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

\[\mathit{DST}(A_1,A_2,t,t_s) = \frac{(v_{1,\mathit{long}}(t) - v_{2,\mathit{long}}(t))^2}{2(d(p_1(t),p_2(t)) - v_{2,\mathit{long}}(t) \cdot t_s)}\]

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