Achieving 100% throughput in an input-queued switch
McKeown, N.; Mekkittikul, A.; Anantharam, V.; Walrand, J.
Communications, IEEE Transactions on
Volume 47, Issue 8, Aug 1999 Page(s):1260 - 1267
Digital Object Identifier 10.1109/26.780463
Summary:It is well known that head-of-line blocking limits the throughput
of an input-queued switch with first-in-first-out (FIFO) queues. Under
certain conditions, the throughput can be shown to be limited to
approximately 58.6%. It is also known that if non-FIFO queueing policies
are used, the throughput can be increased. However, it has not been
previously shown that if a suitable queueing policy and scheduling
algorithm are used, then it is possible to achieve 100% throughput for
all independent arrival processes. In this paper we prove this to be the
case using a simple linear programming argument and quadratic Lyapunov
function. In particular, we assume that each input maintains a separate
FIFO queue for each output and that the switch is scheduled using a
maximum weight bipartite matching algorithm. We introduce two maximum
weight matching algorithms: longest queue first (LQF) and oldest cell
first (OCF). Both algorithms achieve 100% throughput for all independent
arrival processes. LQF favors queues with larger occupancy, ensuring
that larger queues will eventually be served. However, we find that LQF
can lead to the permanent starvation of short queues. OCF overcomes this
limitation by favoring cells with large waiting times
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