On the optimal allocation of users to servers in an emergency service

This paper considers the optimal allocation of users to servers in an emergency medical service, in which two or three ambulances cooperate to serve calls from a region of rectangular shape. Queueing models are often used to approach emergency health services. We analyse three different dispatch policies to determine the best available unit to be sent and introduce a classification of districts in four different classes. Properties of the optimal boundaries, i.e., the ones that minimize the average response time between users and servers and which define districts, given the home locations of servers, are investigated. A two-server model is reviewed, and results are obtained for a three-server model, enlightening a non-monotone behaviour of the shift of the optimal boundaries, with respect to the equidistance curve, in the different states of the system, depending on the utilization ratio, on the policy assumed and on the locations of the servers. This way, it is not possible to give an a priori general rule on the properties of the boundaries of the districts only on the basis of the number of busy servers at the specific time.