𝑤𝑖𝑡ℎ of passengers𝐿𝑜𝑆 <1 in public transport 𝑇 = (6) (Equation (6)) describes the total(𝑇 delay time+𝑆 for∙ (𝐿 PuT. −𝐿 passengers.) )∙𝑞 𝑤𝑖𝑡ℎ 𝐿𝑜𝑆 ≥1

where TdPrT—total PrT delay time, h; TdPrT0—total PrT delay time at the optimal value length of the TdPrT = TdPrT0 SL L1.11 (5) 1.11 marking line at 1.5 trips in one vehicle, h; TdPuT—total− · PuT delay time, h; TdPuT0—total PuT delay time at the optimal value length( of the 1.11 marking line, h; qPuT—average number of passengers per (TdPuT0 + SL L1.11) qPuT with LoS < 1 bus, per./bus; LoS—levelTdPuT of service.= · · 2 (6) (T + SL (L L0) ) qPuT with LoS 1 Based on the results of field observations,dPuT0 · the1.11 fo−llowing· parameters ≥are used in the simulation wheremodel:T trafficdPrT—total intensity PrT delayof PrT time, is 1500, h; T 2000,dPrT0—total 2500 veh./h; PrT delay traffic time intensity at the optimalof PuT is value 120 lengthbus/h. In of the 1.11work, marking the average line at number 1.5 trips of in passengers one vehicle, in h; oneTdPuT bus—total is onePuT of the delay factors time, considered. h; TdPuT0—total For example, PuT delay in timeTyumen, at the in optimal the central value part length of the of city, the 1.11 buses marking of large line, or very h; qPuT large—average capacity number operate of (60% passengers and 20%). per bus,The simulation per./bus; LoS model—level takes of service. into account large-capacity buses. Figures 5 and 6 show the influence of the lengthBased onof thethe results1.11 marking of field observations,line before the the signalized following parametersintersection are and used average in the number simulation of model:passengers traffi perc intensity bus on the of total PrT isdelay 1500, time. 2000, 2500 veh./h; traffic intensity of PuT is 120 bus/h. In the work,By the increasing average the number length of 1.11 passengers marking inline one from bus 20 is to one 80 ofm thebefore factors the signalized considered. intersection, For example, the intotal Tyumen, PrT delay in the time central is reduced part of theby 50%, city, buses and the of largetotal orPuT very delay large time capacity increases operate in different (60% and ways, 20%). Thedepending simulation on the model average takes number into account of passengers large-capacity per bus. buses. For example, Figures5 with and 6a showloading the of influence 20 per./bus, of the lengthtotal PuT of the delay 1.11 time marking increased line before by 120%, the signalizedand with 80 intersection per./bus—128%. and average number of passengers per busWith on an the average total delay number time. of passengers, more than 40 per./bus, an increase in the length of the 1.11 markingBy increasing line will the lead length to an 1.11 increase marking in the line total from delay 20 to time 80 m(Figures before 5b the and signalized 6). With intersection,20 per./bus, thean increase total PrT in delay the length time isof reduced the 1.11 bymarking 50%, and line the will total lead PuT to a delay decrease time in increases the total indelay diff erenttime. ways, depending on the average number of passengers per bus. For example, with a loading of 20 per./bus, the total PuT delay time increased by 120%, and with 80 per./bus—128%. With an average number of passengers, more than 40 per./bus, an increase in the length of the 1.11 marking line will lead to an increase in the total delay time (Figures5b and6). With 20 per. /bus, an increase in the length of the 1.11 marking line will lead to a decrease in the total delay time. SustainabilitySustainability 20202020,,, 12 12,,, 9593xx FORFOR PEERPEER REVIEWREVIEW 88 ofof 1818

(a) (b) Figure 5. Influence of the length of the 1.11 marking line before a signalized intersection on a road FigureFigure 5.5. InﬂuenceInfluence ofof the the length length of of the the 1.11 1.11 marking marking line line before before a signalized a signalized intersection intersection on a roadon a withroad with a bus lane on: (a) total delay time of PrT and PuT; (b) total delay time. awith bus a lane bus on:lane (a on:) total (a) delaytotal delay time oftime PrT of and PrT PuT; and (PuT;b) total (b) delaytotal delay time. time.

Figure 6. Influence of the length of the 1.11 marking line before a signalized intersection on a road with Figure 6. Influence of the length of the 1.11 marking line before a signalized intersection on a road a bus lane and average number of passengers per bus on total delay time. with a bus lane and average number of passengerspassengers perper busbus onon totaltotal delaydelay timetime.. At low traffic intensity PrT, the change in the total delay time from the marking line 1.11 length is At low traffic intensity PrT, the change in the total delay time from the marking line 1.11 length not significant.At low traffic The intensity influence PrT, of the the marking change in line the 1.11 total length delay on time the from total delaythe marking time at line different 1.11 length traffic is not significant. The influence of the marking line 1.11 length on the total delay time at different intensitiesis not significant. PrT is shown The influence in Figure 7ofa. the At 1500marking veh. line/h, the 1.11 length length of theon the 1.11 total marking delay line time has at practically different traffic intensities PrT is shown in Figure 7a. At 1500 veh./h, the length of the 1.11 marking line has notraffic effect intensities on the total PrT delayis shown time. in AtFigure 2000 7a. veh. At/ h,1500 with veh./h, an increase the length in the of markingthe 1.11 marking line 1.11 line length, has practically no effect on the total delay time. At 2000 veh./h, with an increase in the marking line 1.11 apractically small increase no effect in the on total the total delay delay time time. is observed. At 2000 The veh./h, graph with of an the increase total delay in the time marking dependence line 1.11 on length, a small increase in the total delay time is observed. The graph of the total delay time thelength, marking a small line increase 1.11 length, in builtthe total on the delay basis time of empirical is observed. data, atThe LoS graph> 1 (or of at the 2500 total veh. delay/h) has time the dependence on the marking line 1.11 length, built on the basis of empirical data, at LoS > 1 (or at 2500 formdependence of a parabola. on the marking line 1.11 length, built on the basis of empirical data, at LoS > 1 (or at 2500 veh./h) has the form of a parabola. veh./h)With has a highthe form traffi ofc intensitya parabola. PrT, the total delay time with an increase in the length of the marking With a high traffic intensity PrT, the total delay time with an increase in the length of the marking line 1.11With for a high PrT decreasestraffic intensity by 35%, PrT, for the public total transportdelay time it with increases an increase by 130%. in the Therefore, length of an the extremum marking line 1.11 for PrT decreases by 35%, for public transport it increases by 130%. Therefore, an extremum pointline 1.11 appears for PrT where decreases the total by delay35%, for time public is minimal, transport namely, it increases 60 m (Figureby 130%.7b). Therefore, an extremum point appears where the total delay time isis minimal,minimal, namely,namely, 6060 mm (Figure(Figure 7b).7b). Based on empirical data obtained by means of simulation modeling, the dependence of the total delay time from the marking line 1.11 length with traffic intensity equal to PrT 2500 veh./h and with average passenger number equal to 40 per./bus was developed. The dependencies presented in Figure 7b in mathematical form are presented in Equations (7)–(9).

𝑇 = 0.464 − 140.7 ∙ 𝐿. (7) 𝑇𝑇 = 41.39 + 0.015 ∙ (𝐿. −24.5) (8) 𝑇𝑇 = 164.73 + 0.0214 ∙ (𝐿. −42.56) (9) Sustainability 2020, 12, x 9593 FOR PEER REVIEW 9 of 18

Sustainability 2020, 12, x FOR PEER REVIEW 9 of 18

(a) (b)

Figure 7. InfluenceInfluence ofof thethe length length of of the the 1.11 1.11 marking marking line line before before a signalized a signalized intersection intersection on a on road a road with witha bus a lane bus onlane total on delaytotal delay time withtime averagewith average number number of passengers of passengers 40 per. 40/bus per./bus (a) with (a) di withfferent different traffic trafficintensity intensity PrT (b )PrT with (b) tra withffic intensitytraffic intensity PrT 2500 PrT veh. 2500/h. veh./h.

3.2. InfluenceBased on of empiricalthe Length of data the obtained1.5 Marking by Line means before of a simulation Signalized Intersection modeling, on the the dependence Traffic Delay of Time the totalFor delay the time section from of thethe markingmain road line of 1.11regulated length traffi withc with traffi ca intensitybus lane, equalthere is to a PrT traffic 2500 organization veh./h and schemewith average at an passengerintersection number with a equal left turn to 40 from per./ busthe wasfar-left developed. lane (sign The 5.15.1 dependencies “Lane traffic”) presented and an in additionalFigure7b in traffic mathematical light section. form With are presented such a sche inme, Equations only one (7)–(9). lane remains for the movement of PrT in the forward direction, which can lead to traffic co ngestion. To increase the capacity of the road, the T = 0.464 140.7 L (7) bus lane ends at a certain(a )distance beforedPrT the signalized− intersection· 1.11 and is(b marked) with a road sign 5.14.1Figure “Bus lane7. Influence end”. Theof the far-right lengthT of lane the= 41.39is1.11 separated marking+ 0.015 fromline(L before the24.5 second a signalized)2 lane byintersection a 1.5 broken on a roadmarking (8) dPuT · 1.11 − line, andwith in a busthe lanesignalized on total intersection delay time with area, average a 1.7 linumberne, with of apassengers shift in the 40 trajectoryper./bus (a )of with several different lanes. T = 164.73 + 0.0214 (L 42.56)2 (9) Iftraffic the 1.5 intensity marking PrT line(b) with after traffic thed bus intensity lane before PrT 2500 the· veh./h. controlled1.11 − intersection is long, a queue of PrT vehicles may form (Figure 8). In this case, the bus may not have time to pass the intersection in one 3.2. Influence of the Length of the 1.5 Marking Line before a Signalized Intersection on the Traffic Delay Time traffic3.2. Influence light cycle, of the which Length will of the lead 1.5 to Marking an increase Line beinfore the adelay Signalized time. Intersection on the Traffic Delay Time For the section of the main road of regulated traffic with a bus lane, there is a traffic organization For the section of the main road of regulated traffic with a bus lane, there is a traffic organization scheme at an intersection with a left turn from the far-left lane (sign 5.15.1 “Lane traffic”) and an additional scheme at an intersection with a left turn from the far-left lane (sign 5.15.1 “Lane traffic”) and an traffic light section. With such a scheme, only one lane remains for the movement of PrT in the forward additional traffic light section. With such a scheme, only one lane remains for the movement of PrT direction, which can lead to traffic congestion. To increase the capacity of the road, the bus lane ends at a in the forward direction, which can lead to traffic congestion. To increase the capacity of the road, the certain distance before the signalized intersection and is marked with a road sign 5.14.1 “Bus lane end”. bus lane ends at a certain distance before the signalized intersection and is marked with a road sign The far-right lane is separated from the second lane by a 1.5 broken marking line, and in the signalized 5.14.1 “Bus lane end”. The far-right lane is separated from the second lane by a 1.5 broken marking intersection area, a 1.7 line, with a shift in the trajectory of several lanes. line, and in the signalized intersection area, a 1.7 line, with a shift in the trajectory of several lanes. If the 1.5 marking line after the bus lane before the controlled intersection is long, a queue of PrT If the 1.5 marking line after the bus lane before the controlled intersection is long, a queue of PrT vehicles may form (Figure8). In this case, the bus may not have time to pass the intersection in one vehicles may form (Figure 8). In this case, the bus may not have time to pass the intersection in one traffic light cycle, which will lead to an increase in the delay time. traffic light cycle, which will lead to an increase in the delay time.

Figure 8. Scheme of traffic when the bus lane ends before a signalized intersection.

The research hypothesis is that if the distance between the stop line and the sign 5.14.1 “Bus lane end” (the length of the 1.5 marking line before the signalized intersection) increases, the delay time increases for PuT and decreases for PrT. The influence of the length of the 1.5 marking line before a signalized intersection on the delay time of PrT and PuT is described by linear mathematical models (Equations (10) and (11)):

𝑡 =𝑡 −𝑆 ∙𝐿. (10) 𝑡 =𝑡 +𝑆 ∙𝐿 (11) . where tdPrT—average PrT delay time, s; tdPrT0—average PrT delay time at the minimum value length Figure 8. Scheme of tratrafficﬃc when the bus lanelane endsends beforebefore aa signalizedsignalized intersection.intersection. of the 1.5 marking line, s; Sj—parameter of sensitivity to changes in the length of the 1.5 marking line; The research hypothesis is that if the distance between the stop line and the sign 5.14.1 “Bus lane end” (the length of the 1.5 marking line before the signalized intersection) increases, the delay time increases for PuT and decreases for PrT. The influence of the length of the 1.5 marking line before a signalized intersection on the delay time of PrT and PuT is described by linear mathematical models (Equations (10) and (11)):

𝑡 =𝑡 −𝑆 ∙𝐿. (10)

𝑡 =𝑡 +𝑆 ∙𝐿. (11) where tdPrT—average PrT delay time, s; tdPrT0—average PrT delay time at the minimum value length of the 1.5 marking line, s; Sj—parameter of sensitivity to changes in the length of the 1.5 marking line; Sustainability 2020, 12, 9593 10 of 18

The research hypothesis is that if the distance between the stop line and the sign 5.14.1 “Bus lane end” (the length of the 1.5 marking line before the signalized intersection) increases, the delay time increases for PuT and decreases for PrT. The inﬂuence of the length of the 1.5 marking line before a signalized intersection on the delay time of PrT and PuT is described by linear mathematical models (Equations (10) and (11)):

t = t SL L (10) dPrT dPrT0 − · 1.5

t = t + SL L (11) dPuT dPuT0 · 1.5 Sustainabilitywhere tdPrT 2020—average, 12, x FOR PrT PEER delay REVIEW time, s; tdPrT0—average PrT delay time at the minimum value length10 of 18 of the 1.5 marking line, s; SL—parameter of sensitivity to changes in the length of the 1.5 marking line; L1.5—length—length of of the the 1.5 1.5 marking line before thethe signalizedsignalized intersection,intersection, m;m; ttdPuTdPuT—average—average PuT PuT delay time, s; tdPuT0—average0—average PuT PuT delay delay time time at at the the minimum minimum value value length length of of the the 1.5 1.5 marking marking line, line, s. s. Figure 99 showsshows thethe graphgraph ofof thethe dependencedependence ofof thethe averageaverage delaydelay timetime ofof PrTPrT andand PuTPuT onon thethe length of the 1.5 marking line before the signalized intersection.

Figure 9. InfluenceInﬂuence length length of of the the 1.5 1.5 marking marking line line before before a a signalized signalized intersection intersection on a road road with a bus bus lanelane on the average delay time.

If the length of the 1.5 marking line line increases increases fr fromom 50 to 250 m before a signalized intersection, the average delay time for PrT decreases by 50%, andand for PuT it increases by 80%. Such changes in delay time are more signiﬁcantsignificant for PrT. The studystudy hypothesishypothesis is is that that with with a high a high number number of passengers of passengers on public on public transport, transport, with an with increase an increasein length in of length the 1.5 markingof the 1.5 line, marking the total line, delay the timetotal increases,delay time with increases, a low number—it with a low decreases. number—it decreases.The inﬂuence of the length of the 1.5 marking line before a signalized intersection on the total delayThe time influence of PrT is of described the length by aof linear the 1.5 model marking (Equation line before (12)), anda signal on theized total intersection delay time on of PuT—bythe total delaya multiplicative time of PrT two-factor is described model by a (Equationlinear model (13)). (Equation (12)), and on the total delay time of PuT— by a multiplicative two-factor model (Equation (13)). T = T SL L (12) dPrT dPrT0 − · 1.5 𝑇 =𝑇 −𝑆 ∙𝐿. (12) ( (T + SL L ) qPuT with LoS < 1 T = (𝑇dPuT0+𝑆 ∙𝐿· .1.5)∙𝑞· 𝑤𝑖𝑡ℎ 𝐿𝑜𝑆 <1 (13) 𝑇dPuT = 2 (13) (𝑇(TdPuT0+𝑆+ SL∙ ((𝐿L1.5−𝐿L0)))∙𝑞) qPuT with 𝑤𝑖𝑡ℎ LoS 𝐿𝑜𝑆1 ≥1 · . − · ≥ where TdPrT—total—total PrT PrT delay delay time, time, h; h; TdPrTTdPrT0—total0—total PrT PrT delay delay time time at the at theoptimal optimal value value length length of the of the1.5 marking1.5 marking line line at 1.5 at 1.5trips trips in one in one vehicle, vehicle, h; T h;dPuTT—totaldPuT—total PuT PuTdelay delay time, time, h; TdPuT h; T0—totaldPuT0—total PuT delay PuT delay time attime the at optimal the optimal value value length length of the of 1.5 the marking 1.5 marking line, line,h; qPuT h;—averageqPuT—average number number of passengers of passengers per bus, per per./bus;bus, per./ Lbus;0—lengthL0—length of the of 1.5 the marking 1.5 marking line before line before the signalized the signalized intersection intersection at the atminimum the minimum value Tvalued, m. Td, m. Figure 10 shows the influence of the length of the 1.5 marking line before the signalized intersection and average number of passengers per bus on the total delay time. If the length of the 1.5 marking line increases from 50 to 250 m before a signalized intersection, the average delay time for PrT decreases by 50%, and for PuT it increases in different ways, depending on the average number of passengers per bus. For example, with a load of 20 per./bus, the total PuT delay time increased by 100%, and with 80 per./bus—75%. With an average number of passengers, more than 40 per./bus, an increase in the length of the 1.5 marking line will lead to an increase in the total delay time (Figure 10b). The influence of the length of the 1.5 marking line on the total delay time occurs in the form of a parabola. Consequently, there is a point with the optimal value length of the 1.5 marking line, where the total delay time is minimal. Sustainability 2020, 12, 9593 11 of 18

SustainabilityFigure 2020 10 shows, 12, x FOR the PEER inﬂuence REVIEW of the length of the 1.5 marking line before the signalized intersection11 of 18 and average number of passengers per bus on the total delay time.

Sustainability 2020, 12, x FOR PEER REVIEW 11 of 18

(a) (b)

FigureFigure 10.10. InﬂuenceInfluence ofof thethe lengthlength ofof thethe 1.51.5 markingmarking lineline beforebefore aa signalizedsignalized intersectionintersection on:on: ((a)) totaltotal delaydelay timetime ofof PrTPrT andand PuT;PuT; ((bb)) totaltotal delaydelay time.time.

IfWith the a length high traffic of the intensity 1.5 marking PrT line(2500 increases veh./h), fromthe total 50 todelay 250 time m before with aan signalized increase in intersection, the length theof the average marking delay line time 1.5 for PrTfor decreasesPrT decreases by 50%, by and 26%, for PuTfor PuT it increases it increases in different by 130%. ways, Therefore, depending onan theextremum average point number appears of passengers where the per total bus. delay For example,time is minimal, with a load namely of 20, 150 per. /mbus, (Figure the total 11a). PuT delay time increased by 100%,( anda) with 80 per./bus—75%. (b) With an average number of passengers, more than 40 per./bus, an increase in the length of the 1.5 markingFigure 10. line Influence will lead of tothe an length increase of the in 1.5 the marking total delay line timebefore (Figure a signalized 10b). intersection The inﬂuence on: of(a) the total length of thedelay 1.5 marking time of PrT line and on PuT; the total(b) total delay delay time time occurs. in the form of a parabola. Consequently, there is a point with the optimal value length of the 1.5 marking line, where the total delay time is minimal. With a high traffic intensity PrT (2500 veh./h), the total delay time with an increase in the length With a high traﬃc intensity PrT (2500 veh./h), the total delay time with an increase in the length of of the marking line 1.5 for PrT decreases by 26%, for PuT it increases by 130%. Therefore, an the marking line 1.5 for PrT decreases by 26%, for PuT it increases by 130%. Therefore, an extremum extremum point appears where the total delay time is minimal, namely, 150 m (Figure 11a). point appears where the total delay time is minimal, namely, 150 m (Figure 11a).

(a) (b)

Figure 11. Influence of the length of the 1.5 marking line before a signalized intersection on total delay time with average number of passengers 40 per./bus (a) with traffic intensity PrT 2500 veh./h (b) with different traffic intensity PrT.

As the average number of passengers on public transport increases, the total delay time increases. However, at low traffic intensity PrT, the change in the total delay time from the length of the marking line 1.5 is less significant (Figure 11b). At 1500 veh./h, the length of the 1.5 marking line (a) (b) has practically no effect on the total delay time. The graph of the dependence of the total delay time on theFigure length 11. ofInfluenceInfluence the marking of the the length lengthline 1.5, of of the thebuilt 1.5 1.5 onmarkin marking the gbasis line line before beforeof empirical a signalized signalized data, intersection at LoS > 1 on (or total at 2000–2500delay veh./h)time has with the average form of number a parabola. of passengers 40 per./bus per./bus (a)) with tratrafficffic intensity PrT 2500 veh.veh./h/h (b)) with didifferentAtff erentthe minimum tratrafficffic intensityintensity (50 m) PrT.PrT. and maximum (250 m) length of the marking line 1.5, the total delay time is higher (170 and 210 h, respectively) than at 150 m (150 h). Therefore, the length of the marking line 1.5As equal thethe average average to 150 numberm number is optimal of passengersof inpassengers such conditions. on publicon publ transport ic transport increases, increases, the total the delay total time delay increases. time However,increases.Based atHowever, on low empirical traffi atc intensitylow data traffic obtained PrT, intensity the by change means PrT, inthe of the sichangemulation total delayin themodeling, time total from delay the the dependencetime length from of the the of length markingthe total of linethedelay marking 1.5 time is less on line significant the 1.5 length is less (Figure of significant the 11markingb). At(Figure 1500 line veh.11b).1.5 with/h, At the 1500traffic length veh./h, intensity of the the 1.5 lengthPrT marking 2500 of theveh./h line 1.5 has markingand practically average line nohasnumber e practicallyffect onof thepassengers no total effect delay 40on time.per./busthe total The wasdelay graph developed time. of the Th dependencee. graphThe dependencies of the of thedependence total presented delay of time the in ontotal Figure the delay length 11a time ofin onmathematical the length ofform the aremarking presented line 1.5,in Equations built on the (14)–(16). basis of empirical data, at LoS > 1 (or at 2000–2500 veh./h) has the form of a parabola. At the minimum (50 m) and maximum𝑇 = 0.234(250 m) − 165.7length ∙ 𝐿of. the marking line 1.5, the total delay(14) time is higher (170 and 210 h, respectively) than at 150 m (150 h). Therefore, the length of the marking 𝑇 = 68.29 + 0.025 ∙ (𝐿. −62.74) (15) line 1.5 equal to 150 m is optimal in such conditions. Based on empirical data obtained by means of simulation modeling, the dependence of the total delay time on the length of the marking line 1.5 with traffic intensity PrT 2500 veh./h and average number of passengers 40 per./bus was developed. The dependencies presented in Figure 11a in mathematical form are presented in Equations (14)–(16).

𝑇 = 0.234 − 165.7 ∙ 𝐿. (14) 𝑇 = 68.29 + 0.025 ∙ (𝐿. −62.74) (15) Sustainability 2020, 12, 9593 12 of 18 the marking line 1.5, built on the basis of empirical data, at LoS > 1 (or at 2000–2500 veh./h) has the form of a parabola. At the minimum (50 m) and maximum (250 m) length of the marking line 1.5, the total delay time is higher (170 and 210 h, respectively) than at 150 m (150 h). Therefore, the length of the marking line 1.5 equal to 150 m is optimal in such conditions. Based on empirical data obtained by means of simulation modeling, the dependence of the total delay time on the length of the marking line 1.5 with traﬃc intensity PrT 2500 veh./h and average number of passengers 40 per./bus was developed. The dependencies presented in Figure 11a in mathematical form are presented in Equations (14)–(16). Sustainability 2020, 12, x FOR PEER REVIEW 12 of 18

TdPrT = 0.234 165.7 L1.5 (14) − · 𝑇 = 209.87 + 0.035 ∙ (𝐿. − 121.38) (16) T = 68.29 + 0.025 (L 62.74)2 (15) dPuT · 1.5 − 3.3. Influence of the Bus Stop ParametersT = 209.87on the Delay+ 0.035 Time(L 121.38)2 (16) d · 1.5 − A bus stop for embarking and disembarking passengers is an important element of the PuT 3.3. Influence of the Bus Stop Parameters on the Delay Time infrastructure. In Russia, general technical requirements for the elements of bus stops, the rules for their Aplacement bus stop on for highways, embarking and and their disembarking provision with passengers technical is anmeans important of traffic element management of the PuTare regulatedinfrastructure. by the In industry Russia, standard general technical OST 218.1.002-2003. requirements The for regulation the elements allows of for bus changing stops, the the rules length for oftheir the placementloading area on in highways, a range from and 20 their to 60 provision m. To make with PuT technical accessible, means the regulatory of traffic management documentation are recommendsregulated by thespacing industry stops standard 350–600 OST m between 218.1.002-2003. each ot Theher. regulationConsidering allows the district-based for changing thestructure length of thethe loadingterritory, area the in location a range fromof bus 20 stops to 60 m.does To makenot coincide PuT accessible, with the the recommendations regulatory documentation for their location.recommends spacing stops 350–600 m between each other. Considering the district-based structure of the territory,A bus stop the can location be placed of bus before stops the does signalized not coincide intersection with the under recommendations three conditions: for their location. A bus stop can be placed before the signalized intersection under three conditions: • There is a large passenger-forming point or an entrance to an underground pedestrian crossing beforeThere isthe a largeintersection; passenger-forming point or an entrance to an underground pedestrian crossing • • Thebefore traffic the intersection;capacity of the street before the intersection is greater than after the intersection; • ImmediatelyThe traffic capacity after the of theintersection, street before there the is intersection an approach is greaterto the transport than after engineering the intersection; structure • (bridge,Immediately tunnel, after overpass) the intersection, or there is there a railway is an crossing. approach to the transport engineering structure • (bridge,Bus stops tunnel, are usually overpass) located or thereat the is exit a railway from the crossing. signalized intersection (after it), but with some exceptions, they can be located before the intersection. In both cases, with a high traffic intensity of Bus stops are usually located at the exit from the signalized intersection (after it), but with some PuT and PrT, traffic delays may occur (Figure 12). When creating new bus stops or reconstructing a exceptions, they can be located before the intersection. In both cases, with a high traffic intensity of PuT road with the existing designers of the road facility, it is necessary to determine the optimal and PrT, traffic delays may occur (Figure 12). When creating new bus stops or reconstructing a road parameters. with the existing designers of the road facility, it is necessary to determine the optimal parameters.

(a) (b)

Figure 12. Scheme of traffic traﬃc near the bus stop when it is located: ( a) after the intersection; ( b)) before the intersection.

In a situation shown in Figure 12b, the bus stop is located before the signalized intersection, and the time delays are longer than when the bus stop is placed after the intersection. The paper considers the most common placing of a bus stop after a signalized intersection. The research hypothesis is that if the length of the bus stop loading area increases, the delay time for PrT and PuT decreases; if the removal distance from the signalized intersection to the bus stop decreases, the delay time for PrT and PuT increases. The main delays for PrT and PuT in this situation consist of waiting for the arrival of buses at the bus stop, leaving the bus stop, and waiting for a permitting traffic signal. With an increase in the length of the bus stop loading area, the capacity the possible number of buses that can embark and disembark passengers increase. Thus, the wait time for a bus in the queue for entering the bus stop loading area decreases. The influence of the length of the loading area and the removal distance of the bus stop on the average delay time of PrT and PuT is described by linear, two-factor, additive mathematical models (Equations (17) and (18)):

𝑡 =𝑡 −𝑆 ∙𝐿 −𝑎∙𝐿 (17) Sustainability 2020, 12, 9593 13 of 18

In a situation shown in Figure 12b, the bus stop is located before the signalized intersection, and the time delays are longer than when the bus stop is placed after the intersection. The paper considers the most common placing of a bus stop after a signalized intersection. The research hypothesis is that if the length of the bus stop loading area increases, the delay time for PrT and PuT decreases; if the removal distance from the signalized intersection to the bus stop decreases, the delay time for PrT and PuT increases. The main delays for PrT and PuT in this situation consist of waiting for the arrival of buses at the bus stop, leaving the bus stop, and waiting for a permitting traﬃc signal. With an increase in the length of the bus stop loading area, the capacity the possible number of buses that can embark and disembark passengers increase. Thus, the wait time for a bus in the queue for entering the bus stop loading area decreases. The inﬂuence of the length of the loading area and the removal distance of the bus stop on the average delay time of PrT and PuT is described by linear, two-factor, additive mathematical models (Equations (17) and (18)):

Sustainability 2020, 12, x FOR PEER REVIEW 13 of 18 t = t S L a Lb (17) dPrT dPrT0 − 1· dis − · LA 𝑡 =𝑡 −𝑆 ∙𝐿 −𝑐∙𝐿 (18) t = t S L c Ld (18) dPuT dPuT0 − 2· dis − · LA where tdPrT—average PrT delay time, s; tdPrT0—average PrT delay time at the minimum value of the where tdPrT—average PrT delay time, s; tdPrT0—average PrT delay time at the minimum value of the bus bus stop length, s; Sj—parameter of sensitivity to changes in variables; LLA—length of the bus stop stop length, s; SL—parameter of sensitivity to changes in variables; LLA—length of the bus stop loading loading area, m; Ldis—removal distance of the bus stop from the signalized intersection, m; tdPuT— area, m; Ldis—removal distance of the bus stop from the signalized intersection, m; tdPuT—average PuT average PuT delay time, s; tdPuT0—average PuT delay time at the minimum value of the bus stop delay time, s; t —average PuT delay time at the minimum value of the bus stop length, s; a, b, c, length, s; a, b, cdPuT, d—0the model parameter of the power function. d—the model parameter of the power function. Figure 13 shows graphs of dependences of the average delay time on the length of the bus stop Figure 13 shows graphs of dependences of the average delay time on the length of the bus stop loading area. loading area.

(a) (b)

FigureFigure 13.13. InﬂuenceInfluence ofof thethe lengthlength ofof thethe busbus stopstop loadingloading area onon thethe averageaverage delaydelay time of: ( a) PrT; ((bb)) PuT.PuT.

TheThe influenceinfluence of of the the length length of of the the bus bus stop stop loading loading area area on theon the average average delay delay time time of PrT of andPrT PuTand (FigurePuT (Figure 13) is described13) is described by a power by a power function function and depends and depends on several on factors: several PuT factors: traffic PuT intensity,time traffic intensity, spent ontime embarking spent onand embarking disembarking and disembarking passengers, and passengers PrT traffic, and intensity. PrT traffic If the lengthintensity. of the If the bus length stop loading of the areabus increases,stop loading the averagearea increases, delay time the foraverage PrT and delay PuT time decreases. for PrT This and is duePuT todecreases. a decrease This in the is queuedue to of a busesdecrease arriving in the at queue the bus of stop. buses arriving at the bus stop. FigureFigure 1414 showsshows graphsgraphs ofof thethe dependencedependence ofof thethe averageaverage delaydelay timetime onon thethe removalremoval distancedistance ofof thethe busbus stop.stop. The influence of the removal distance of the bus stop from the signalized intersection on the average delay time of PrT and PuT (Figure 14) is linear and depends on several factors: PuT traffic intensity, throughput of the signalized intersection, time spent on embarking and disembarking passengers, and PrT traffic intensity. A significant decrease in the delay time occurs with an increase in the loading area length to 30 m, and the removal distance to 30 m. A further increase in the length of the loading area has a less intensive effect. Consequently, there are optimal parameters of the bus stop, at which further changes in parameters will be insignificant and ineffective. Since changing the parameters of the bus stop reduces the delay time for PrT and PuT, a comparison of changes in different modes of transport (by calculating the total delay time of the i-th mode of transport and total delay time) is not required. The analysis of the research results showed that the parameters of the infrastructure for public transport affect the travel time, and, consequently, the efficiency of public transport. Taking into account the average time delay of PrT and PuT, all dependencies are linear, monotonically decreasing or increasing. It is not enough to draw a conclusion about the effectiveness of measures for the development of infrastructure for public transport by the values of the average delay time of one vehicle separately for PrT and PuT. It is necessary to take into account the loss of time of all users of these transport systems. In this case, the minimum loss of time is achieved with other parameters of the infrastructure for PuT. Sustainability 20202020,, 1212,, 9593x FOR PEER REVIEW 14 of 18

(a) (b)

Figure 14. InfluenceInﬂuence of of the the removal removal distance distance of of the the bus bus stop stop on on the the average average delay delay time time of: of:(a) PrT; (a) PrT; (b) (PuT.b) PuT.

The novelty influence of ofthe the research removal results distance lies in of the the establishment bus stop from of the new signalized dependencies: intersection on the average delay time of PrT and PuT (Figure 14) is linear and depends on several factors: PuT traffic • Delay time on the length of the marking 1.11 before the regulated intersection on the road with intensity, throughput of the signalized intersection, time spent on embarking and disembarking the bus lane; passengers, and PrT traffic intensity. • Delay time on the length of the marking 1.5 before the regulated intersection on the road with A significant decrease in the delay time occurs with an increase in the loading area length to the bus lane; 30 m, and the removal distance to 30 m. A further increase in the length of the loading area has a less • Delay time on the length of bus stop loading area; intensive effect. Consequently, there are optimal parameters of the bus stop, at which further changes • Delay time on the removal distance of the bus stop from the regulated intersection. in parameters will be insignificant and ineffective. SinceThe results changing and the dependencies parameters ofobtained the bus stopare universa reduces thel and delay can time be applied for PrT andto other PuT, city a comparison transport ofsystems, changes for in the di followingfferent modes reasons: of transport (by calculating the total delay time of the i-th mode of transport• Technical and total characteristics delay time) of is notvehicles required. (car, bus, truck) operated in the USA, EC, Russia are Theapproximately analysis of at the the research same level; results showed that the parameters of the infrastructure for public transport• The road affect rules the travel adopted time, in and, different consequently, world countries the efficiency are often of public alike, transport. since these Taking countries into account(including the average Russia) time have delay joined of PrT the and Vienna PuT, allConvention dependencies on Road are linear,Traffic; monotonically decreasing or• increasing.Traffic organization It is not enough schemes to (including draw a conclusion Bus lane and about Bus the stop) effectiveness are approximately of measures the same for the in developmentdifferent ofcountries; infrastructure for public transport by the values of the average delay time of one vehicle• The separately versatility for of PrTsoftware and PuT. products It is necessary for traffic tomodeling; take into account the loss of time of all users of these• The transport problem systems. of traffic In jams this case,and improving the minimum the lossservice of time level is is achieved typical for with large other cities parameters in all world of the infrastructurecountries. for PuT. The novelty of the research results lies in the establishment of new dependencies: The established dependencies will specify measures to optimize the parameters of the public Delay time on the length of the marking 1.11 before the regulated intersection on the road with •transport infrastructure (length of the marking 1.11 or 1.5 before the regulated intersection on the roadthe with bus the lane; bus lane, bus stop parameters). This allows municipal authorities and urban transport Delay time on the length of the marking 1.5 before the regulated intersection on the road with the •planners to improve the quality of passenger traffic and, in some cases, the efficiency of traffic management.bus lane; Additionally, the following effects are obtained: Delay time on the length of bus stop loading area; • Reducing the number of citizens’ complaints about the work of public transport and increasing Delay time on the removal distance of the bus stop from the regulated intersection. • the satisfaction of citizens with the work of municipal authorities; • The resultstravel time and for dependencies urban residents obtained will aredecrease; universal and can be applied to other city transport systems,• The forefficiency the following of highways reasons: will increase due to a more even loading of the road lanes and an Technicalincrease in characteristics the service life ofof the vehicles asphalt (car, concrete bus, truck)pavement operated on the inlanes the for USA, private EC, vehicles; Russia are • approximatelyThe level of aggression at the same and level; the number of conflicts on the part of drivers of private transport will decrease by reducing the idle time at intersections; The road rules adopted in different world countries are often alike, since these countries (including • The number of emergency situations will decrease due to a more even movement of traffic flows Russia) have joined the Vienna Convention on Road Traffic; and a decrease in the number of line changes on a limited section of the road; Traffic organization schemes (including Bus lane and Bus stop) are approximately the same in • Emissions of pollutants with car exhaust gases will decrease. different countries; Sustainability 2020, 12, 9593 15 of 18

The versatility of software products for traﬃc modeling; • The problem of traﬃc jams and improving the service level is typical for large cities in all • world countries.

The established dependencies will specify measures to optimize the parameters of the public transport infrastructure (length of the marking 1.11 or 1.5 before the regulated intersection on the road with the bus lane, bus stop parameters). This allows municipal authorities and urban transport planners to improve the quality of passenger traffic and, in some cases, the efficiency of traffic management. Additionally, the following effects are obtained:

Reducing the number of citizens’ complaints about the work of public transport and increasing • the satisfaction of citizens with the work of municipal authorities; The travel time for urban residents will decrease; • The efficiency of highways will increase due to a more even loading of the road lanes and an • increase in the service life of the asphalt concrete pavement on the lanes for private vehicles; The level of aggression and the number of conflicts on the part of drivers of private transport will • decrease by reducing the idle time at intersections; The number of emergency situations will decrease due to a more even movement of traffic flows • and a decrease in the number of line changes on a limited section of the road; Emissions of pollutants with car exhaust gases will decrease. • The introduction of separate lanes for public transport will make it possible to more effectively use the priority of crossing intersections for public transport through adaptive control of traffic lights.

4. Conclusions The results show that when LoS < 1, optimization of the parameters of the bus lane and bus stop is not required; however, the largest number of passengers, in cars and buses, is on the road network during peak hours. Based on the simulation results, at high traffic intensity (LoS 1), corresponding to ≥ peak hours, the influence of the parameters of the infrastructure for public transport on the delay time is not linear and it is possible to determine the optimal value’s length of the marking line 1.11 or 1.5. In the paper, the proposed mathematical model is derived from using simulation modeling. This model has some limitations. We assume that bus-overtaking maneuvers are prohibited and that the probability that the bus on each berth first finishes passenger serving is identical when all the berths are occupied. In addition, we assume that passengers board and disembark at a fixed time. Transport modeling makes it possible to determine the optimal parameters of the infrastructure for PuT on the road according to the criterion of traffic management efficiency. These parameters must be taken into account in the design of new and reconstruction of existing highways. Unfortunately, at present, insufficient attention is paid to the infrastructure for public transport in the design of roads. The country’s authorities began to pay increased attention to the development of public transport in Russian cities. Programs for renewing the rolling stock of fixed-route transport in cities and co-financing of costs from the federal budget have appeared. However, the purchase of new rolling stock alone cannot solve the goals set in the urban transport planning documents. A set of measures is required to reduce the proportion of movements by private transport and improve the quality of public transport. Traffic simulation is very widespread in the world. Its application allows you to “look into the future” and assess transport demand and road conditions in a situation that is not currently observed. According to some European studies, in order to maintain a social distance to reduce the risk of COVID-19 disease, the carrying capacity of public transport while maintaining passenger traffic that sufficed before the pandemic should increase by 2.5 times. The authors of the article plan to continue research on the topic and conduct field tests in order to assess the compliance of the research results with the actual parameters of the total delay time. The existing road and transport infrastructure in large cities of Russia was created according to outdated regulatory documents and often does not Sustainability 2020, 12, 9593 16 of 18 meet new challenges, such as the growth of motorization, the introduction in cities of measures to prioritize public transport, and the impact of the COVID-19 pandemic on society, the economy and the transport system cities. Therefore, according to the authors, to update the regulatory documents requires research on this topic.

Author Contributions: Conceptualization, Z.D.; formal analysis, F.A.; investigation, F.A.; project administration, F.A.; methodology, F.A.; supervision, Z.D.; validation, Z.D.; data curation, F.A.; funding acquisition, Z.D.; writing—review and editing, F.A., Z.D. All authors have read and agreed to the published version of the manuscript. Funding: The article was prepared as part of the implementation of a state assignment in the field of science for scientific projects carried out by teams of researchers in scientific laboratories of higher educational institutions subordinate to the Russian Ministry of Education and Science on the project: “New patterns and solutions for the functioning of urban transport systems in the paradigm ‘Transition from owning a personal car to mobility as a service’” (No. 0825-2020-0014, 2020–2022). Conflicts of Interest: The authors declare no conflict of the interest.

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