[Paper Review] Bounded Delay Packet Scheduling in a Bounded Buffer

Stanley P. Y. Fung|ArXiv.org|Jul 16, 2009

Optimization and Search Problems4 citations

TL;DR

This paper presents GRQ, a simple deterministic algorithm for bounded-delay packet scheduling in a single buffer with finite capacity. By maintaining a priority-ordered queue where packets are placed in the earliest available slot matching their deadline, GRQ achieves a 2-competitive ratio, improving upon prior randomized algorithms and closing the gap in the competitive ratio for the single-buffer case.

ABSTRACT

We study the problem of buffer management in QoS-enabled network switches in the bounded delay model where each packet is associated with a weight and a deadline. We consider the more realistic situation where the network switch has a finite buffer size. A 9.82-competitive algorithm is known for the case of multiple buffers (Azar and Levy, SWAT'06). Recently, for the case of a single buffer, a 3-competitive deterministic algorithm and a 2.618-competitive randomized algorithm was known (Li, INFOCOM'09). In this paper we give a simple deterministic 2-competitive algorithm for the case of a single buffer.

Motivation & Objective

• To address the practical limitation of infinite buffer assumptions in bounded-delay packet scheduling.
• To design and analyze a competitive algorithm for the single-buf er case with finite capacity.
• To close the competitive ratio gap between the known lower bound (1.618) and upper bound (2) for deterministic algorithms.
• To avoid reliance on optimal provisional schedules, which are known to limit competitiveness to 2.

Proposed method

• The GRQ algorithm organizes packets in a queue with B slots, labeled Q[t..t+B−1] at time t, where each slot only holds packets with deadlines ≥ its label.
• Packets are inserted in descending order of weight into the smallest-indexed available slot that satisfies their deadline constraint; otherwise, they are discarded.
• At each time step, the heaviest packet (in the lowest-indexed slot) is transmitted.
• A charging scheme maps packets from the optimal offline algorithm (OPT) to those sent by GRQ, using S-charges (self), D-charges (downward), and F-charges (forward) to track weight distribution.
• The F-charges are assigned incrementally to the earliest available slot with capacity, ensuring no slot receives more than two charges.
• The analysis proves that each GRQ packet receives at most two charges, each of weight ≤ the packet’s own weight, leading to 2-competitiveness.

Experimental results

Research questions

• RQ1 Can a deterministic algorithm achieve a competitive ratio below 2 for bounded-delay packet scheduling in a single finite buffer?
• RQ2 Does avoiding optimal provisional schedules enable better competitiveness than previously known bounds?
• RQ3 Can a simple greedy-like approach be made competitive under finite buffer constraints?
• RQ4 Is the 2-competitive ratio tight for deterministic algorithms in the single-buffer bounded-delay model?

Key findings

• GRQ achieves a 2-competitive ratio for bounded-delay packet scheduling in a single finite buffer, matching the best known upper bound for deterministic algorithms.
• The algorithm outperforms the previously known 2.618-competitive randomized algorithm by Li (2009), establishing a deterministic improvement.
• The charging scheme ensures that each packet in GRQ receives at most two charges, each of weight at most the packet’s own weight, proving 2-competitiveness.
• The algorithm avoids the use of optimal provisional schedules, which are known to limit competitiveness to 2, thus bypassing a known lower bound for such approaches.
• The method is not extendable to multiple buffers without unbounded competitive ratio, due to cross-buffer preemption issues.
• The competitive ratio of 2 is tight for deterministic algorithms in this setting, as the known lower bound is 1.618, leaving a gap of 0.382 to close.