Table 1 Notations

\(i,j,n\)

i, j is customer id, \(i,j=\text{0,1},2,\dots ,M\), M is the number of customers, 0 is the delivery center; n is the traffic node.

k

Delivery vehicle number \(\left(k=\text{1,2},\dots ,K\right)\), K is the number of vehicles.

\({e}_{i},{l}_{i}\)

Earliest and latest time for customer i.

\({x}_{ijk}\)

Binary variable on whether vehicle k moves from i to j. \({X}_{ijk}\) is the set of\({x}_{ijk}\)

\({x}_{ijk}^{+},{x}_{ijk}^{-}\)

\({x}_{ijk}^{+}\) is the route added to \({x}_{ijk}\) after a demand change; \({x}_{ijk}^{-}\) is the route reduced from \({x}_{ijk}\) after a demand change.

\({x}_{ijk}^{++},{x}_{ijk}^{--}\)

\({x}_{ijk}^{++}\) is the route added to \({x}_{ijk}^{+}\) after a change in road conditions; \({x}_{ijk}^{--}\) is the route reduced from \({x}_{ijk}^{-}\) after a change in road conditions.

\({d}_{ij}\)

Distance between i and j.

\({D}_{k}\)

Endurance of vehicle k.

\({t}_{ik},{t}_{jk}\)

Arrival time of vehicle k at i and j.

\({t}_{ijk}\)

Time required for vehicle k to travel from i to j.

\({b}_{ik}\)

Departure time of vehicle k from i, \({b}_{ik}\ge 0\).

w _i

Weight of goods for customer i.

\({W}_{k}\)

Capacity of vehicle k.

\({v}_{ijk}^{m}\)

Speed of vehicle k at time m of the travel from i to j.

\({d}_{ijk}^{m}\)

Distance travelled by vehicle k from i to j at time slot m.

\({r}_{ij}^{m}\)

Road conditions of the section from i to j at time slot m.

o

Time slot, \(o=\text{1,2},\dots O\), O is the number of time slot.

\({\pi }^{o}\)

Time interval \({\pi }^{o}=\left[{\zeta }_{o}, {\xi }_{o}\right]\), \({\zeta }_{o}\) and \({\xi }_{o}\) are the left and right time boundary of\({\pi }^{o}.\)

V

Number of vehicles on the current road segment.

Q

Number of edge computing devices (ECD).

\({\lambda }_{V2V}\)

Data transmission rate based on V2V technology.

\({\lambda }_{V2I}\)

Data transmission rate based on V2I technology.

\({\omega }_{v}\)

Data amount of vehicle v computing task transferred to the edge server.