Pedestrian Risk Index (PRI)#

Description#

The PRI estimates the conflict probability and severity for pedestrian crossing scenarios by combining the TTZ with the impact speed [Cafiso2011]. It is defined for a scenario with a vehicle \(A_1\) and a VRU \(P\) both approaching a conflict area \(\mathit{CA}\). The scenario shall include a unique and coherent conflict period \([t_{c_\mathit{start}}, t_{c_\mathit{stop}}]\) where \(\forall\,t \in [t_{c_\mathit{start}}, t_{c_\mathit{stop}}]:\,\mathit{TTZ}(P, \mathit{CA}, t) < \mathit{TTZ}(A_1, \mathit{CA}, t) < t_s(A_1, t)\). Here, \(t_s(A_1, t)\) is the time \(A_1\) needs to come to a full stop at time \(t\), including its reaction time, leading to

\[\mathit{PRI}(A_1, \mathit{CA}) = \int_{t_\mathit{c_\mathit{start}}}^{t_{c_\mathit{stop}}}(s_{imp}(A_1, \mathit{CA}, t)^2 \cdot (t_s(A_1, t) - \mathit{TTZ}(A_1, \mathit{CA}, t))) \mathrm{dt},\]

where \(s_\mathit{imp}\) is the predicted speed at the time of contact with the pedestrian crossing. The PRI thus quantifies over two aspects of a whole scenario: the temporal difference is claimed to be a surrogate for the accident probability, whereas the impact speed is approximate for its severity. One possibility of estimating \(s_\mathit{imp}\) is defined by the authors as

\[s_\mathit{imp}(A_1, \mathit{CA}, t) = \sqrt{\|v_1(t)\|_2^2+2a_{1,\mathit{long,min}}(t) (d(p_1(t),p_\mathit{CA}(t)) - \|v_1(t)\|_2 t^r_1)} \text{,}\]

where \(t_i^r\) is the reaction time of actor \(A_i\). Note that depending on the DMM, other formulae for \(s_\mathit{imp}\) may be employed.

Properties#

Run-time capability#

Theoretically possible, but primary design goal is a-posteriori analysis

Target values#

Faded markings: 1992, visible markings: 1623, visible markings, speed bump: 407, raised visible markings, speed bump: 161 [Cafiso2011]

Subject type#

Pedestrian

Scenario type#

Scenarios with a unique and coherent conflict period, where one vehicle and pedestrian both approach a pedestrian crossing

Inputs#

\(a_\mathit{1,long,min}\), \(t_i^r\), for each \(t \in [t_{c_\mathit{start}}, t_{c_\mathit{stop}}]\): \(v_i(t)\), \(v_p(t)\), \(t_s(A_i,t)\), \(d(A_i, Z)\), \(d(P, Z)\)

Output scale#

\((0,\infty)\), risk number (m²/s³), interval scale

Reliability#

Depends on reliability of TTZ, but with the advantage of being robust against ‘jumps’ in TTZ due to integration over time

Validity#

High if all assumptions hold, due to consideration of severity and probability, but dependent on validity of TTZ and \(v_\mathit{imp}\); no empirical analysis available

Sensitivity#

High, as constant velocity model can be considered an adverse estimation of future development at pedestrian crossings

Specificity#

Medium, as prediction model does not consider reactive behavior of participants on each other

Prediction model#

Same as TTA