*3.2. Data Sample*

The analyzed road network consists of national and regional two-lane rural and suburban roads, and various types of intersections (roundabouts, signalized and non-signalized intersections).

The TTIS reroutes traffic from the main route R1 (national roads R-NT-P-Z) to alternative routes (regional and national roads between Z and R, including changing points J, CZ, P, and NT) (Figure 1) characterized by various geometric standards. The road sample covered by the TTIS is made up of 156.4 km of road (including 81.5 km of regional road and 74.9 km of national road) [2].

Furthermore, the Safety Performance Functions (SPFs) for road sections and intersections were calibrated on a larger sample composed of data from two-lane roads. Those roads are located in the same region close to the routes covered by the TTIS and with similar geometric and traffic characteristics, but not affected by the system. This did not introduce any bias because there is a negligible effect of the TTIS on safety in the primary road network. This emerged from the results of the estimation of a Crash Modification Factor (CMF) which assumed a value not far from 1 [2]. That additional sample is made up of 322.9 km of road, including 184.3 km of regional road and 138.6 km of national road. This approach allows us to predict the average crash frequency for different road categories (regional and national) and intersection types (roundabouts, signalized and non-signalized intersections) comprising the network influenced by the TTIS. Tables 1 and 2 report the summary statistics of the variables describing the sample used for the calibration of the SPFs. Roads in the system were divided into homogenous segments in terms of traffic volume (AADT), area (rural, suburban), and horizontal alignment. Intersections were categorized based on traffic control organization. Single-lane roundabouts and signalized and non-signalized four-leg intersections were distinguished. For each homogeneous segmen<sup>t</sup> [14,15], the segmen<sup>t</sup> length and the Curvature Change Rate (CCR) (Table 1) were defined as geometric covariates. For each segmen<sup>t</sup> and intersection, the AADT (for intersections, both the major and minor road AADT were considered) and the number of crashes, fatalities, and injuries were collected to provide the final dataset used in the SPF calibration (Table 1, while Table 2 reports the same for intersections). AADT and crash data were recorded from 2009 to 2014.

In order to assess the TTIS in terms of travel time and safety performance, the different alternative routes, consisting of sections (Table 3), were distinguished, i.e., R1 (main, the most selected route), R2, R3, and R4 (Figure 1 and Table 4). Each route is a combination of national or/and regional road sections and may be selected by the drivers between Rabka (R) and Zakopane (Z). Routes are made up of sections defined between the main intersections and can include the same segments, e.g., Route R2 (R-NT-B-P-Z) contains sections R-NT and P-Z, which are part of route R1 as well. The alternative route (for the main route R1) consisting of only regional roads is route R3.


**Table 1.** Summary statistics of the dataset of road segments (Annual Average Daily Traffic—AADT—is theminimumandmaximuminthewholeperiodofanalysis/CCR—CurvatureChangeRate).




**Table 4.** Description of the analyzed road network covered by the TTIS by route.


## **4. Methodological Approach**

The evaluation of the TTIS safety performance and travel time was carried out with the use of the following methodologies:

1. the calibration of SPFs for each road category and location (i.e., national/regional and rural/suburban roads) and for each intersection type (roundabouts, signalized and non-signalized intersections). This study aims to assess road safety in the entire road network included in the TTIS by juxtaposing the total predicted number of crashes for routes in various configurations of traffic distribution within the road network covered by the system; and

2. the assessment of travel time for routes included in the TTIS, based on the observed relationship between tra ffic volume and speed (for road sections) and delay (for intersections) with reference to tra ffic volume variability.

Regardless of the model calibration for segments or intersections, crashes observed at a site i in the year t (Yi,t) are typical time series data across years and can, therefore, be represented by the following simplified model structure Equation (1):

$$\text{Yi}, \text{t} = \text{trend} + \text{regression term} + \text{random effects} + \text{local factors}, \tag{1}$$

where "trend" refers to a long-term movement due to a change in the risk factors with time, the "regression term" is of the same form as the Safety Performance Functions (SPFs), "random effects" account for latent variables across the sites, and the "local factors" refer to the dispersion between the normal safety level for similar locations and the safety level for the specific site. Random effects and local factors both contribute to the dispersion of crash counts as compared to the mean value estimated by the regression term.

The use of the Negative Binomial (NB) distribution to represent the distribution of crash counts is commonly accepted [16]. Therefore, when excluding trend e ffects (i.e., the phenomenon is stationary), Generalized Linear Models (GLMs) are especially useful in the context of tra ffic safety, for which the distribution of accident counts in a population often follows the negative binomial distribution [17,18]. In the present research work, the analysis was performed without considering possible variation in the predicted number of crashes due to the time trends because of the limited period of analysis and the target of the research work.

Considering all this, and consistent with the state of the art in developing these models, a generalized linear modeling approach and model form was used in the elaboration, considering a negative binomial error distribution for either SPF calibrated for road sections or intersections. The important property of the GLM is the flexibility in specifying the probability distribution for the random component [19–21]. The model parameter estimation was performed following the maximum likelihood calibration methodology. The dispersion parameter obtained by the model calibration indicates how far the model is from a Poisson distribution, which is typically lower when a longer period is considered (lower data dispersion). Therefore, the value of the intercept is the average value in the whole period of 6 years [22–24].

#### *4.1. Safety Performance Function Calibration for Road Segments*

To compare the safety performance in terms of predicted crashes due to the changes in the Annual Average Daily Tra ffic (AADT) (which is the only parameter which varies due to the TTIS), ad hoc SPFs were calibrated using, as independent AADT variables, the horizontal alignment (the value of the Curvature Change Rate—CCR) and the section length on di fferent categories of roads (national/regional) and in di fferent locations (rural/suburban). The inclusion of other covariates, such as the segmen<sup>t</sup> length (L) and the horizontal alignment, helps in isolating the contribution of AADT. The inclusion of exponents for both L and AADT improves the adaptability of the model to di fferent conditions for other variables not included in the model [25].

As a result of the previous consideration in developing SPF models, Equation (2) shows the selected model form:

$$\mathbb{E}(\mathbf{Y}) = \exp(\alpha) \text{ \* } \text{AADT}^{\otimes} \text{ \* L}^{\gamma} \text{ \* } \exp(\delta^{\star} \text{CCR}), \tag{2}$$

where: E(Y) is the yearly predicted number of crashes; L is the segmen<sup>t</sup> length [m]; AADT is the annual average daily tra ffic [veh./day]; and α, β, γ, and δ are regression terms.

For the regional suburban area, the variable CCR was not statistically significant and, therefore, was removed from the model.

The results of the regression analysis, obtained by using a maximum likelihood calibration methodology, are reported in Table 5. Those SPFs returned the predicted average number of crashes per year for every road section of the network based on road category and location.


**Table 5.** Regression coefficient, standard error, and p-value of the Safety Perfomance Functions (SPFs) for road segments.

The best safety performances were observed on sections of national roads in rural areas (because of better geometrical standards), and the worst were in suburban areas (because of the high observed speed). Regional roads have similar safety performances in rural and suburban areas (Figure 3).

**Figure 3.** SPF diagram for segments in different road locations and road categories, with CCR equal to zero (tangent).

#### *4.2. Safety Performance Function Calibration for Intersections*

To estimate the predicted crash frequency for intersections, a unique SPF was calibrated using, as a categorical variable, the different intersection types, i.e., NS: non-signalized, R: roundabout, S: signalized, with a similar approach to [26]. This difference in the approach to the regression analysis between road sections and intersections was mainly due to the small sample size for each single intersection type. Only AADT was statistically significant, with a p-value lower than 0.05, and therefore it was used in the models for the major and minor roads. The model form is shown in Equation (3) and the results of calibration are shown in Table 6 and Figure 4.

$$\text{E(Y)} = \exp(\alpha) \text{ \* } \text{AADTma}^{\otimes} \text{ \* } \text{AADTmi}^{\gamma} \text{ \* } \exp(\delta \text{i} \text{°Cat}), \tag{3}$$

where: E(Y) is the yearly predicted number of crashes; AADTma is the average annual daily traffic for major roads [veh./day]; AADTmi is the average annual daily traffic for minor roads [veh./day]; Ca is the categorical variable related to the type of intersection (NS: non-signalized, R: roundabout, S: signalized); α, β, and γ are regression terms of the continuous variables; and δi is the regression term of the categorical variables.


**Table 6.** Regression coefficient, standard error, and p-value of the intersection SPFs.

**Figure 4.** SPF diagram for different intersection types.

The safest intersections are the roundabouts followed by signalized intersections, while the worst performance is from non-signalized intersections, as expected (Figure 4). Therefore, the predicted crash likelihood of users traveling on alternative routes will be dependent on the type of road, the length of travel, and the number and types of intersections on the selected route.

#### *4.3. Assessment of Travel Time and Variability of Tra*ffi*c Volume*

In order to evaluate the impact of traffic distribution on road safety, it is important to assess travel time for each route based on individual road segments and over entire networks, similar to [27]. Travel time has an impact on route selection by drivers, and as result, it affects the traffic distribution. The relationships between traffic volume and speed (for each road category and road location) were estimated by the authors.

Based on empirical data, from the TTIS for each section, Figure 5 presents the relationships between speed and directional traffic volumes for national and regional roads and rural and suburban areas. In order to evaluate the traffic performance for intersections, delays as a measure of effectiveness were calculated based on the Highway Capacity Manual approach [28]. To calculate delays at the intersections, 10% of the share of peak-hour AADT was assumed. Based on travel time for sections and delays for intersections, travel time for each route was computed and compared with data from the TTIS to validate the approach.

**Figure 5.** Impact of traffic volume on speed for various sections of the TTIS.

In order to evaluate traffic volume variability in the TTIS, yearly traffic distributions for each route were compared (Figure 6). The rerouting of traffic during peak periods is reported in Figure 6 as it was used in Scenario 3.

**Figure 6.** Variability of traffic volume during the year based on data from the TTIS.

The results presented in [1] confirm the need for an overall assessment of the safety performance of the system, not only for road sections, but also for intersections. The assessment of safety and tra ffic performance of road networks is a complex problem due to possible changes in tra ffic distribution at the intersections. Therefore, three di fferent scenarios were assumed for the analysis of the impact of tra ffic distribution on road safety and travel time:


The operation of the TTIS in terms of road safety and travel time were evaluated based on crash and tra ffic data.

The first scenario allows us to assess the impact of tra ffic volume on travel time and road safety for the main route R1, in order to show how the system operates (an increase in tra ffic volume with a 10% step) and indicate threshold values of tra ffic volume that should activate the TTIS. The second scenario allows us to assess the impact on road safety when travel time is balanced for the fastest routes, which means the system should start to work. The last scenario shows how the TTIS is working in the peak period (summertime) during tra ffic rerouting based on travel time.

#### **5. Results and Discussion**

In the present research work, three scenarios of rerouting are presented. Scenario 0 simulates the actual conditions based on observed data; an alternative scenario simulates an increase of 150% in tra ffic volume (Scenario 1) for the best route in terms of road standards, i.e., R1; a second alternative scenario considers the travel time of R1 equal to the route which consists of only regional roads and is the most selected alternative route for R1, i.e., R3; and the third alternative scenario considers the highest tra ffic volume (peak tra ffic) registered by the system (in August) for all routes. Those three alternative scenarios were helpful in getting values related to road safety measures or travel time and provide a basis for comparison among the di fferent routes in di fferent conditions.

The results of all analyzed scenarios are included in Table 7. In this table, the ratio of values for crashes and travel time as a sum of both road sections and intersections are also included. These values are calculated in relation to the main route R1 (Equation (4)).

$$\text{ratio} = \text{Ri/R1},\tag{4}$$

where: Ri is the value of the number of crashes or travel time for the i-th route.

A value of the ratio lower than 1 indicates that the conditions of safety or/and travel time, in comparison to the main route R1, are better.

The results indicate that for a tra ffic volume equal to the observed AADT (Scenario 0), route R1 has the lowest travel time (at least 41% in comparison to route R2, and even 85% of route R4), but the lowest number of crashes are predicted for route R3 (45% of crashes of R1).

The increase in tra ffic only for main route R1 to 150% of AADT causes an increase in travel time and the number of crashes, as expected, taking into account the increase in risk exposure. In Figure 7, the impact of the increase in AADT for route R1 on safety and travel time by *ratio* is presented.

An increase in tra ffic volume equal to 143.56% of travel time is the same for routes R1 and R3 (Scenario 2). In this case, the number of crashes for routes R2, R3, and R4 is lower than for route R1. The safest route is R3, where a reduction of 88% in the predicted number of crashes, compared with main route R1, is observed.


**Table 7.** Values of crashes and travel time for all routes (the lowest values are in bold).

Therefore, the safest route, R3, is very attractive, even in the condition of a high share of rerouting (Scenario 3), which can, in general, cause an increase in crashes (about 50% of crashes compared with the predicted one for route R1) during the peak period (158% of AADT). Despite the benefit to road safety, the benefits to travel time are limited to 6% (Figure 7, Scenario 2) in the case of the same increase in AADT for all routes. For the changing of traffic, as for Scenario 3, the faster route is R1. In other words, this latter condition means that the TTIS is saturated.

Analysis indicates that the best alternative route (for main route R1) in the TTIS is route R3 (Figure 8; Figure 9).

Routes R2 and R4 are not competitive compared with routes R1 and R3, both in terms of delay and safety performance. R2 is not competitive because of the greater value of travel time and predicted crash frequency in comparison to R1. It can be a good alternative route in case of local and temporary traffic interruptions on road sections belonging to other routes due to, e.g., crash occurrences or construction works. Route R4 is too long to be competitive and it is rarely used as an alternative route.

The best alternative for the main route R1 is route R3, mainly due to road safety matters. It results in a lower value of AADT (max AADT for R3 is equal to 8954 veh/day) and greater reserves of capacity. An increase in the number of crashes for R3 is lower compared with the main route R1 and is equal to 80% when considering the same percentage increase in traffic volume. In other words, it is possible to reroute 20% more vehicles to route R3 than to main route R1 to obtain the same road safety level. Therefore, it is possible to reroute more traffic in the system to R3. Travel time in peak traffic is also competitive despite the longer routes.

One of the main problems in the evaluation of the TTIS performance is related to driver choices or, in other words, how drivers use information from VMSs to select routes. Data about the variability of traffic (Figure 6) allows us to compare data on traffic distribution for one year. The peak period in the year is related to the activities of the region, whose function is mainly recreation. Based on those data (for August), the authors assume that differences in the main route R1 are the result of rerouting caused by the TTIS (higher AADT for R3 and R4).

 **Figure 7.** Crash (**a**) and travel time (**b**) ratio for increase in traffic volume only for route R1.

**Figure 8.** Travel time ratio for increase in traffic volume for all routes.

**Figure 9.** Impact of traffic volume increase for all routes on crashes.

The same data indicate that, during wintertime (January and February), drivers prefer to use national roads (R1 and R2). It can be related to geometrical parameters (lower for regional roads) and the winter maintenance standard of roads (better for national roads).
