## 2 Framework of DRP Strategy and Problem Formulation
### Centralized CAVs Crossing Sequencing Problem Formulation  
We designate the segments within the OZ as organizing segments and regard them as conveyors, with the MZ at the center of the intersection viewed as a processing point. At this point, leveraging the methodology of the CRP problem, a centralized CSP can be established. Figure 3 depicts how a signal-free intersection can be transformed into a storage system consisting of a set of organizing segments and a group of CAVs. Let \(M=\{1,\ 2,\ 3,\ 4\}\) denote the identification of organizing segments, \(N=\{1,\ldots,\ n\}\) represent the identification of CAVs, and \(n\in\mathbb{N}^{+}\) denote the total number of CAVs on the four organizing segments. For organizing segment \(k\in M\), \(n_{k}\in\mathbb{N}^{+}\) denotes the number of CAVs on it, and the identification of the \(j\in[1,\ n_{k}]\)-th CAV on organizing segment \(k\) is denoted as \(\sum_{i=1}^{k-1}n_{i}+j\). It is important to note that there is no strict precedence between the sequences of CAVs entering the MZ from different organizing segments. However, considering that overtaking increases travel delay [21], each organizing segment operates internally following the FIFO principle. Therefore, if there is more than one CAV on organizing segment \(k\), the \(p\in[1,\ n_{k}]\)-th CAV on the segment should enter the MZ before the \(q\in[p,\ n_{k}]\)-th CAV on the same organizing segment. When two consecutive CAVs, \(i\) and \(j\), entering the MZ pose a potential collision risk, a collision avoidance cost \(C_{ij}\) is incurred, measured in seconds, with the specific calculation method detailed in reference [22]. On the other hand, when CAV \(i\) and CAV \(j\) do not pose a collision risk, no collision avoidance cost is incurred. Based on this assumption, we further propose that, for any three distinct CAVs \(x\), \(y\), and \(z\), the sum of their collision avoidance costs satisfies the inequality \(C_{x,y}+C_{x,z}\geq C_{y,z}\). Therefore, the key to the CSP lies in adjusting the sequence of CAVs entering the MZ to minimize the total collision avoidance cost. Figure 2: Framework of DRP strategy. In the subsequent step, we define a directed network wherein each node \(V_{i}\) corresponds to a CAV \(i\) on the organizing segments, thereby constituting the node set \(V_{OS}=\left\{V_{1},\ldots,\ V_{n}\right\}\). We delineate \(R=\left\{V_{j}\in V_{OS}\big{|}j=\sum_{i=1}^{k-1}n_{i}+1,\forall k\in M\right\}\) as the assortment of nodes corresponding to the nearest CAVs on each organizing segment to the MZ, and \(E=\left\{V_{j}\in V_{OS}\big{|}j=n_{k}+\sum_{i=1}^{k-1}n_{i},\forall k\in M \right\}\) as the collection of nodes associated with the farthest CAVs on each organizing segment from the MZ. Specifically, \(R_{k}\) and \(E_{k}\) symbolize the nodes aligned with the closest and farthest CAVs from the MZ on organizing segment \(k\), respectively. Subsequently, we establish a collection of directed arcs, denoted as \(A_{OS}\). An arc \(\left(V_{i},\ V_{j}\right)\) exists within \(A_{OS}\) if CAV \(j\) can promptly succeed CAV \(i\) into the MZ, for instance, when CAV \(i\) and CAV \(j\) are proximate or situated on distinct organizing segments. The cost attributed to arc \(\left(V_{i},\ V_{j}\right)\) equals the collision avoidance cost \(C_{i,j}\) between CAV \(i\) and CAV \(j\). Additionally, we introduce a virtual node \(V_{s}\) and two arrays of virtual arcs, namely \(A_{r}\) and \(A_{e}\). \(A_{r}=\left\{\left(V_{s},\ V_{j}\big{|}V_{j}\in R\right)\right.\) symbolizes the arcs originating from \(V_{s}\) to each node within \(R\), whereas \(A_{e}=\left\{\left(V_{j},\ V_{s}\big{|}V_{j}\in E\right\}\right.\) represents the arcs from each node within \(E\) to \(V_{s}\). The expenses associated with these virtual arcs are established at 0. In recapitulation, the CSP quandary can be articulated as the quest for the minimum-cost pathway within the directed network \(G=\left(V,A\right)\), depicted in Figure 4, where \(V=\left\{V_{S}\right\}\ \bigcup\ V_{OS}\), \(A=A_{OS}\ \bigcup\ A_{r}\ \bigcup\ A_{e}\).