Abstract
We give a memoryless scale-invariant randomized algorithm ReMix for Packet Scheduling that is e/(e−1)-competitive against an adaptive adversary. ReMix unifies most of previously known randomized algorithms, and its general analysis yields improved performance guarantees for several restricted variants, including the s-bounded instances. In particular, ReMix attains the optimum competitive ratio of 4/3 on 2-bounded instances. Our results are applicable to a more general problem, called Item Collection, in which only the relative order between packets’ deadlines is known. ReMix is the optimal memoryless randomized algorithm against adaptive adversary for that problem.
Highlights
In this paper, we consider the problem of Packet Scheduling, introduced by Kesselman et al [14]
Among such algorithms are the EDFβ algorithms, RMIX, and our algorithm REMIX—reader is advised to keep this in mind, because we present it for the more popular setting of Packet Scheduling
While the paper of Bienkowski’s et al [3] focuses on deterministic algorithms for Item Collection, it does provide a lower bound for memoryless randomized algorithms, matched by REMIX, cf
Summary
We consider the problem of Packet Scheduling, introduced by Kesselman et al [14] (under the name Buffer Management with Bounded Delay). We prefer to call the problem Packet Scheduling since it is equivalent to a single machine scheduling of unit-length jobs, with given weights, release times and deadlines; the last two restricted to integer values. In this setting, the goal is to maximize the total weight of jobs completed before their respective deadlines. As the process of managing a packet queue is inherently a real-time task, we model it as an online problem This means that the algorithm, when deciding which packets to transmit, has to base its decision solely on the packets which have already arrived at a switch, without the knowledge of the future
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