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Delay bounds for packetizing time-varying fluid policies with speedup and lookahead in single server systems

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3 Author(s)
Yim, R. ; Div. of Eng. & Appl. Sci., Harvard Univ., Cambridge, MA, USA ; Rosenblum, M. ; Tarokh, Vahid

We consider an online, processor sharing system with a single server in a packet-switched network where the processor multiplexes packets from multiple input ports onto the same output link. Under a fluid model, in which incoming data is treated as infinitely divisible, the multiplexer allocates its output capacity to serve fractions of packets from all input ports simultaneously (which we call a fluid policy). However, due to the packet nature of the network traffic, a multiplexer scheduler must approximate this fluid policy by a schedule in which only whole packets are sent (which we call a packetized policy). We assume that at each time instant, the aggregate service rate demanded by a fluid policy is no greater than the output link capacity. Then, for a single server with N input ports, and a scheduler using speedup s of at least 2 and a lookahead window of L≥0 time steps, we prove bounds on worst-case maximum additional delay D. In particular, we show that ([Ne-s]-L-2)+≤D min {([Ne1-s]-L)+, [Ne-s]}. In the case when no lookahead is used (L=0), a tighter bound can be obtained: ([Ne-s]-2)+≤D≤[Ne-s}.

Published in:

INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE  (Volume:4 )

Date of Conference:

13-17 March 2005