Algorithms for Scheduling Weighted Packets with Deadlines in a Bounded Queue

TL;DR

This paper introduces online algorithms for scheduling packets with deadlines in a finite-capacity queue, achieving competitive ratios of 3 deterministically and approximately 2.618 randomly, without stochastic assumptions.

Contribution

It presents the first deterministic and randomized memoryless online algorithms with proven competitive ratios for the finite-queue packet scheduling problem.

Findings

Deterministic 3-competitive online algorithm.

Randomized approximately 2.618-competitive online algorithm.

Novel analysis method beyond classical potential functions.

Abstract

Motivated by the Quality-of-Service (QoS) buffer management problem, we consider online scheduling of packets with hard deadlines in a finite capacity queue. At any time, a queue can store at most $b \in \mathbb Z^+$ packets. Packets arrive over time. Each packet is associated with a non-negative value and an integer deadline. In each time step, only one packet is allowed to be sent. Our objective is to maximize the total value gained by the packets sent by their deadlines in an online manner. Due to the Internet traffic's chaotic characteristics, no stochastic assumptions are made on the packet input sequences. This model is called a {\em finite-queue model}. We use competitive analysis to measure an online algorithm's performance versus an unrealizable optimal offline algorithm who constructs the worst possible input based on the knowledge of the online algorithm. For the finite-queue model, we first present a deterministic 3-competitive memoryless online algorithm. Then, we give a randomized ($\phi^2 = ((1 + \sqrt{5}) / 2)^2 \approx 2.618$)-competitive memoryless online algorithm. The algorithmic framework and its theoretical analysis include several interesting features. First, our algorithms use (possibly) modified characteristics of packets; these characteristics may not be same as those specified in the input sequence. Second, our analysis method is different from the classical potential function approach.