In this work, we clarify, extend and solve an open problem concerning the computational complexity for packet scheduling algorithms to achieve tight end-to-end delay bounds. We first focus on the difference between the time a packet finishes service in a scheduling algorithm and its virtual finish time under a GPS (General Processor Sharing) scheduler, called GPS- relative delay . We prove that, under a slightly restrictive but reasonable computational model, the lower bound computational complexity of any scheduling algorithm that guarantees O (1) GPS-relative delay bound is Ω ( log 2 n ) (widely believed as a "folklore theorem" but never proved). We also discover that, surprisingly, the complexity lower bound remains the same even if the delay bound is relaxed to O ( n a ) for 0‹ a ⋵1. This implies that the delay-complexity tradeoff curve is "flat" in the "interval" O (1), O ( n )). We later extend both complexity results (for O (1) or O ( n a ) delay) to a much stronger computational model. Finally, we show that the same complexity lower bounds are conditionally applicable to guaranteeing tight end-to-end delay bounds. This is done by untangling the relationship between the GPS-relative delay bound and the end-to-end delay bound.
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On fundamental tradeoffs between delay bounds and computational complexity in packet scheduling algorithms
Xu, Jun; Lipton, Richard J.
Follow ACM SIGCOMM Computer Communication Review
, Volume 32 (4)
Association for Computing Machinery – Oct 1, 2002
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