Lower Bounds on Queuing and Loss at Highly Multiplexed Links

Explicit and delay-driven congestion control protocols strive to preclude overflow of link buffers by reducing transmission upon incipient congestion. In this paper, we explore fundamental limitations of any congestion control with respect to minimum queuing and loss achievable at highly multiplexed links. We present and evaluate an idealized protocol where all flows always transmit at equal rates. The ideally smooth congestion control causes link queuing only due to asynchrony of flow arrivals, which is intrinsic to computer networks. With overprovisioned buffers, our analysis and simulations for different smooth distributions of flow interarrival times agree that minimum queuing at a fully utilized link is O(sqrt(N)), where N is the number of flows sharing the link. This result raises concerns about scalability of any congestion control. However, our simulations of the idealized protocol with small buffers show its surprising ability to provide bounded loss rates regardless of the number of flows. Finally, we experiment with RCP (Rate Control Protocol) to examine how existing practical protocols compare with our idealized scheme in small-buffer settings

Quantifying full phenological event distributions reveals simultaneous advances, temporal stability and delays in spring and autumn migration timing in long-distance migratory birds

Acknowledgements We thank all Fair Isle Bird Observatory staff and volunteers for help with data collection and acknowledge the foresight of George Waterston and Ken Williamson in instigating the observatory and census methodology. We thank all current and previous directors of Fair Isle Bird Observatory Trust for their contributions, particularly Dave Okill and Mike Wood for their stalwart support for the long-term data collection and for the current analyses. Dawn Balmer and Ian Newton provided helpful guidance on manuscript drafts. We thank Ally Phillimore and two anonymous referees for helpful comments. This study would have been impossible without the Fair Isle community's invaluable support and patience over many decades, which is very gratefully acknowledged. WTSM and JMR designed and undertook analyses, wrote the paper and contributed to data collection and compilation, MB contributed to analysis and editing, all other authors oversaw and undertook data collection and compilation and contributed to editing.Peer reviewedPostprin