Deceleration to Safety Time (DST)#
Description#
For an actor \(A_1\) following another actor \(A_2\), the DST metric calculates the deceleration (i.e. negative acceleration) required by \(A_1\) in order to maintain a safety time of \(t_s \ge 0\) seconds under the assumption of constant velocity \(v_2\) of actor \(A_2\) [Hupfer1997] [Schubert2010]. The corresponding formula can be written as
and extends the concept of the \({a}_{\mathit{long,req}}\) by requiring deceleration to a safety distance \(v_{2,\mathit{long}}(t) \cdot t_s\), under the assumptions of constant velocity of \(A_2\), i.e. \(a_2=0\). In particular, for \(t_s = 0\), the DST agrees with the constant acceleration version of the \({a}_{\mathit{long,req}}\) metric.
Properties#
Run-time capability#
Yes
Target values#
\(<1\) m/s² (adaption)
\(<2\) m/s² (reaction)
\(<4\) m/s² (considerable reaction)
\(<6\) m/s² (heavy reaction)
\(\geq 6\) m/s² (emergency braking) for \(t_s = 0\) [Hupfer1997]
Subject type#
Road vehicles (automated and human)
Scenario type#
Designed for car following, but can be extended to any scenario that potentially necessitates a braking maneuver
Inputs#
Positions \(p_i\) and velocities \(v_i\) for \(i \in \{1, 2\}\) and a safety time \(t_s\)
Output scale#
\((-\infty, \infty)\), acceleration (m/s²), ratio scale
Reliability#
Comparable to \({a}_{\mathit{long,req}}\)
Validity#
Comparable to \({a}_{\mathit{long,req}}\), but depends on the validity of chosen value of \(t_s\) under the given circumstances, and assumption of constant velocity; was exemplarily shown to have improvements over TTC and PET [Hupfer1997]
Sensitivity#
Comparable to \({a}_{\mathit{long,req}}\), large \(t_s\) increases sensitivity
Specificity#
Comparable to \({a}_{\mathit{long,req}}\), large \(t_s\) decreases specificity
Prediction model#
Time window#
Limited, due to assumption of constant velocity
Time mode#
Linear time