An algorithm for improved delay-scaling in input-queued switches
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11134_2021_9726_ReferencePDF.pdf
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Author(s)
Weng, Wentao
Srikant, R.
Date Issued
January 15, 2022
Publisher
Springer US
Citation
Weng, Wentao and Srikant, R. 2022. "An algorithm for improved delay-scaling in input-queued switches."
Version
Author's final manuscript
Abstract
Abstract
We consider an
$$n\times n$$
n
×
n
input-queued switch with uniform Bernoulli traffic and study the delay (or equivalently, the queue length) in the regime where the size of the switch n and the load (denoted by
$$\rho $$
ρ
) simultaneously become large. We devise an algorithm with expected total queue length equal to
$$O((n^{5/4}(1-\rho )^{-1})\log \max (1/\rho ,n))$$
O
(
(
n
5
/
4
(
1
-
ρ
)
-
1
)
log
max
(
1
/
ρ
,
n
)
)
for large n and
$$\rho $$
ρ
such that
$$(1-\rho )^{-1} \ge n^{3/4}$$
(
1
-
ρ
)
-
1
≥
n
3
/
4
. This result improves the previous best queue length bound in the regime
$$n^{3/4}< (1-\rho )^{-1} < n^{7/4}$$
n
3
/
4
<
(
1
-
ρ
)
-
1
<
n
7
/
4
. Under same conditions, the algorithm has an amortized time complexity
$$O(n+(1-\rho )^2 n^{7/2} / \log \max (1/\rho ,n))$$
O
(
n
+
(
1
-
ρ
)
2
n
7
/
2
/
log
max
(
1
/
ρ
,
n
)
)
. The time complexity becomes O(n) when
$$(1-\rho )^{-1} \ge n^{5/4}.$$
(
1
-
ρ
)
-
1
≥
n
5
/
4
.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s11134-021-09726-7
