In this paper, the location of emergency service (ES) vehicles is studied on fully connected networks. Queuing theory is utilized to obtain the performance metrics of the system. An approximate queuing model the (AQM) is proposed. For the AQM, different service rate formulations are constructed. These formulations are tested with a simulation study for different approximation levels. A mathematical model is proposed to minimize the mean response time of ES systems based on AQM. In the model, multiple vehicles are allowed at a single location. The objective function of the model has no closed form expression. A genetic algorithm is constructed to solve the model. With the help of the genetic algorithm, the effect of assigning multiple vehicles on the mean response time is reported.