Table 1 Coefficient di and ci.

From: A car-following model of CAVs integrating state information from multiple leading and single following vehicles

Coefficient

Expression di

Coefficient

Expression ci

d1

\(\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} {V^{\prime}_F}\left( {{h_c}} \right)+\left( {1 - \eta } \right){V^{\prime}_B}\left( {{h_c}} \right)\)

c1

\(\mu \sum\limits_{{l=1}}^{m} {{\zeta _l}\left( {2l - 1} \right) - \left( {1 - \mu } \right)}\)

d2

\(\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} \left( {2l - 1} \right){V^{\prime}_F}\left( {{h_c}} \right) - \left( {1 - \eta } \right){V^{\prime}_B}\left( {{h_c}} \right)\)

c2

\(\rho \sum\limits_{{l=1}}^{m} {{\varsigma _l}l - \left( {1 - \rho } \right)}\)

d3

\(\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} \left( {3{l^2} - 3l+1} \right){V^{\prime}_F}\left( {{h_c}} \right)+\left( {1 - \eta } \right){V^{\prime}_B}\left( {{h_c}} \right)\)

c3

\(\mu \sum\limits_{{l=1}}^{m} {{\zeta _l}\left( {3{l^2} - 3l+1} \right)+\left( {1 - \mu } \right)}\)

d4

\(\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} {V^{\prime\prime\prime}_F}\left( {{h_c}} \right)+\left( {1 - \eta } \right){V^{\prime\prime\prime}_B}\left( {{h_c}} \right)\)

c5

\(\rho \sum\limits_{{l=1}}^{m} {{\varsigma _l}{l^2}+\left( {1 - \rho } \right)}\)

d5

\(\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} \left( {4{l^3} - 6{l^2}+4l - 1} \right){V^{\prime}_F}\left( {{h_c}} \right) - \left( {1 - \eta } \right){V^{\prime}_B}\left( {{h_c}} \right)\)

  

d6

\(\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} \left( {2l - 1} \right){V^{\prime\prime\prime}_F}\left( {{h_c}} \right) - \left( {1 - \eta } \right){V^{\prime\prime\prime}_B}\left( {{h_c}} \right)\)

  
  1. Near the critical point, by setting \(b=\eta \sum\limits_{{l=1}}^{m} {{\xi _l}} {V^{\prime}_F}\left( h \right)+\left( {1 - \eta } \right){V^{\prime}_B}\left( h \right)\), the second-order and third-order terms of ε in Eq. (21) can be eliminated. As a result, Eq. (18) is simplified to: