Lower and Upper Bounds on FIFO Buffer Management in QoS Switches |
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Authors: | Matthias Englert Matthias Westermann |
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Affiliation: | (1) Department of Computer Science, RWTH Aachen, 52056 Aachen, Germany |
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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
if the buffer size tends to infinity and an optimal competitive ratio of
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
which is the best known upper bound on the competitive ratio of this problem. In addition, we give a lower bound of
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.
Supported by the DFG grant WE 2842/1. A preliminary version of this paper appeared in Proceedings of the 14th Annual European
Symposium on Algorithms (ESA), 2006. |
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Keywords: | Online algorithms Buffer management Computer networks Quality of service |
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