Englert, Matthias and Westermann, Matthias (2009) Lower and upper bounds on FIFO buffer management in QoS switches. Algorithmica, Volume 53 (Number 4). pp. 523-548. doi:10.1007/s00453-008-9236-5

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Abstract

We consider the management of FIFO buffers for network switches providing differentiated services. In each time step, an arbitrary number of packets arrive and only one packet can be sent. The buffer can store a limited number of packets and, due to the FIFO property, the sequence of sent packets has to be a subsequence of the arriving packets. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy can drop packets, and the goal is to maximize the sum of the values of sent packets.
For only two different packet values, we introduce the account strategy and prove that this strategy achieves an optimal competitive ratio of $\sqrt{2}-(\sqrt{5+4\sqrt{2}}-3)/2\approx 1.282$ if the buffer size tends to infinity and an optimal competitive ratio of $(\sqrt{13}-1)/2\approx 1.303$ for arbitrary buffer sizes. For general packet values, the simple preemptive greedy strategy (PG) is studied. We show that PG achieves a competitive ratio of $\sqrt{3}\approx 1.732$ which is the best known upper bound on the competitive ratio of this problem. In addition, we give a lower bound of $1+1/\sqrt{2}\approx 1.707$ on the competitive ratio of PG which improves the previously known lower bound. As a consequence, the competitive ratio of PG cannot be further improved significantly.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Journal or Publication Title:	Algorithmica
Publisher:	Springer Verlag
ISSN:	0178-4617
Book Title:	Algorithmica
Official Date:	1 April 2009
Dates:	Date Event 1 April 2009 Published 25 October 2008 Available 8 October 2008 Accepted 15 December 2006 Submitted
Volume:	Volume 53
Number:	Number 4
Page Range:	pp. 523-548
DOI:	10.1007/s00453-008-9236-5
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Deutsche Forschungsgemeinschaft (DFG)
Grant number:	WE 2842/1 (DFG)
Version or Related Resource:	A preliminary version of this paper appeared in Proceedings of the 14th Annual European Symposium on Algorithms (ESA), 2006.

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