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Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMA-based cellular networks wherein the bandwidth of the cells is partitioned into regions with different frequency reuse factors. To date, FFR techniques have been typically been evaluated through system-level simulations using a hexagonal grid for the base station locations. This paper instead focuses on analytically evaluating the two main types of FFR deployments - Strict FFR and Soft Frequency Reuse (SFR) - using a Poisson point process to model the base station locations. The results are compared with the standard grid model and an actual urban deployment. Under reasonable special cases for modern cellular networks, our results reduce to simple closed-form expressions, which provide insight into system design guidelines and the relative merits of Strict FFR, SFR, universal reuse, and fixed frequency reuse. Finally, a SINR-proportional resource allocation strategy is proposed based on the analytical expressions and we observe that FFR provides an increase in the sum-rate as well as the well-known benefit of improved coverage for cell-edge users.