This paper focuses on robust location strategies for a fleet of ambulances in cities in order to maximize service levels under unexpected demand patterns. Our work is motivated by the fact that when small parts of networks incur emergencies according to a heavy-Tailed distribution, the structure of the network under resource constraints results in the entire system behaving in a heavy-Tailed manner. To address this, metrics other than average-case need to be used. We achieve robust location strategies by including risk metrics that account for tail behavior and not average performance alone. Because of the exponentially large solution space for locating K ambulances in N locations on the network, our approach is based on an efficient algorithm that allows for optimizing based on these risk metrics. We show that optimizing based on risk measures can account for spatiotemporal patterns and prevent the extent of delay cascades that are typically seen in heavy-Tailed arrival distributions. From our computational results based on data from a large Asian city, we show that planning with some robustness metrics as targets leads to solutions that perform well in heavy-Tailed demand scenarios.