Optical buffering based on fiber delay lines (FDLs) has been proposed as a means for contention resolution in an optical packet switch. In this article, we propose a queuing model for feedback-type shared-per-node recirculating FDL optical buffers in asynchronous optical switching nodes. In this model, optical packets are allowed to recirculate over FDLs as long as the total number of recirculations is less than a pre-determined limit to meet signal loss requirements. Markov Modulated Poisson Process (MMPP)-based overflow traffic models and fixed-point iterations are employed to provide an approximate analysis procedure to obtain blocking probabilities as a function of various buffer parameters in the system when the packet arrival process at the optical switch is Poisson. The proposed algorithm is numerically efficient and accurate especially in a certain regime identified with relatively long and variably-sized FDLs, making it possible to dimension optical buffers in next-generation optical packet switching systems.