Performance Approximation of Emergency Service Systems with Priorities and Partial Backups

An approximate procedure is presented for priority emergency service systems with partial backups where requests for service with a given origin and priority can be responded to by a certain subset of response units. We introduce and analyze the family of queuing and loss systems with partial service and use them to approximate the distribution of the number of busy response units, which in turn enables us to estimate the average server workloads, immediate and delayed dispatch rates, and waiting delays as system performance measures. We consider systems with zero and infinite queue capacities and let the dispatching policies and service times depend on call priority and customer and server locations. The validity of the approximation model and its computational aspects are studied through numerous tests and a realistic application of locating a fleet of ambulances in downtown Montréal.

The online appendix is available at https://doi.org/10.1287/trsc.2017.0810.