Abstract: Emergency management services, such as emergency medical service, disaster relief, and homeland security, are required to be located in specific locations according to realistic situations. They are supposed to reach the scene within a target time and deliver emergency management services. In light of time-varying traffic conditions, these services should be relocated accordingly. Further, equality should be accounted for to provide reasonable service distribution. Traditional regional coverage models rarely explicitly consider equality issue. In particular, the relationships between service distribution and model constraints are usually not modeled given time-varying traffic conditions with complex road networks. Based on recent progress in regional coverage modeling, this study extends traditional location set covering models and establishes a time-varying emergency management service coverage model that explicitly considers equality. We further introduce an efficient solution algorithm and perform a comprehensive comparative analysis of three equality constraints. The experiments with Wuhan road networks demonstrate that our model can obtain more equable service coverage than traditional models, thus promoting the quality of emergency management services.