Randomized two-valued bounded delay online buffer management

In the bounded delay buffer management problem unit size packets arrive online to be sent over a network link. The objective is maximize total weight of before their deadline. this paper we are interested in two-valued variant problem, where every packet has either low (1) or high priority (α>1). We show that optimal randomized competitive ratio against an oblivious adversary 1+(α−1)∕(α2+α).