**4. Deviation Analysis**

The deviation analysis aims to identify the network links which are the most avoided by all cyclists who registered GPS traces. The analysis starts with the following basic assumption: given the choice of two routes with identical properties (same safety, pavement, environment, etc.), cyclists would always choose the shortest one. If this is true, the cyclist would only accept a longer route if it offered better properties (safer, quieter, etc.). From a different perspective, if certain road links are avoided by deviating on alternative links, then the avoided links are supposed to possess fewer attractive characteristics with respect to the alternative, even though these characteristics may be good in the absolute sense. In an ideal bicycle network, no cyclists should feel constrained to take a longer route due to some repellant characteristics of the shortest route, or due to the better characteristics of longer routes. The most "avoided links" of the city's road network are therefore identified with the km of deviation caused to cyclists. The total deviation metric *DMi* for each road link *i* is calculated in the following way:


$$DM\_i = \sum\_{j \in \mathcal{I}} \sum\_{k=1}^{K\_j} \delta\_{ijk} \cdot d\_{jk} \tag{1}$$

where <sup>δ</sup>*ijk* = 1 if *SRjk* contains link *i*, otherwise 0. Let *Li* be the length of link *i*; then the partial deviation is given by *djk* = *i*∈*DR jk Li* − *i*∈*SR jk Li*.

**Figure 9.** Illustration of the calculation of the total deviation metric for the non-overlapping route section between nodes A and B.

Figure 9 shows links 1, 2 and 3 which are not chosen, despite they are part of the shortest route (solid line); whereas, links 4, 5 and 6 are part of the chosen route (dashed line). In case of the non-overlapping section between node A and B shown in Figure 9, the chosen route *DRjk* is constituted by links 4, 5 and 6, while the shortest route section *SRjk* contains links 1, 2 and 3. The partial deviation *djk* of links in *SRjk* equals to *djk* = L4 + L5 + L6 − (L1 + L2 + L3). The total deviation metric for the central part of Bologna network is shown in Figure 10.

**Figure 10.** Total deviation metric determined for the central part of Bologna network.

The highest total deviation metric can been seen on the main radial roads from and into the city center. As seen in Figure 10, these are also roads with high bicycle flows. This means that many cyclists actually do use these radial roads but also many try to avoid them. Note that there are also roads in the city center with high bicycle flows, but generating almost no deviations. For a discussion of these findings, see Section 5.

On average, the chosen route parts are 20% longer with respect to the shortest route parts. Analyzing the road attributes of the chosen part and the shortest part of all non-overlapping sections of all trips, the causes for the deviations become clearer—see the first three columns of Table 1. As expected, cyclists accept deviations in order to travel on roads with: (1) a high share of reserved bikeways, (2) a high share of low priority roads (roads with one lane per direction and speed limits of 30 km/h), (3) a low intersection density, and (4) a low share of mixed access, such as lanes with bike/bus access or lanes where bikes and pedestrians are allowed. This last result confirms the findings of the research carried out by Bernardi et al. [39], in which the authors quantified the effects and frequencies of disturbances on bicycle facilities, particularly from pedestrians and buses.

**Table 1.** Road link attributes of chosen and shortest routes of non-overlapping sections and on overlapping sections.


The statistics of the road link attributes of the overlapping sections of each trip (i.e., all links where the chosen and shortest routes coincide) are presented in the last column of Table 1. It becomes evident that the values of the mixed road access share, the reserved bikeway share and the intersection density are in between the values of the shortest route (column 1) and the chosen route (column 2) of the non-overlapping sections. One could conclude that cyclists tend to deviate if road attribute values are below/above those of the overlapping sections. An exception is the low priority road share, where the overlapping sections show values even below that of the shortest route.

In order to shed more light on the decision of individuals to accept deviations, a Logit model is calibrated, where the user has the choice between two alternatives of non-overlapping route segments (as illustrated in Figure 9), where one of the alternatives is the shortest route. The systematic utility function *Vi* of alternative *i* is defined as:

$$V\_i = \beta\_1 D\_i + \beta\_2 B\_i + \beta\_3 L P\_i \tag{2}$$

where *Di* is the distance of the route segment, *Bi* is the share of exclusive bikeway, and *LPi* is the share of low priority roads as percentage of the respective distance. The set of observations has been prepared as follows. In a first subset, the route sections have been considered, where the chosen route is different from the shortest route. In a second subset, route sections have been identified, where the shortest route completely coincides with the chosen route. In this case, a longer route alternative (that has not been chosen by the cyclist) has been generated as follows: the second shortest route that connects the extremities of the shortest route section is determined such that the second shortest route section does not overlap with the shortest route section. This is similar to the method applied by Marchal et al. [36]. In this way, a route alternative is generated that is the closest possible to the chosen (and shortest) route alternative. In order to avoid a bias towards longer or shorter distances, the size of the first and second observation subset are kept equal.

The calibration resuls of a total of 4678 observations is shown in Table 2. The attributes chosen are all significant and R<sup>2</sup> = 0.160. The small parameter values result in Odds ratios close to one, which is reasonable considering that attribute values are in the order of 10−2–10−3. Other attributes like the node density or the share of mixed bikeway access have turned out not to be significant when included in this model. The signs of the model parameters are reasonable—see also the discussion in Section 6. The calibration has been repeated with GPS traces in Bologna from the ECC of the year 2015. The result of this calibration shows parameter values within the standard error bounds of the result from ECC of the year 2016 shown in Table 2.


**Table 2.** Calibration results of Logit model from Equation (2).

One can use Equation (2) to estimate the deviation necessary to equilibrate the systematic utilities of both route alternatives. Setting *V*1 = *V*2, and resolving for the deviation yields in

$$(D\_1 - D\_2 = \frac{\beta\_2}{\beta\_1}(B\_2 - B\_1) + \frac{\beta\_3}{\beta\_1}(LP\_2 - LP\_1),\tag{3}$$

which is the difference in distance, depending on the difference in exclusive bikeway share and the difference in low priority road share. The deviation *D*1 − *D*2 obtained from Equation (3) ensures a path choice probability of 50%.
