In this paper we propose an analytic framework for estimating blocking probability in an asynchronous optical burst switch with wavelength conversion and a multi-channel feed-back fibre delay line. Burst arrivals are of general renewal type and burst lengths exponentially distributed. Example solutions for gamma-distributed arrivals are compared with discrete-event simulations. To the authors' knowledge, this is the first analytic model of such a switch for general renewal arrival statistics. © 2011 IEEE.