Numerous approaches have attempted to develop systems that more appropriately manage street crossings in cities in recent years. Solutions range from intelligent traffic lights to complex, centralized protocols that evaluate the policies that vehicles must comply with at intersections. Such works attempt to provide traffic-control strategies at intersections where the complexity of a dynamic environment, with vehicles crossing in different directions and multiple conflict points, pose a significant challenge for city traffic optimization. Traditionally, a traffic-control system at an intersection gives the green light to one lane while keeping the other lanes on red. But there may be situations in which there are different levels of vehicle priority; for example, emergency vehicles may have priority at intersections. Thus, this work proposes a distributed junction-management protocol that pays special attention to emergency vehicles. The proposed algorithm implements rules based on the distributed intersection management (DIM) protocol; such rules are used by vehicles while negotiating their crossing through the intersection. The proposal also seeks to affect the traffic flow of non-priority vehicles minimally. An evaluation and comparison of the proposed algorithm are presented in the paper.