Proportional fair scheduling (PFS) has been adopted as a standard solution for fair resource allocation in modern wireless cellular networks. With the emergence of heterogeneous networks with widely varying user loads, it is of great importance to characterize the performance of PFS under bursty traffic, which is the case in most wireless streaming and data transfer services. In this letter, we provide the first analytical solution to the performance of PFS under bursty on-off traffic load. We use the Gaussian approximation model to derive a closed-form expression of the achievable user data rates. In order to further improve the accuracy of our baseline analytical solution for multi-cell networks, we design a hybrid approximation by employing multi-interference analysis. The simulation results verify that our model guarantees extremely low data rate estimation error, which is further insensitive to changes in session duration, traffic load and user density.