Abstract
It is known that many variables influence traffic, yet very little is known about the weight of each factor in the dynamics of traffic in cities of developing countries, in many cases due to their peculiar traffic regulations. In this work, we search for the variables that have the most significant impact on the average travel speed of three distinct types of vehicles: passenger cars, taxis, and buses. First, we developed a tool featuring algorithms that simulate ordinary overtaking and car-following behaviors, along with controls for setting vehicles’ actions, particularly buses’ and taxis’ stops. Then, we chose a particular zone to study, based on its common geometry and the particular traffic infrastructure (speed bumps, traffic lights, and bus stops) inside it. Later on, three experiments were carried out, with the following results. (1) Both the buses’ arrival frequency and curbside bus stops affect the passenger cars’ average travel speed. The buses’ response was affected by the bus bay and curbside bus stops. The buses’ speed tendency influenced neither the passenger cars’ nor buses’ response. (2) Taxis’ arrival frequency, stopping frequency, and speed tendency were found to influence the passenger cars’ response. Taxis’ response was altered by taxis’ speed tendency, while buses’ response was affected by taxis’ arrival frequencies. (3) The number of speed bumps, the arrival frequency of passenger cars, and their speed conditions (homogeneous and heterogeneous) affect the passenger cars’ response. We expect that the findings presented in this study, along with the recommendations made from the results, may pave the way for better road design public policies.
1. Introduction
The main objective of the present study is to achieve a better understanding of low travel speed. We conducted all research in an area with compromised vehicle velocity. The zone under study possesses regular traffic infrastructure, such as speed bumps, traffic lights, and bus stops. It also has regular city traffic, i.e., buses, taxis, and passenger cars (hereafter just cars).
The appropriate combination of factors to sustain acceptable traffic speed (i.e., below but close to the speed limit) while avoiding undesirable traffic speed (i.e., far below the speed limit) is a functional problem under intense investigation in the field (e.g., references [1–8]). In the present investigation, we want to identify the variables that most affect the average travel speed. To do so, we will answer the following three questions:(1)Are the buses’ arrival frequency and speed tendency, bus bay, and curbside bus stops the variables that influence the average travel speed of cars and buses?(2)Are the taxis’ arrival frequency, stopping frequency, and speed tendency the variables that affect the average travel speed of cars, taxis, and buses?(3)Are the number of speed bumps, cars’ arrival frequency, and cars’ speed conditions (homogeneous and heterogeneous) the variables influencing the cars’ average travel speed?
Developing countries face serious traffic problems [9] and some of these not count with field traffic data to conduct investigations, so that new technologies as traffic simulations are a suitable (economic) choice. We employed an in-house developed simulator to model the interaction between cars, buses, and taxis. Such smart interactions, and reactions to traffic infrastructure, allowed our simulator to show which variables have stronger effects on the average travel speed. Henceforth, we performed a set of simulations to answer our research questions.
Some variables are associated with driver behavior (e.g., the speed tendency—see definition below), while others are related to traffic infrastructure (e.g., speed bumps). By detecting the variables that impact speed and how they affect it, we gain further understanding about what causes detrimental effects. Hence, we gain further understanding that may lead to better public policies.
The literature review that follows presents several well-proven models that, unfortunately, fall short in answering our specific research questions, yet it proves that such a task is possible. In addition, it presents references that investigated the effect of buses, taxis, and traffic infrastructure such as speed bumps. In our work, we investigate the effect of several factors on the vehicles’ average travel speed that the literature suggests have an impact on traffic.
The rest of this work is organized as follows. In Section 2, we present the literature review. Section 3 deals with the method: avenue under study, design of the simulation tool, and experimental details. In Section 4, we present the statistical results of each experiment and compare the simulations’ outcome (the average travel speed, also called response or output) in order to gain insight of the variables that affect it. Finally, in Section 5, we summarize the conclusions of our work and state the contributions we made.
2. Literature Review
2.1. Buses
The implications of improper bus stop locations in New Delhi, India, were investigated in [10]. In India in 2001, the percentage of fatal crashes that occurred near a bus stop was 6.2%, and in 2009, it was 7.0% [11]. In this study, it was observed a deficiency of sufficient space to stop and perform maneuvers and also pedestrian activity outside regulations. The effect of bus stops on traffic is analyzed in [12]. This paper correlated the traffic flow stability with bus stops and normalized density. The finding in a two-lane-30 km-long highway, where vehicles cannot overtake during buses’ boarding/alighting periods, is that six or more bus stops affect the stability of traffic flow.
The relation between bus impact time and curb lane capacity of roadways in Beijing is presented in [13]. The bus impact time (without dwell time) is the amount of time since the bus starts to decelerate until it stops (in a bus bay stop), plus the time since accelerates to re-enter the road until it reaches another vehicle’s speed. With data from 15 bus bay stops, it was found that the relation between average bus arrival frequency and average bus impact time is best explained with a power model.
The work described in [14] deals with simulations of non-lane-based heterogeneous traffic. Distinct flow measurements of the vehicles’ average speed for a 400 m road length (200 m on each side of a bus stop) were done. The simulation considered curbside and bus bay bus stops and dwell times of 10 s, 20 s, and 30 s. The investigation in [15] analyzes the relationship between volume and speed in the presence of bus bay or curbside stops (using midblock location) with a bus arrival frequency of 10 min. In the case of vehicles per hour per lane = 480 and curbside stops, the speed difference between dwell times (20 s, 40 s, and 60 s) is quite small (about 2.5 mph between each other). Moreover, there is no significant speed difference for the bus bay stop case regardless of the dwell time.
In [16], simulations are used to establish the impact of the bus occupancy ratio (number of buses/number of vehicles) on traffic flow capacity. It was observed that traffic flow decreases as the occupancy ratio increases. The variables studied were speed and brake response time of cars and buses, safety following-distance, deceleration capabilities, and occupancy ratio. Reference [17] also utilizes simulations that consider the space occupation rate of buses (the sum of all circulating buses’ length divided by the sum of the lanes’ length) and the space occupation rate of cars, in order to analyze the influence of buses on other vehicles.
2.2. Taxis
Taxis have a significant effect on traffic, as shown in the following references. In [18], a study in Nanjing, China, identifies the percentage of taxis and cars that were involved in one of the following risk-taking behaviors: failure to yield the right-of-way, sudden lane change, inadequate stop, unnecessary passing, and failure to stay in lane. In these five situations, taxis’ percentage was greater than that of cars.
In [19], the presence of taxis in a road section and its impact on vehicle dynamics was studied. Employing simulations, three taxi behaviors were explored: (1) a taxi makes a stop to pick up or drop off passengers, (2) a taxi slows down to inquire destination information, and (3) a taxi circulates at low speed seeking for customers. In another study [20], the time that taxis utilize to pick up or drop off passengers (blockage time) is investigated. Measurements were made in outlet legs of signalized intersections in Rasht City, Iran. From the observations of four intersections, the average parking maneuver was 7.37 s, and the average blockage time was 11.31 s (ranging from 8.85 s to 12.56 s).
Passenger car units per hour (PCU/h) and speed range regions were measured in the center of Patras, Greece [21]. An augmented Naïve Bayesian network was developed to associate variables. The results determine the order of importance of the relevant variables: travel speed, volume, taxis%, motorcycles%, trucks%, cars%, and buses%. It was found that the taxis percentage (among all vehicles percentages) is the major contributor to the speed-volume relation.
2.3. Bumps and Speed-Calming Devices
In [22], the study centered on determining if speed bumps actually reduce the vehicles’ speed. For this, speed observations were made in Cagliari, Italy, where the set speed limit was 50 km/h. The speed bump geometry was 30 mm high and 600 mm wide, and the speed bump was made of rubber. Their intended purpose is to protect crosswalk areas located about 20–25 m after them. In 30% of the cases, the 85th percentile speed (at the speed bump) was higher than the speed limit, 26% lied between 45 and 50 km/h, and for the remaining cases, the speed was under 45 km/h.
The social perspective towards the installation of speed bumps on Nigerian highways was studied in [23], via questionnaires. In one survey, 72% of persons answered that without bumps the vehicles’ speed is very high, 14.57% responded just high, and the remaining percentages were 6.86% and 6.57%, corresponding to low and very low speeds, respectively. In another questionnaire, 52.86% answered that bump speed is low and 29.14% responded very low, while 3.14% and 14.86% corresponded to very high and high speeds, respectively.
In [24], the study centered on speed bumps and their effectiveness in reducing vehicles’ speed in Nanjing, China. The mean speed at the bump position, 500 m after, and 500 m before (control locations) was measured. T-tests showed that the speed difference at the bump and at the control locations is significant.
Reference [25] presents a study of the effectiveness of three-dimensional speed markings (i.e., painted on the road) and speed bumps. This infrastructure was intended to reduce the speed on work zones with a speed limit of 40 km/h. The speed bump effectively reduced the average speed, which was 11 km/h behind the speed bump.
The average speed to traverse a 1400 m road (with speed limit = 50 km/h) before and after the installation of 3 sinusoidal speed humps and 2 chicanes was measured in [26]. Before the speed-calming measure installation, the overall mean speed was 53.5 km/h. After the installation, this value changed to 49.4 km/h, concluding that the speed-calming devices indeed have a speed-reduction effect.
In [27], modelling was done on the vehicles’ speed profile in York, England. This was modelled on roads with the following traffic calming devices: speed tables, humps, cushions, and chicanes. To explain the speed profile, the following variables were considered: entry speed, distance to the next calming device, distance from the passed device, and calming device presence (absence).
3. Materials and Methods
3.1. Avenue Selection
We were interested in a place with low speed (see [28]). The selected avenue was Miguel Hidalgo, in Lerma (Mexico state), since its geometry (two lanes, same direction both), its traffic infrastructure, and the vehicle speed on it are common in Mexico state. Thus, the results in this work could apply to places with similar characteristics. Following [24], the avenue was divided into four segments, each of 500 m length. Specific traffic conditions occur in each segment because each has different traffic infrastructure (see Table 1). The observations mentioned in this work were extracted from video recordings made in October 2017. Additionally, the traffic lights’ cycle times were set in the simulator to match the real timings closely. The speed bumps on segments , and force the vehicles to reduce the speed to , a similar value as reported in [25].
Segment has two speed bumps at location 141 m (measured from the start of the segment) and 397 m. has two speed bumps at 85 m and 260 m, one curbside bus stop at 99 m, and one bus bay bus stop at 488 m. has one traffic light at 163 m and one bus bay bus stop at 220 m. has three speed bumps at 137 m, 211 m, and 440 m, two traffic lights at 46 m and 87 m, one bus bay bus stop at 65 m, and one curbside bus stop at 445 m.
3.2. Simulation Tool
We choose Unity Engine (used for traffic analysis in [29, 30]) to develop a simulation tool (scripts and scenario). In the simulator, variables related to vehicles can be set, such as the taxis’ stopping frequency and the buses’ dwell time. Also, it measures the vehicles’ travel speed to traverse an avenue segment. The C# scripts to regulate the vehicles’ behavior are presented as algorithms. For overtaking, see Algorithm 1. For accelerating, decelerating, and follow another vehicle, see Algorithm 2.
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The overtaking algorithm was designed to be consistent with expected human behavior. The need for overtaking is triggered when a vehicle desires to attain a higher speed than the vehicle in front, which for some reason circulates slowly, or when in the proximity there is a static obstacle, as it can be a bus or a taxi that is completely stationary. Additionally, a vehicle overtakes only when it is safe to do so. In Algorithm 1, the Overtaking() function allows a vehicle to overtake if there is no collision risk, which depends on the speed of the vehicles located ahead and behind in the other lane of the current vehicle, and if there is no vehicle at its side. The first IF detects the need to overtake comparing the speed of the current vehicle (and the speed tendency) with the speed of the vehicle in front. It also accounts for the AD of the latter. The second IF detects the convenience to overtake comparing the speed of the vehicle in front with the speed of the vehicle in front in the other lane and the distances and . The speed tendency (or preferred speed, hereafter used interchangeably) is the top speed that a vehicle will try to reach without exceeding it. The distance between vehicles is measured from the front of the current vehicle to the back of the vehicle ahead.
In Algorithm 2, for maximum acceleration and for maximum deceleration, similar to the values presented in [31]. Variable is defined in equation (1), is defined in equation (2) (an analogue formula applies to ; just replace with ), and is defined in equation (3). The constant is approximately the mean perception-brake response time observed in [32]. Constant is in the headway mode range presented in [33], which is 1.8 to 2.2 s for densities between 20 and 80 PCU/km. If the distance between the current vehicle and the vehicle in front is less than or equal to the safe distance between the two, the current vehicle decelerates; otherwise, the algorithm applies the following rules: (1) if the headway is larger than or equal to the headway tendency plus 0.3 seconds, the current vehicle accelerates, (2) if the vehicle speed is larger than or equal to the 110% of the speed tendency, the current vehicle neither accelerates nor decelerates, (3) if the headway is less than or equal to the headway tendency minus 0.3 s, the current vehicle decelerates, and (4) if the headway is in the interval (1.8 s, 2.1 s], the current vehicle AD = 0. The speed is limited in case 2, and in case 4, a relaxation state is reached in which there is no need of taking AD actions.
Even though Algorithm 1 cannot include 100% of the human reaction possibilities to decide when and how to overtake and Algorithm 2 cannot do the same for the AD actions when following another vehicle, these cover common intuitive behaviors. The vehicles considered in the simulations of the experiments that follow are of three types: cars (width = 1.7 m and length = 4.2 m), taxis (same geometry as cars), and buses (width = 2.5 m and length = 10.3 m).
The variable flow for a certain vehicle type varies from one simulation to another around the observed value in the avenue under study in calm hours. Thus, the traffic dynamics of each simulation could be consistent with that of other avenues with equal number of lanes and comparable flow for each vehicle type. As random processes were not included in the traffic (out of the scope), there is no need to run multiple simulations per variable configuration to achieve output convergence. The simulation time of each simulation of the three experiments is 900 s.
3.2.1. Experiment 1: Buses’ Related Variables
Simulations in experiment 1 were configured as follows: the entrance speed of all vehicles is 40 km/h, and buses’ dwell time is 30 s (the time they wait at bus stops), following the range from 8 to 35 s reported in [34]. After the dwell time, a bus in a bus bay stop tries to re-enter the circulation if possible. If not, after 10 s (by a programmed rule), a vehicle circulating in the lane adjacent to the bus stop, and behind the bus, decelerates to allow the bus to re-enter. For the curbside bus stop, the dwell time is also 30 s, during which the circulation of the vehicles behind is obstructed. Buses circulate only in the rightmost lane and therefore do not overtake. If a vehicle overtakes, it waits for 5 s to do it again in case it has to, imitating a driver who does not overtake immediately once it has; instead, it waits to understand the traffic around him before attempting to perform an overtaking maneuver once again. A car arrives per lane every 7.5 s (or per avenue each 3.75 s). The cars’ speed tendency is 60 km/h. The average travel speed (ATS) is calculated with equation (4), the travel speed of the -th vehicle is , is the length of the j-th segment, and is the time that the -th vehicle needs to traverse . Subindex T indicates the vehicle type, T = {car (c), bus (b), taxi (t)}. is the total number of vehicles of type T in the simulation.
Segment is the scenario of the simulations of experiment 1. We selected four variables (factors): time interval between buses arrival (), buses’ speed tendency (), a bus stop obstructing the circulation (curbside stop, denoted as BS1), and a bus stop in a space designated to not interfere with circulation (bus bay stop, denoted as BS2). The time interval between buses per avenue takes values around 100 s (from observations each a bus enters the avenue), and hence = {50 s, 100, 150, 200}. Buses’ speed tendency ranges between 30 and 60 km/h; therefore, = {30 km/h, 40, 50, 60}. The presence of factor BS1 (or BS2) is set with 1 and absence with 0, and thus BS1 = {1, 0} and BS2 = {1, 0}.
The variables’ values of each simulation are presented in Table 2, along with the average travel speed of cars () and buses (). An orthogonal experimental design was adopted, following the approach in [35]. In Table 2, columns 2 through 5 conform an orthogonal array.
The minimum number of simulations (NS) to obtain meaningful results is calculated with the following equation (see [36]):
Index i = 1…k is used to enumerate cases. The i-th case corresponds with a number of levels and the number or factors with that many levels. = number of factors and = number of levels. In experiment 1, we have two factors with four levels and two factors with two levels, and hence . Nevertheless, 16 simulations were performed for completeness.
3.2.2. Experiment 2: Taxis’ Related Variables
The simulation parameters from experiment 1 remain mostly the same for experiment 2, with the following differences: a bus arrives every 86 s, vehicles entrance speed is 30 km/h, and buses’ and cars’ speed tendency is fixed at 60 km/h. To perform simulations, we selected segment which has one bus bay stop and one traffic light (green time = 30 s, yellow = 3 s, and red = 27 s).
The objective is to determine which variables related to taxis have an impact on the average travel speed of cars (), buses (), and taxis (). The variables are speed tendency of taxis = {40 km/h, 50, 60}, time interval between taxis per avenue (from observations each a taxi enters in one of the two lanes) = {9 s, 18, 27}, and the time interval between stops (i.e., when a taxi makes a stop to drop off or pick up customers and after 5 seconds, the time lapse until it decelerates to stop for the same reason) TS = {30 s, 45, 60}. The taxi blockage time, to pick up or drop off passengers, is 5 s. This time is set relatively short as taxis stop at any lane. In the avenue under investigation, taxis have a defined route and collect and drop customers during their journey and transport as many clients as they can carry.
Table 3 shows the variables’ values in an orthogonal array (columns 2 to 4) and the measured average travel speed of each vehicle type. The array has three factors with three levels each; therefore, . Nonetheless, we perform two more simulations for completion.
3.2.3. Experiment 3: Cars’ and Traffic Infrastructure Related Variables
The objective is to determine the impact of (1) speed bumps, (2) the time interval between cars, and (3) cars’ preferred speed (heterogeneous and homogeneous speed cases), in the cars’ average travel speed. For our simulations, we selected segment , which has three speed bumps and two intersections with a traffic light in each one. Seven cars enter the avenue per intersection per traffic light cycle. The first traffic light, numbered in the traffic flow direction, has a green time = 42 s, yellow = 3 s, and red = 45 s. The second has a green time = 67 s, yellow = 3 s, and red = 20 s. The cars from upstream enter with a speed of 40 km/h and from the perpendicular streets at 15 km/h. A car decelerates to a speed of 10.8 km/h to pass a speed bump (see [25]).
Speed bumps are denoted with B = {3, 2, 1, 0}. The value of B is associated with the number of speed bumps in the simulation, e.g., if B = 2, one speed bump is removed (from downstream to upstream) and two remain. The time interval between cars per avenue is or that per lane is . The cars’ preferred speed is = {HE, HO}. In the heterogeneous (HE) case, the speed is uniformly and randomly assigned so that 50% of the cars’ preferred speed = 60 km/h and that of the other half = 40 km/h. In the homogeneous (HO) case, the preferred speed = 50 km/h for all cars. is calculated considering the cars traveling from the start of , excluding the cars from perpendicular streets. Table 4 shows the variables’ values and the output of each simulation. Columns 2 to 4 conform an orthogonal array, with (one factor with four levels and two factors with two levels) plus two more for completeness.
4. Results and Discussion
4.1. Experiment 1
ANOVA was conducted to determine the factors influencing a response (the average travel speed of a vehicle type). The analysis of variance results, with the data in Table 2, is presented in Table 5. In the following, considering 90% confidence intervals (unless otherwise mentioned), a factor with value <0.1 influences the response, i.e., it is significant.
With as the response, factors and BS1 are significant. Factor BS2 does not influence , as a bus does not interrupt the circulation when it waits in a bus bay stop. Also, as cars are able to overtake slow buses most of the time, factor is not influencing the response.
If is the response, factor is slightly significant (with 80% confidence intervals, 0.1866 < 0.2), while factors BS1 and BS2 (curbside and bus bay stops, respectively) both impact , as a bus waits during the dwell time either if it is in a bus bay or a curbside stop. BS2 is impacting slightly more the response than BS1, mainly because a bus spends time to re-enter in the circulation lane if it is in a bus bay stop. Factor is not influencing since buses (ideally) do not interfere with each other not even at the shortest time between buses’ arrival (50 s).
Simulation 8 ( = 43.1593 km/h) is compared with a new simulation (numbered 17, not shown in the respective table), with factors = 100 s, = 60 km/h, BS1 = 1, BS2 = 0, and response = 40.9953 km/h. Then, BS1 does change. The percentage (P) of reduction, since buses stop at the curbside stop (simulation 17), is calculated with equation (6) (which calculates a loss, or a gain, in percentage). Thus, with = 43.1593 km/h and = 40.9953 km/h, there is an loss of 5.01% from simulation 8 to simulation 17.
drops if there is a curbside stop. To measure the loss, we compare simulations in pairs, with same and different BS1 (the other influencing factor). Comparing simulation 3 vs 4, the response drops to 10.74%. From 8 vs 7, it drops to 5.23%. From 12 vs 11, it drops to 3.08%. From 15 vs 16, it drops to 2.45%. Then, the response’s loss drops as of the compared simulations increases.
Also, is influenced by . We compared simulations with same BS1 = 1 and different . By comparing simulation 7 vs. 4, the response drops to 6.13%. From 10 vs 7, it drops to 2.15%, and from 16 vs 11, it drops to 0.64%. Again, we observe that the percentage becomes smaller as the compared values become larger. Yet, when comparing simulations with same BS1 = 0 and different , we notice almost the same response: the of simulation 3 is 43.01 km/h, that of 6 is 43.02 km/h, and that of 12 and 15 is 43.13 km/h. Hence, without curbside stop, the buses’ arrival time interval in the range 50 s to 200 s has no impact in the .
With being the response, ANOVA shows that both BS1 and BS2 significantly affect . Comparing simulation 8 (BS1 = 0, BS2 = 0) with 4 (BS1 = 1, BS2 = 1), the response percentage loss is 61.07%. There is no evident response difference between simulation 12 (), with a bus bay stop (BS2 = 1), and simulation 16 (), with a curbside stop (BS1 = 1). Considering simulations 1, 6, 15, and 12, all with BS1 = 0 and BS2 = 1, increases from simulation 1 to 12 in 20.95%, since variable also increases (from 30 to 60 km/h).
4.2. Experiment 2
ANOVA results (with data in Table 3) are presented in Table 6. All factors impact , factor affects , and factor affects . In addition, considering 80% confidence intervals, and also have an effect in , and also has an effect in .
From Table 3, simulation 4 has the lowest , with and at minimum values. Simulation 8 presents the highest , with and at maximum values. Thus, the relevance of in is made evident.
The percentage gain between simulation 4 (minimum values of and ) and simulation 6 (maximum values of and ), both with , is 9.47%.
We compare simulation 2, with and at minimum values, and simulation 8, with and at maximum values, both with , finding an gain of 12.86%.
We perform two more simulations: simulation 10, with , resulting in ; simulation 11, with , resulting in . Comparing simulation 10, with and minimum values, and simulation 11, with and maximum values, both with = 50 km/h, the gain is 14.94%.
To evidence the significant impact of in , we cluster simulations according to speed tendency in three groups (see Table 7). Notice that, by arranging data, first in subgroups of SLt, then inside these subgroups by ascending TS, the table self-orders in ATSt. Hence, is firstly affected by and secondly by .
The factor significantly influencing is . In Table 3, simulations 1, 2, and 3, with , present close values of , with the average being . For simulations 4, 5, and 6, with , the response is increasing along with , with the average being . The same occurs for simulations 7, 8, and 9, with and average response of . Then, is firstly affecting , followed by . Comparing simulation 3 () and 9 (), both with , the response gain is 9.04%.
4.3. Experiment 3
ANOVA results (with data in Table 4) are shown in Table 8. All factors impact .
To compare simulations with different number of speed bumps and other factors at equal values, additional simulations were performed (see Table 9).
By reducing B, increases. With and (likely for real traffic), we compare simulations with a different number of bumps. Comparing simulation 2 (B = 3) and simulation 12 (B = 2), there is a gain of 9.95%. Comparing simulation 2 vs 6 (B = 1), the gain is 18.12%. Comparing simulation 2 vs 16 (B = 0), the gain is 30.61%. Following this comparison logic, with and , we obtained gains of 6.84%, 19.0%, and 27.67%. With and , gains are 8.88%, 19.97%, and 36.04%. With and , gains are 9.23%, 21.29%, and 41.58%. Averaging the gain results with 3 speed bumps vs 2, the gain is 8.72%. The average gain of 3 speed bumps vs. 1 is 19.59%, and increases to 33.97% for the average gain of 3 speed bumps vs. no speed bumps. It is clear that regardless of the values of and , speed bumps harm the response.
The response in homogeneous traffic without speed bumps is approximately the same regarding , for simulation 15 () and for simulation 8 (). Following this idea, we calculate the response gain comparing simulation 5 vs 14 (1 speed bumps each), simulation 11 vs 4 (2 speed bumps each), and simulation 1 vs 10 (3 speed bumps each). The average percentage gain of the four cases is 2.88%.
In heterogeneous traffic without speed bumps, there is a notorious response difference between a simulation with and one with , corresponding to simulation 7 () and simulation 16 (), respectively. Following the idea, we compare simulation 13 vs 6 (1 speed bumps each), simulation 3 vs 12 (2 speed bumps each), and simulation 9 vs 2 (3 speed bumps each), to calculate the response gain. The average percentage gain of the four cases is 7.04%. Then, in heterogeneous traffic, the response changes because is more evident.
The average speed tendency in heterogeneous traffic () is 50 km/h (50% of the cars’ speed tendency = 40 km/h and 50% is 60 km/h), and the average speed tendency in homogeneous traffic () is also 50 km/h (100% of the cars’ speed tendency = 50 km/h). Even though that in both traffic configurations (HE and HO) the average speed tendency is the same, the average travel speed is different. There is an percentage gain of a simulation with over one with , both with and same B. Simulation 10 vs 2 (with 3 speed bumps each) presents a gain of 3.51%. Simulation 4 vs 12 (with 2 speed bumps each) presents a gain of 2.51%. Simulation 14 vs 6 (with 1 speed bumps each) presents a gain of 5.13%. Simulation 8 vs 16 (with 0 speed bumps each) presents a gain of 7.81%. The average gain of the four cases is 4.74%. Also, there is an percentage gain of a simulation with over one with , both with and equal B. Simulation 1 vs 9 (with 3 speed bumps each) presents a gain of 5.08%. Simulation 11 vs 3 (with 2 speed bumps each) presents a gain of 7.43%. Simulation 5 vs 13 (with 1 speed bumps each) presents a gain of 7.1%. Simulation 15 vs 7 (with 0 speed bumps each) presents a gain of 16.53%. The average gain of the four cases is 9.04%. The advantage of homogeneous over heterogeneous traffic is evident.
4.4. Research Questions
The answers to our investigative questions are as follows:(1)It was found that a curbside stop and the time interval between buses’ arrival (in that order of relevance) modify the cars’ average travel speed. Buses’ average travel speed is affected by bus bay and curbside stops.(2)The time lapse between taxis’ arrival, speed tendency, and frequency to make a stop impact (in the order presented before) the cars’ average travel speed. Taxis’ average travel speed is influenced mainly by taxis’ speed tendency. Taxis’ arrival frequency influences buses’ average travel speed.(3)It was found that the three factors: speed bumps, speed tendency configuration, and time interval between cars arrival, significantly affect (in the order presented) the cars’ average travel speed.
5. Conclusions
The percentage loss (due to the curbside bus stop) of the compared simulations with same and different BS1 ranges from 2.45% to 10.74%. Then, from a traffic design perspective, it is preferable to avoid curbside stops, so that buses do not make stops in a way that obstructs circulation. Instead, bus bay stops are suitable, since BS2 has no significant effect on . From the simulations compared with same BS1 = 1 and different (as this variable affects ), the percentage loss is in the range 0.64% to 6.13%. Therefore, could be adjusted based on a supply and demand basis.
The percentage gain, if a bus travels at the minimum preferred speed (30 km/h) compared with the maximum (60 km/h), is 20.95%. Thus, the connection between buses’ preferred speed and is evident.
As TS influences , it could be beneficial that taxis had designated spots (similar to bus bay stops for buses, or even sharing these) to not obstruct the circulation when these pick up or drop off customers. In this way, a taxi is not motivated to travel at low speed (since is influencing and ) trying to find customers along the way. As impacts and , if the number of taxis circulating do not match the number of customers (as it is likely in the avenue under study), it is recommended to find the values (considering time and day) that balance supply and demand.
In experiment 3, we found that B affects , regardless of and . By gradually removing speed bumps, we noticed improvements in the response. For the avenue studied and other similar avenues, we suggest that if a speed bump is not in a space that actually benefits pedestrians, it should be removed. With B = 0 and , there was no response improvement when extending . With , for both homogeneous and heterogeneous cases, improves as cars arrive less frequently. As influences and as is connected with the number of cars in circulation which in turn increases year after year, persons with transportation needs could be motivated, through better public transport services and adequate infrastructure, to use other means of transportation rather than private vehicles, such as public transport or bicycles (this poses the problem of a dedicated bicycle lane). As impacts and as homogeneous speeds were proven convenient than heterogeneous, it is important to have suitable traffic infrastructure (quality streets with the right capacity, proper quantity, and location of speed bumps and traffic lights, among others) since drivers partly decide their driving speed considering that, so more drivers could be motivated to reach an acceptable speed (without exceeding the legal speed limit) and keep it.
The contributions are summarized as follows:(1)The simulation tool: it allows for the manipulation of the driving behavior for cars, taxis, and buses. For the last two, the frequency and period of stops can be set. The simulator offers the option to measure the speed of each vehicle separately.(2)As the scenario to perform simulations, it was selected a common two-lane one-way avenue with regular traffic infrastructure: speed bumps, traffic lights, and bus stops. The vehicles’ interaction dynamic was designed to be intuitive and implemented with algorithms. Although the variables that influence speed in other locations might not be the same than those detected in this study, the method and analysis presented in this investigation are applicable to analogue situations.(3)With the method presented, we identified among the selected variables related to each vehicle type, which most significantly affect the travel speed.(4)The results may help to identify traffic problems and to propose solutions in the realm of public policies and infrastructure improvements, and consequently, people’s quality of life could be improved. Even more importantly, traffic mitigation has the added benefit of decreasing the greenhouse emissions of vehicles.
Data Availability
The simulation data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.