Erlang loss models for the static deployment of ambulances

How should one allocate a fleet of ambulances to fixed bases with the goal of keeping response times to calls as small as possible? We present two new models for this problem, both of which are based on the Erlang loss formula. The first model is stylized, and shows that allocating ambulances in proportion to the offered load is not necessarily optimal and can often be substantially improved upon. The second model can be used to screen potential allocations to try to identify top candidates for further investigation. Computational experiments on the first model provide insights on how we should modify ambulance allocations in response to different levels of offered load. Computational experiments on the second model compare this model with the so-called A-hypercube model and show that the our model has comparable, and in many cases, better performance in terms of the accuracy of the estimates of performance measures. Thus, our models can be used as pre-screening tools to identify promising ambulance allocations and these promising ambulance allocations can subsequently be evaluated carefully through simulation.