Table 1 Notations of model parameters...

Table 1

Notations of model parameters and variables

Notation	Description
$b_{i} ({\bar{b}}_{i})$	The outbound (inbound) bandwidth for link i (cycles)
$w_{i} ({\bar{w}}_{i})$	The part of a green duration before (after) the green band in outbound (inbound) direction (cycles)
$τ_{i} ({\bar{τ}}_{i})$	The queue clearance time (cycles)
$θ_{i}$	The offset of intersection i (cycles)
$n_{i} ({\bar{n}}_{i})$	Integer variables to represent the number of signal cycles
$r_{s_o u t, i} ({\bar{r}}_{s_o u t, i})$	The total red duration at the left(right) side of outbound straight-moving phase at intersection i (cycles)
$r_{l_o u t, i} ({\bar{r}}_{l_o u t, i})$	The total red duration at the left(right) side of outbound left-turning phase at intersection i (cycles)
$r_{s_i n, i} ({\bar{r}}_{s_i n, i})$	The total red duration at the left(right) side of inbound straight-moving phase at intersection i (cycles)
$r_{l_i n, i} ({\bar{r}}_{l_i n, i})$	The total red duration at the left(right) side of inbound left-turning phase at intersection i (cycles)
$g_{s_o u t, i}$	The green duration of outbound straight-moving phase at intersection i (cycles)
$g_{s_i n, i}$	The green duration of inbound straight-moving phase at intersection i (cycles)
$g_{l_o u t, i}$	The green duration of outbound left-turning phase at intersection i (cycles)
$g_{l_i n, i}$	The green duration of inbound left-turning phase at intersection i (cycles)
$δ_{i} ({\bar{δ}}_{i})$	Binary decision variable that represents the phase sequences at intersection i
$d_{i} ({\bar{d}}_{i})$	Distance of link i in outbound(inbound) direction
$v_{m a x}$	The limited maximum average velocity of CAVs
$v_{m i n}$	The limited minimum average velocity of CAVs
$t_{m a x, i} ({\bar{t}}_{m a x, i})$	The maximum travel time for CAVs on link i in outbound(inbound) direction
$t_{m i n, i} ({\bar{t}}_{m i n, i})$	The minimum travel time for CAVs on link i in outbound(inbound) direction
$λ_{i} ({\bar{λ}}_{i})$	The difference between maximum and minimum travel time on link i in outbound(inbound) direction

Notation	Description
$b_{i} ({\bar{b}}_{i})$	The outbound (inbound) bandwidth for link i (cycles)
$w_{i} ({\bar{w}}_{i})$	The part of a green duration before (after) the green band in outbound (inbound) direction (cycles)
$τ_{i} ({\bar{τ}}_{i})$	The queue clearance time (cycles)
$θ_{i}$	The offset of intersection i (cycles)
$n_{i} ({\bar{n}}_{i})$	Integer variables to represent the number of signal cycles
$r_{s_o u t, i} ({\bar{r}}_{s_o u t, i})$	The total red duration at the left(right) side of outbound straight-moving phase at intersection i (cycles)
$r_{l_o u t, i} ({\bar{r}}_{l_o u t, i})$	The total red duration at the left(right) side of outbound left-turning phase at intersection i (cycles)
$r_{s_i n, i} ({\bar{r}}_{s_i n, i})$	The total red duration at the left(right) side of inbound straight-moving phase at intersection i (cycles)
$r_{l_i n, i} ({\bar{r}}_{l_i n, i})$	The total red duration at the left(right) side of inbound left-turning phase at intersection i (cycles)
$g_{s_o u t, i}$	The green duration of outbound straight-moving phase at intersection i (cycles)
$g_{s_i n, i}$	The green duration of inbound straight-moving phase at intersection i (cycles)
$g_{l_o u t, i}$	The green duration of outbound left-turning phase at intersection i (cycles)
$g_{l_i n, i}$	The green duration of inbound left-turning phase at intersection i (cycles)
$δ_{i} ({\bar{δ}}_{i})$	Binary decision variable that represents the phase sequences at intersection i
$d_{i} ({\bar{d}}_{i})$	Distance of link i in outbound(inbound) direction
$v_{m a x}$	The limited maximum average velocity of CAVs
$v_{m i n}$	The limited minimum average velocity of CAVs
$t_{m a x, i} ({\bar{t}}_{m a x, i})$	The maximum travel time for CAVs on link i in outbound(inbound) direction
$t_{m i n, i} ({\bar{t}}_{m i n, i})$	The minimum travel time for CAVs on link i in outbound(inbound) direction
$λ_{i} ({\bar{λ}}_{i})$	The difference between maximum and minimum travel time on link i in outbound(inbound) direction

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