Emergency (medical, fire or criminal) Management Systems (EMSs) are crucial for ensuring public safety and security. Typically in many cities, less than 20% of the cases received by EMSs belong to the extremely serious category and require immediate help. Rest of the incidents typically are less serious and thereby allow more flexibility in response time. Therefore, for efficient management of EMS requests, several EMSs now categorise an incoming emergency request into a priority level based on well studied ``triaging" methods. Leading research on optimising emergency response has either focussed on data-driven models for settings with homogenous incidents or on generic heuristics (that are not data-driven) in multi-priority incident settings. In this paper, we provide data-driven models that employ tiered optimisation of allocation and dispatch simultaneously to ensure high priority incidents are served effectively. To that end, we make the following contributions in this paper: (1) For a given dataset of historical incidents, we first provide an optimisation model that maximises the percentage of highest priority incidents served within a threshold response time, while ensuring threshold response times for other priority incidents. Apart from optimising the allocation, this optimisation model also provides a detailed dispatch strategy that fits the given set of historical incidents well; (2) To better handle high variance (spatial and temporal) in arrival of high priority incidents, we reserve a set of ERVs for high priority incidents. Our second contribution is in modifying our optimisation model to reserve a subset of ERVs for high priority incidents while considering a minor modification to nearest available ERV dispatch strategy; and (3) Finally, using a real-world EMS data set, we experimentally demonstrate that our solution with a detailed dispatch strategy outperforms the existing benchmark approach. Moreover, due to the presence of few high priority incidents and significant spatio-temporal uncertainty associated with them, we show that a simple dispatch strategy with reserved ERVs outperforms the detailed dispatch strategy.