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Police patrolling intends to enhance traffic safety by mitigating the risks associated with vehicle crashes and accidents. From a view of operations, patrolling requires an effective distribution of resources and often involves area delineations for this distribution purpose. Given constraints such as budget and human resources for traffic safety, delineating geographic areas optimally for police patrol areas is an important agenda item. This paper considers two p-median location models using segments on a street network as observational units on which traffic issues such as vehicle crashes occur. It also uses two weight sets to construct an enhanced delineation of police patrol areas in the City of Plano, Texas. The first model for the standard p-median formulation gives attention to the cumulative number of motor vehicle crashes from 2011 to 2021 on the major transportation networks in Plano. The second model, an extension of this first p-median one, uses balancing constraints to achieve balanced spatial coverage across patrol areas. These two models are also solved with network kernel density count estimates (NKDCE) instead of crash counts. These smoothed densities on a network enable consideration of uncertainty affiliated with this aggregation. The analysis results of this paper suggest that the p-median models provide effective specifications, including their capability to define patrol areas that encompass the entire study region while minimizing distance costs. The inclusion of balancing constraints ensures a more equitable distribution of workloads among patrol areas, improving overall efficiency. Additionally, the model with NKDCE results in an improved workload balance among delineated areas for police patrolling activities, thus supporting more informed spatial decision-making processes for public safety.