Simulative assessment of patrol car allocation and response time

Capacity planning of police resources is crucial to operating an effective and robust police service. However, due to the high operational heterogeneity and variability among different calls for service, key performance estimates that link resource allocation and utilization to emergency response times are a challenging task in and of itself. In the literature, two main instruments are proposed to provide appropriate estimates: queueing models, which yield closed-form expressions for key performance characteristics under limiting assumptions, and simulation models, which seek to capture more of the real-world structure of police operations at the cost of increased computational effort. Utilizing an extensive dataset comprising over two million calls for service, we have created a discrete-event simulation tailored to capture police operations within a major metropolitan area in Germany. Our analysis involves comparing this simulation against an implementation of the widely cited multiple car dispatch queueing model by Green and Kolesar (1989) found in the literature. Our findings underscore that our simulation model yields significantly improved estimates for key performance indicators reflective of real-world scenarios. Notably, we demonstrate the consequential impact on resource allocation resulting from these enhanced estimates. The superior accuracy of our model facilitates the development of capacity plans that align more effectively with actual workloads, consequently fostering heightened security measures and cost efficiencies for society. Additionally, our study involves rectifying discrepancies in the presentation of the queueing model and highlighting three specific areas for future research.