On the Geometry of Emergency Service Medical Provision in Cities

The enormity of many cities today poses special problems for authorities supplying emergency medical services. The scale of the emergency system and variations in the operating conditions rule out some of the traditional methods developed to deal with the complexities involved. In cities the provision of services is affected not only by the daily varying locations of the populations at risk, but also by the prevailing traffic and weather conditions that can hinder ambulance access to the site of an incident or to a treatment facility. The controlling authorities of these services nevertheless like to maintain the highest possible levels of service given the available resources. They are interested in knowing which facilities to open and when, what resources and staffing levels are required, and what the long-term and short-term implications of changing operating conditions and of other unforeseen circumstances are on operating standards. In this paper the authors present research into a set of methods that are designed to assist in finding solutions to these problems or, at least, in understanding how to deal with them. The methods are based on the efficiency of movement in cities, particularly the time it takes to access different locations in different traffic conditions, and on the likelihood of incidents occurring at different times of the day. Initial results are presented based on the London area, but the main conclusions are transferable to many other cities of comparable scale. The distinguishing feature of the methods is that they are based on a type of non-Euclidean geometry that arises from the generalized profiles of the average speeds of traffic flow in cities.