Design model of a twisted and folded Clos network with multi-step grouped intermediate switches guaranteeing admissible blocking probability

Haruto Taka; Takeru Inoue; Eiji Oki

doi:10.1364/JOCN.513898

Journal of Optical Communications and Networking
Vol. 16,
Issue 3,
pp. 328-341
(2024)
•https://doi.org/10.1364/JOCN.513898

Design model of a twisted and folded Clos network with multi-step grouped intermediate switches guaranteeing admissible blocking probability

Haruto Taka, Takeru Inoue, and Eiji Oki

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Haruto Taka, Takeru Inoue, and Eiji Oki, "Design model of a twisted and folded Clos network with multi-step grouped intermediate switches guaranteeing admissible blocking probability," J. Opt. Commun. Netw. 16, 328-341 (2024)

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Abstract

A future data center network is expected to be constructed by a Clos network consisting of optical-circuit switches to deal with traffic growth. A previous model addressed a Clos-network design problem that divides the set of intermediate switches by each role for request routing to guarantee an admissible blocking probability to maximize the switching capacity. However, the previous model divides the set of intermediate switches into at most only two groups, and there is room for a more flexible design by increasing the number of divisions. This paper proposes a design model that generalizes the number of divisions to increase the switching capacity while guaranteeing an admissible blocking probability. We formulate the design model as an optimization problem. We introduce two algorithms to obtain a feasible solution that satisfies the constraints of the optimization problem. Numerical results showed that the proposed model can increase the switching capacity as the number of divisions increases.

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Parameters	Descriptions
$N$	Number of ports in a switch
$a$	Number of switches that we can use
$p$	Probability of arrival rate of a request
$S$	Number of steps
$ϵ$	Admissible blocking probability in the network
Variables	Descriptions
$n$	Natural number variable that is the number of ports that are used in an input-output switch
$k$	Natural number variable that is the number of input-output switches in the network
$n_{s}^{s n b}$	Integer variable that is the number of ports that satisfy the SNB condition in the $s$ th-step group, $s \in [1, S]$
$m_{s}$	Integer variable that is the number of intermediate switches in the $s$ th-step group, $s \in [1, S]$
$v_{s}$	Integer variable that is the number of links between an input-output switch and an intermediate switch in the $s$ th-step group, $s \in [1, S]$
$ϵ_{s}$	Real number variable that is the upper bound of the blocking probability up to the $s$ th step, $s \in [1, S]$

Parameters	Descriptions
$N$	Number of ports in a switch
$a$	Number of switches that we can use
$p$	Probability of arrival rate of a request
$S$	Number of steps
$ϵ$	Admissible blocking probability in the network
Variables	Descriptions
$n$	Natural number variable that is the number of ports that are used in an input-output switch
$k$	Natural number variable that is the number of input-output switches in the network
$n_{s}^{s n b}$	Integer variable that is the number of ports that satisfy the SNB condition in the $s$ th-step group, $s \in [1, S]$
$m_{s}$	Integer variable that is the number of intermediate switches in the $s$ th-step group, $s \in [1, S]$
$v_{s}$	Integer variable that is the number of links between an input-output switch and an intermediate switch in the $s$ th-step group, $s \in [1, S]$
$ϵ_{s}$	Real number variable that is the upper bound of the blocking probability up to the $s$ th step, $s \in [1, S]$

Abstract

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Equations (26)

Journal of Optical Communications and Networking