Analysing queueing behaviour in void-avoiding fibre-loop optical buffers

Abstract

In optical packet/burst switching, fibre-loop optical buffers provide a compact and effective means of contention resolution. In case of a fixed packet length, the involved loop length is typically chosen matched (equal to the packet length), and the loops are arranged in parallel, constituting a single-stage buffer. In this contribution, we investigate the performance of such a buffer in an asynchronous network setting, assuming (batch-)Poisson arrivals and assuming a so-called void-avoiding schedule (VAS). We show that by time discretisation, the fibre-loop system behaviour can be captured by a particular type of exhaustive polling model. Performance measures such as the moments of the queue content and packet delay for the discretised as well as for the asynchronous optical buffer model are obtained. We illustrate our approach by various numerical examples obtain several insights, including the contra-intuitive finding that under the VAS, both the standard deviation and the coefficient of variation of the queue content are lower than under other regular scheduling disciplines.