Abstract
We consider scheduling information units called frames, each with a delivery deadline. Frames consist of packets, which arrive online in a roughly periodic fashion, and compete on allocation of transmission slots. A frame is deemed useful only if all its packets are delivered before its deadline. We focus on a “proportional” variant, where the value of each frame is proportional to its size, but the sizes and periods of the frames are arbitrary. We give a constant-competitive algorithm for this setting, assuming bounded jitter and some slack in the frames’ deadlines, the latter of which is necessary. Using standard techniques, our algorithm yields polylog-competitive algorithms for general instances with slack and bounded jitter.
Highlights
In many networking settings, the flows entering the network have a nice periodic or almost periodic structure
The network would like to guarantee the flows a pre-specified quality of service (QoS), where one of the most basic QoS guarantees is a deadline by which the transfer would be completed
A frame is considered completed if all its packets are delivered before the frame’s deadline, and the goal of a scheduling algorithm is to maximize the number of completed frames
Summary
The flows entering the network have a nice periodic or almost periodic structure. We note that the classic preemptive job scheduling problem of maximizing (weighted) throughput on a single machine (Kalyanasundaram and Pruhs 2000, 2003; Dürr et al 2012; Lucier et al 2013) corresponds to a special case of the problem we study in which all frames have period 1 and no jitter For such setting, a combination of constant-competitive deterministic algorithm for proportional variant (Baruah et al 1992) and the “classify and randomly select” technique (Awerbuch et al 1994) yields an algorithm with competitive ratio logarithmic in the max-to-min ratio of frames densities.
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