Analysis of fibre-loop optical buffers with a void-avoiding schedule

The major growth of personalised video streaming and the paradigm shift towards big data all add to the bandwidth requirements of Internet users, urging network providers to provision them with more capacity. While current optical fibre networks in theory offer capacities of over 10 Tbit/s per fibre, such transmission speeds are rarely achieved in practice. This is due to the fact that optical packets need to traverse multiple intermediary nodes on their path from origin to destination, while it is hard to temporarily store the packets in case these nodes are congested. A possible solution to this problem is to send the packets into fibre delay loops when the transmission line of an intermediary node is occupied. This buffering strategy is different from classical buffering in the sense that once the transmission line becomes available, a waiting packet first needs to traverse the remainder of its delay loop before it is ready for possible transmission. In this presentation, we analyse the stationary number of optical packets being delayed in fibre loops simultaneously at an intermediate node, under the assumption that a transmission is initiated as soon as the transmission line and any packet is available for transmission (the so-called void-avoiding schedule). We also study the stationary amount of delay incurred by a packet before it is transmitted. The analysis turns out to have surprising links with particular queueing systems, and results turn out to be strikingly simple and familiar. This presentation is based on joint work with Wouter Rogiest and Dieter Fiems (Ghent University).