4.1.1. Definition 1 (Resource Experience)

We define *resource experience* to quantify the dissatisfying experience per resource about which an agent cares.

Let


The *resource experience* is then defined as the *dissatisfying* experience of agent *j* on resource *Ak* along the path *π<sup>j</sup>* :

$$D\left(\pi^{j}, A\_{k}\right) = \sum\_{v\_{p}|v\_{p}\in\pi\_{/v\_{p}}} \mathbf{1}\left(A\_{k}(\boldsymbol{e}\_{pq}^{j}) \ge \varepsilon\_{k} \wedge A\_{k}^{j}(\boldsymbol{e}\_{pq}^{j}) < \varepsilon\_{k}\right) \cdot \mathbf{g}(\boldsymbol{e}\_{pq}^{j}),\tag{6}$$

where **1**(·) is the indicator function, whose value is one if the logical condition is true, else zero; *ε<sup>k</sup>* ∈ *ε* = {*ε*1, ... ,*εL*} is the *satisfying value* regarding the resource *Ak*, which is a positive real value; *g*(*e j pq*) is the edge cost regarding travel time/distance given by the graph model; and *<sup>A</sup><sup>j</sup> k*(*e j pq*) is formulated as:

$$A\_k^j(\boldsymbol{\varepsilon}\_{pq}^j) = \frac{A\_k(\boldsymbol{\varepsilon}\_{pq}^j)}{\sum\_{k \in I} \mathbf{1}\left(\boldsymbol{\varepsilon}\_{pq}^k = \boldsymbol{\varepsilon}\_{pq}^j\right)}.\tag{7}$$

Obviously, *A<sup>j</sup> k*(*e j pq*) = *Ak*(*e j pq*) if and only if no other agents are physically moving along with agent *j* on the edge *e j pq*. The allocated resource value *<sup>A</sup><sup>j</sup> k*(*e j pq*) quantifies the level of interference incurred by other agents when they physically move together. In contrast, the traditional hard-collision setting will always label a collision to the agent *j* and all other involved agents whenever *A<sup>j</sup> k*(*e j pq*) is (even slightly) smaller than *Ak*(*e j pq*). The resource experience is implemented as an attribute of the vertex class and can be calculated incrementally using Algorithm 1.
