the power system. If $w=0$, the impact of EV charging on the grid is not considered at all, and a non-zero value of $w$ implies some impact on the grid—the larger $w$ is, the larger the impact is. Generally, if the focus is on the charging provider’s profit, a small $w$ is used. In practice, the value of $w$ needs to be determined, e.g., with the help of heuristic and empirical data.

Quality-of-Service Constraints
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We use two quality-of-service (QoS) metrics for the service provider: (1) the average service delay probability $\Upsilon_k$, and (2) the average service coverage $\Xi_k,\;(k=1,2,3)$.

$$\Upsilon_k=\frac{1}{N}\sum_{i=1}^N\upsilon_{i,k},$$

$$\Xi_k=\frac{1}{N}\sum_{i=1}^N\xi_{i,k},$$

where $\upsilon_{i,k}$ is the average service delay probability for the $i$-th EV owner getting the EV charged at service provider $k$. For the $i$th EV owner, $\upsilon_{i,k}$ is defined as the ratio of the number of delayed charging to the total number of charging attempts; $\xi_{i,k}$ is the average number of accessible Level $k$ charging stations along the route from origin to destination. Notice that $\upsilon_{i,k}$ and $\xi_{i,k}$ are random variables that depend on the travel patterns of all EVs, the urban road network and the charging stations. It is, thus, difficult to use a simple formula to compute 