Online Algorithms for Scheduling Weighted Packets with Deadlines in Bounded Buffers

We consider online algorithms for scheduling weighted packets with deadlines in multiple sizebounded buffers. There are m ≥ 1 buffers B1, B2, . . . , Bm. At any time, a buffer Bi can store at most bi ∈ Z packets. Packets arrive over time. Each packet is associated with a non-negative value, an integer deadline, and a target buffer that it can reside in. In each time step, only one pending packet is allowed to be sent. Our objective is to maximize the total value gained by delivering packets before their respective deadlines in an online manner. We call this model a single-buffer model (when m = 1) or a multi-buffer model (when m > 1). The single-buffer model generalizes the bounded-delay model (Hajek. CISS 2001. Kesselman et al. STOC 2001). Competitive analysis is employed to measure an online algorithm’s performance. For the single-buffer model, we first show that the lower bound of competitive ratios of a family of deterministic online algorithms is 2 — all previously known deterministic algorithms for the boundeddelay model fall in this category. Then we present a 3-competitive deterministic algorithm and a randomized 2.618-competitive algorithm. For the single-buffer model, no previously known algorithm has a competitive ratio better than 9.82 (Azar, Levy. SWAT 2006). The multi-buffer model has been studied by Azar and Levy (Azar, Levy. SWAT 2006) and they developed a 9.82-competitive deterministic algorithm. We propose a deterministic algorithm for the multi-buffer model achieving a competitive ratio of 6.828. Our algorithms as well as their analysis have several interesting features. We design algorithms for both models using the same generic algorithmic framework: greedily maintaining the packets in the buffers with (possibly) modified characteristics. Our analysis is different from the classic potential function approach. For the single-buffer model, we apply a simple charging scheme which depends on a modification of the packets in the adversary’s buffer. We then prove that a set of invariants hold at the end of each time step. For the multi-buffer model, we create an intermediate weaker adversary that gains at least 1/c1 of what an optimal offline algorithm gains. Then we prove that compared with this weaker adversary, our algorithm is at least c2-competitive. Altogether, our algorithm is (c1 · c2)-competitive. Department of Computer Science, George Mason University. [email protected].