2.2.3. Time-Dependent Speed Calculation Method

In real life, road conditions are complex and not static. Thus, vehicle speed in each period was calculated according to formula *v<sup>p</sup> ij* = *<sup>v</sup>*0/*ρp*. The relationship between speed and time is shown in Figure 2.

**Figure 2.** Speed–time relationship.

Ichoua et al. [41] believe that vehicle speed tends to be constant in each subdivided *p* period. Therefore, the CV-GVRP divided the total time of a day into periods, i.e., [*B*1, *F*1], [*B*2, *F*2], ..., [*Bp*, *Fp*]. The speed in each period remained unchanged; the length of the *p* period is *Hp*; the driving time in the *p* period is ; the distance to be driven after the end of *p* period is *L<sup>p</sup> ij*; meanwhile, *dij* = ∑ *p*∈*P dp ij* and *t p ij* represent the driving time in *p* period. The total driving time was calculated as follows:

Step 1: First, calculate *d<sup>p</sup> ij* <sup>=</sup> *Lpv<sup>p</sup> ij*. If *dij* <sup>&</sup>lt; *<sup>d</sup><sup>p</sup> ij*, calculate *t p ij* <sup>=</sup> *dij*/*v<sup>p</sup> ij* next to proceed to Step 3, or calculate *L<sup>p</sup> ij* <sup>=</sup> *dij* <sup>−</sup> *<sup>d</sup><sup>p</sup> ij* , *t p ij* = *Lp*.

Step 2: To calculate the vehicle's driving time in the remaining period, let *ξ* = 1 and the vehicle run in period *<sup>p</sup>* + *<sup>ξ</sup>*, *<sup>d</sup>p*+*<sup>ξ</sup> ij* <sup>=</sup> *Hp*+*ξvp*+*<sup>ξ</sup> ij* ; if *<sup>d</sup>p*+*<sup>ξ</sup> ij* <sup>≤</sup> *<sup>L</sup><sup>p</sup> ij*, *t p*+*ξ ij* <sup>=</sup> *Hp*+*<sup>ξ</sup>* , *<sup>L</sup>p*+*<sup>ξ</sup> ij* = *Lp ij* <sup>−</sup> *<sup>d</sup>p*+*<sup>ξ</sup> ij* and *ξ* = *ξ* + 1, then repeat this step. Otherwise, calculate *t p*+*ξ ij* <sup>=</sup> *<sup>d</sup>p*+*ξ*−<sup>1</sup> *ij* /*vp*+*<sup>ξ</sup> ij* to proceed to Step 3.

Step 3: The total vehicle travel time *tij* = ∑ *p*∈*P t p ij* is obtained and the section (*i*, *j*) driving

time computation is finished.
