Queueing models for police-fire merger analysis

Cities with under 100,000 in population expend a significant portion of their budgets on emergency services. One option that a number of these cities have considered for improving service and cutting costs is training personnel to handle both police and fire roles. In this paper we describe a hierarchy of models that we have used to assess the performance viability of a merger as well as to design specific deployment plans. The modeling environment is more complex than a traditional police or fire system. We need to model the response pattern of four or more patrol units along with the simultaneous dispatch of fire equipment from one or more fire stations. The major contribution of the paper is the manner in which a series of models is linked together to forecast a wide range of performance measures under differing dispatch assumptions. We use a queueing model of police patrol to calculate steady state probabilities and expected delays without preemption. We then model two types of preemptive dispatch strategies utilized in responding initially to a major fire by superimposing a binomial distribution on the basic queueing model. There is also a travel time simulation model to calculate conditional expected response time statistics. The queueing models and the travel time simulation are then combined to estimate unconditional expected values. Lastly, we describe a simulation model used to address transient performance issues that are of concern during a major fire.