Operating Speed Prediction Models for Tangent Segments: A Brief Review

This paper provides a review of studies aimed at developing operating speed prediction models for road tangent sections. The review included many studies, conducted in different geographical areas of the world, in terms of road classification, types of vehicles, techniques and devices used in data collection, number of study sites, the principle adopted in extracting the free-flow speed, as well as the topography that the road path passes through and grads of the studied sections. Moreover, this review mentioned the analysis methods adopted in the modeling, and included the model formulas that the researchers have reached in their studies, as it showed all the geometric elements and traffic characteristics that appeared in the models as independent variables. The author has avoided critiquing or evaluating the methodologies of the reviewed research and accordingly this paper has been prepared for documentation only. The author aims primarily to save the effort and time of graduate students and researchers interested in modeling the operating speed on straight segments, as all data and information are arranged in tables and coordinated for this purpose.


Introduction
Vehicle speed is the most important factor in the design process for the various geometric elements of roads. Speed is the key value in assessing design consistency and the primary reference in driver behavior and traffic safety research [1,2]. In the design stage, the design engineer selects a value of speed known as "design speed" and then the design values of all road features are calculated. Krammes [3], however, reported that the design of highway features based on design speed does not necessarily yield uniformity of operating speeds. Therefore, researchers have started to promote the operating speed concept in an attempt to reduce the disparities of operating speeds.
The operating speed is defined in the Green Book by the American Association of State Highway and Transportation Officials [4] as "the speed at which drivers are observed operating their vehicles during free-flow conditions. The 85th percentile of the distribution of observed speeds is the most frequently used measure of the operating speed associated with a particular location or geometric feature".
In other words, eighty-five percent of drivers do not exceed the value of operating speed under free-flow conditions, and for calculation purposes, it is expressed to the 85th percentile free-flow speed [5]. Among other measures, operating speed can be used to evaluate the design consistency of roadways by evaluating the difference between speeds on successive elements [6]. With the widespread development of the concept of "Operating Speed", many models of operating speed prediction on curved sections have been developed for roads with two lanes (e.g. [7][8][9][10]), and for multilane roads (e.g. [11][12][13][14][15][16][17]). Through a review of literature, it can be concluded that the studies concerned with modeling the relationship between operating speed and elements of straight sections (tangents) and analyzing their properties are less than studies of speeds on curved sections. This paper aims to provide a comprehensive review of studies that have developed operating speed prediction models on straight sections of various types of roads in different geographic regions of the world. The reviewed information was arranged in tables to facilitate reading by researchers, as it included the classification of the studied roads, the types of vehicles, the techniques and devices used in data collection, the number of study sites, the principle adopted in extracting the free flow speed, the terrain that the road path passes through, as well as the grades of the studied sections.
The remaining sections of this paper are structured as follows: the Second Section provides a review of what has been mentioned in the literature regarding tangents as geometric design elements. In the Third Section, the schemes and methodologies that have been followed in the literature are described. The Forth Section presents the models that were developed. The references are included in the end of this paper.

Tangent as a Geometric Design Element
Tangent grade and tangent length were important factors for the researcher in the operating speed approach. Boroujerdian [8] divided the study sections into two categories; upgrade and downgrade, and conducted analyzes for each category independently. On the other hand, Andueza [18] analyzed spot speeds of passenger vehicles measured at the middle points of 36 tangents. The longest straight section was 555 m in this study. The author recommended a further study of the impact of highway geometric characteristics on free-flow speeds of vehicles on long tangent sections. Polus et al. [19] assembled the study sites into four groups based on the tangent length (TL) and radii of preceding (R1) and succeeding (R2) horizontal curves: Group 1: TL≤150 m and R1 and R2≤250 m, Group 2: 150 m<TL≤1000 m and R1 and R2≤250 m, Group 3: 150 m<TL≤1000 m and 250 m<R1 and R2≤1000 m, and Group 4: TL>1000 m and R1 and R2>1000 m. Separate prediction models for the 85 th percentile speed were developed for each of the four groups separately. Model of Group 1 showed that the operating speed is determined primarily by the radii, while the Group 2 model showed that the length of the tangent and the radii are the significant variables. The authors indicated that the models for Group 3 and Group 4 sections are preliminary and they need additional data. Ottesen and Krammes [20] measured speeds of free-flowing passenger cars on long tangent sections at which desired speeds were believed to be attained. A minimum tangent length of 244 m (800 ft) was specified in this study. Pérez-Zuriaga et al. [21] selected tangents with lengths greater than 90 m to develop the operating speed model. The authors reported that speed cannot be fully developed on short tangents because of the influence of the adjacent curves. Dell'Acqua and Russo [22] associated the predictive operating speed models with the segment length. Two models were developed; the first was for the tangents with a length of less than 500 m and the second for tangents with a length greater than 500 m.
Moreover, in terms of the sequence of design elements or alignment combinations on two-lane two-way roads, the horizontal curves were classified into two classes; simple curve and continuous curve, and the straight sections classified as independent or non-independent design elements. Al-Masaeid et al. [23] defined the simple horizontal curve as a circular curve preceded by a straight tangent section with a length of at least 800 m and suggested that a tangent less than 300 meters in length is considered to be a non-independent element. Lamm et al. [24] indicated that a tangent length of up to 260 m (850 ft) may be considered an independent tangent if the traffic speed is approximately 80 km/h. On the other hand, Alkherret et al. [11] divided tangents of multilane highways based on length into three groups; the first group included the shortest of 300 meters, the second included the longest of 500 meters, and the third group included what was in between. The authors performed several analyzes and concluded that the tangent with length less than 300 m may be considered a non-independent design element. Table 1 presents a summary of the schemes and methodologies reported in the previous studies that developed models to predict operating speed on tangent sections in different geographical areas of the world. These studies are arranged in descending order of date. The information listed in the table included: the country in which the study was carried out, road classification, number of study sites, the topography that the road path passes through and grads of the studied sections, types of vehicles, techniques, and devices used in data collection, as well as principle adopted in extracting the free-flow speed. Some information was not provided by the authors, so it is denoted as N/A. Table 1, most studies have focused on two-lane rural roads while speed studies on other roads (multilane urban/ rural and mountain roads) were limited. The number of study sites ranged from 7 to 251. However, few researchers have expanded their studies to include several classes of roads. Leong et al. [25] used data collected at 16 sites of four-lane divided and undivided highways located in rural and suburban areas. Thiessen et al. [31] selected 126 tangents on urban arterial and 123 tangents on urban collectors. Nie and Hassan [43] analyzed driver speed behavior on horizontal curves and tangents of two-lane rural highways and urban and suburban roads. Fitzpatrick et al. [49] prepared a study to explore the relationship between operating speed and roadway features of tangent sections. The authors selected 79 tangents to collect speed data: 35 on urban/suburban arterial, 22 on urban/suburban collector, 13 on local streets, and 9 on rural arterial. On the other hand, the study sites were similar in their gradations. In general, most of the sites were located in flat terrain areas or with little slope. The large longitudinal grades of the studied tangents were mentioned in only two papers (± 11% in [8] and ± 12% in [26]).

As shown in
The majority of the studies were analyzed the speeds of passenger cars (PC) and developed their prediction models. Two studies did not include the PC speeds in the analysis. Cardoso [52] studied light and heavy vehicles, while Hernández et al. [26] devoted his paper to heavy vehicles only. Also, some researchers have included other classes of vehicles (such as heavy and light trucks, and buses) in their studies. Among those, four researchers [9, 23, 25, and 51] classified vehicles into several classes and developed a set of models accordingly, as described later.
Besides, the review showed that several data collection techniques were used to record vehicle speed. Speed guns (Radar/Laser guns) and Global Positioning System (GPS) technology were the most commonly used by researchers. Video image analysis has been used to calculate speed in some research [8, 25, 29, and 37]. Also, driving simulators were adopted by three researchers [35, 38, and 46]. However, the technique used to collect the speed data had a major role in determining speed measurements: continuous or spot. Continuous speed data were collected in all the research that used GPS technology and the driving simulator technique. Wang et al. [45] reported that the speed profile data from GPS equipment can provide detailed and accurate information about acceleration and deceleration behavior. Pérez Zuriaga et al. [21] mentioned that it is possible, with this technology, to collect a large amount of continuous speed data without significant influence on drivers. Using vehicles equipped with GPS, Jacob and Anjaneyulu [9] conducted a pilot study to identify the speed observation locations and then used stopwatches to measure the time taken by vehicles to travel over a marked trap length of 15 to 20 m. On the other hand, Bella [46] stated that simulation is an innovative, useful, and increasingly used technique due to its high efficiency and the ease of data collection with it.
As mentioned previously, only free-flow speeds are included in the analysis for modeling purposes. In this matter, some researchers have adopted low traffic flow as evidence for the free flow condition [26, 27, 32, 39 and 45]. Montella et al. [35] and Bella et al. [38] controlled this condition using a driving simulation technique. The rest of the researchers characterized the speed of free flow depending on the headway time. As shown in Table 1, the minimum headway time value was 5 seconds in most cases. Thiessen et al. [31] analyzed their data based on headways ranged between 2 and 10 sec and indicated that using a 2-sec headway's threshold is sufficient and higher values are not necessary for the analysis of operating speeds on urban roads.

Operating Speed Models
Speed models developed in previous research along with analysis approaches are listed in Table 2. As shown, the multiple linear regression method (MLR) was the preferred approach by most researchers in developing the speed prediction models. The multiple non-linear regression analysis (MNLR) was used in two studies [9,52], while the simple regression was used in one study [34]. Also, the Ordinary Least Squares (OLS) method was used in speed modeling. In Italy, Dell'Acqua and Russo [22] and Esposito et al. [41] adopted the OLS method to develop the 85th percentile speed models on rural roads. In the USA, Figueroa Medina and Tarko [47] used two approaches for modeling panel data: OLS-PD without random effects and generalized least squares (GLS) with random effects (RE).

Civil Engineering Journal
Vol. 7, No. 12, December, 2021 2154 The model formulas allow predicting any user-specified percentile (from 5th to 95th percentile speed). Moreover, Dinh and Kubota [39] used a simultaneous equation regression with a three-stage least-square (3SLS) estimator for the modeling effort. Furthermore, Singh et al. [10] and Semeida [40] preferred to use the Artificial Neural Network (ANN) for analysis.
On the other hand, the development of the 85 th percentile speed prediction models has been the main goal of most researchers. Prediction models for space mean speed were developed in four studies ([8, 29, 39, 44]). Boroujerdiana et al. [8] presented standard deviation speed models in addition to space mean speed models. Moreover, Wang et al. [45] developed two models: the first was with the 85th percentile speed and the second with the 95th percentile speed as dependent variables. Cardoso [52] developed models for the 15 th and the 85 th percentiles of observed free speeds. Figueroa Medina and Tarko [47] developed a model that allowed the user to calculate percentages from 5 to 95 for speed prediction. By reviewing the models developed in various previous studies, the following notes can be drawn:  There are researches presented several models according to the type of vehicle [25,26,9,23,51], tangent length [19,22,45], tangent grade [8], and speed limit [10,28,49,50].
 Tangent length is the most variable shown in speed models as a predictor.
 The independent variables in rural road models are less than in urban roads.
However, equations, dependent and independent variables, and the coefficient of determination (R 2 ) for each model are detailed in Table 2.  Where: PSL = posted speed limit; SN = skid number; and IRI = international roughness index.

Zedda and Pinna [29]: Forward Multiple Linear Regression
Two models were developed:  Model 1-space mean speed for all roads

Thiessen et al. [31]: Ordinary Least-Squares Applied to Panel Data (OLS-PD)
Three models were developed: Where: Rbef = radius of the previous curve; Raft = radius of the following curve; and T = tangent length.

Boroujerdiana et al. [8]: Multiple Linear Regression
Mean and standard deviation speed models for Downgrade sections:

Semeida [40]: Stepwise Multiple Linear Regression and Artificial Neural Networks (ANN)
The best regression model:

Singh et al. [10]: Neural Networks Analysis
Four models were developed: Model 1: with posted speed but without accident data.
Model 2: without posted speed and without accident data.

Dell'Acqua et al. [42]: Multiple Linear Regression
Five points were selected for speeds collecting: center, starting, finishing, and quarters of tangents

Bella [46]: Multiple Linear Regression
The length of tangents range from 150 m to 2200 m. Two models were developed; all tangents were used in the first, while tangents with 150 m long were excluded in developing the second model.  Where: Vt15 = 15th percentile of tangent speed (km/h); Vt85 = 85th percentile of tangent speed (km/h); Rp = radius of the preceding curve segment (m); LW = combined lane width (m); SW = shoulder width (m); L = length of the tangent segment (m); and Rf = radius of the next curve segment (m).

Krammes et al. [53]: Multiple Linear Regression
On long tangent (>244 m): the statistically significant variables were the geographic region and the terrain.

Conclusion
This paper aimed to provide a comprehensive review of studies that have developed operating speed prediction models on straight sections of various types of roads in different geographic regions of the world. The information included the classification of the studied roads, the types of vehicles, the techniques and devices used in data collection, the number of study sites, the principle adopted in extracting the free-flow speed, the terrain that the road path passes through, as well as the grades of the studied sections. The previous literature review showed that Tangent grade and length were essential factors for the researcher in the operating speed approach and most studies have focused on two-lane rural roads, while studies on other types of roads were limited. In addition, the majority of the studies were concerned with the speeds of passenger cars. Moreover, most of the study sites were located in flat terrain areas or with a slight slope. On the other hand, Speed guns and laser guns were the most commonly used to measure vehicle speed, and some research used video image analysis to calculate speed. However, driving simulators were adopted by three researchers for their high efficiency and ease of data collection. According to Operating Speed Models, the multiple linear regression method (MLR) was the preferred approach by most researchers in developing speed prediction models. By reviewing the models developed in various previous studies, it can be concluded that tangent length is the most variable shown in speed models as a predictor, and the independent variables in rural road models are less than in urban roads. This study provides data and information about straight-segment operating speed to save time and effort for researchers. The author recommended a further study of the impact of highway geometric characteristics on the free-flow speeds of vehicles on long tangent sections.

Data Availability Statement
Data sharing is not applicable to this article.

Funding
The author received no financial support for the research, authorship, and/or publication of this article.

Acknowledgements
The author is thankful respectively to Yarmouk University (Irbid-Jordan) for their support.

Conflicts of Interest
The author declare no conflict of interest.