This study develops a realistic queueing model for a variety of dispatching procedures typically implemented in police departments. The model provides a useful tool for the planning and design of efficient dispatching protocols, extending the applicability of most models proposed to date by overcoming some of their limitations. Some of these limitations of existing models are the inability to dispatch a number of incidents to a single call or to hold patrol cars in reserve to a single call or to hold patrol cars in reserve for emergencies. Following a review of literature relevant to the model, the paper discusses how to derive various measures of operational performance, including the delay probability and the mean delay in queue experienced by a priority call. The paper's remaining sections discuss loss systems and extensions and variants of the model (e.g., to allow an upper and lower bound on the number of patrol units required by any given call rather than to have every call request a specific number of units). Appended mathematical calculations and 16 references.