One to Rule Them All: a General Randomized Algorithm for Buffer Management with Bounded Delay

We give a memoryless scale-invariant randomized algorithm for the Buffer Management with Bounded Delay problem that is e/(e-1)-competitive against an adaptive adversary, together with better performance guarantees for many restricted variants, including the s-bounded instances. In particular, our algorithm attains the optimum competitive ratio of 4/3 on 2-bounded instances. Both the algorithm and its analysis are applicable to a more general problem, called Collecting Items, in which only the relative order between packets' deadlines is known. Our algorithm is the optimal randomized memoryless algorithm against adaptive adversary for that problem in a strong sense. While some of provided upper bounds were already known, in general, they were attained by several different algorithms.