Network Performance Trade-Off in Modular Data Centers With Optical Spatial Division Multiplexing

Li Yan; Matteo Fiorani; Ajmal Muhammad; Massimo Tornatore; Erik Agrell; Lena Wosinska

doi:10.1364/JOCN.10.000796

Journal of Optical Communications and Networking
Vol. 10,
Issue 9,
pp. 796-808
(2018)
•https://doi.org/10.1364/JOCN.10.000796

Network Performance Trade-Off in Modular Data Centers With Optical Spatial Division Multiplexing

Li Yan, Matteo Fiorani, Ajmal Muhammad, Massimo Tornatore, Erik Agrell, and Lena Wosinska

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Li Yan, Matteo Fiorani, Ajmal Muhammad, Massimo Tornatore, Erik Agrell, and Lena Wosinska, "Network Performance Trade-Off in Modular Data Centers With Optical Spatial Division Multiplexing," J. Opt. Commun. Netw. 10, 796-808 (2018)

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Abstract

Modular design based on spatial division multiplexing switches is a promising way to improve the capacity and reduce the cabling complexity of data center networks. However, due to the coexistence of mice and elephant flows, in modular data center networks a trade-off between the blocking probability and total throughput arises. In fact, blocking elephant flows would lead to a relevant penalty on the throughput but a small penalty on the blocking probability. In this paper, we investigate the relation between the blocking and throughput in modular data center networks based on optical spatial division multiplexing. We combine the two metrics linearly by a weight factor that prioritizes them relatively. To solve the resource allocation problem, we propose both mixed integer linear programming formulations and close-to-optimal heuristics for three different spatial division multiplexing switching schemes. Simulation results demonstrate that a carefully chosen weight factor is necessary to achieve a proper balance between the blocking probability and throughput for all the schemes.

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Symbol	Meaning
$P$	Set of PODs
$T$	Set of connection requests
$T^{s}$	A subset of $T$ selected by the spatial element assignment
$Γ$	Set of spatial elements in an SDM fiber
$Ω$	Set of spectral slots per spatial element in an SDM fiber
$T_{i}$	Set of requests connecting POD $i \in P$
$T_{i}^{2}$	$T_{i}^{2} = {(u, v) \| u, v \in T_{i}, u \neq v}$ for $i \in P$
$H_{u}$	Set of candidate spectral–spatial superchannels for connection $u \in T$ in A3, where each element $h \in H_{u}$ has the form of $(κ_{u h}, λ_{u h})$
$f_{u}$	Required number of spectral slots by connection $u \in T$ in A1 and A2
$κ_{u h}$	Number of spectral elements required by the candidate $h \in H_{u}$ of connection $u \in T$ in A3
$λ_{u h}$	Number of spatial elements required by the candidate $h \in H_{u}$ of connection $u \in T$ in A3
$t_{u}$	Requested bit rate of connection $u \in T$
$t_{ave}$	$t_{ave} = \frac{1}{\| T \|} \sum_{u \in T} t_{u}$
$β$	Weight factor in the objective

Symbol	Meaning
$x_{i u k} \in {0, 1}$	Equals 1 if the connection $u \in T$ in A1 uses the spatial element $k \in Γ$ in the fiber connecting POD $i \in P$
$y_{u} \in {0, 1}$	Equals 1 if $u \in T$ is successfully provisioned
$w_{u} \in N^{+}$	Index of the first spectral slot assigned to $u \in T$
$δ_{u v} \in {0, 1}$	Equals 1 if the first spectral slot assigned to $u$ is smaller than the first spectral slot assigned to $v$ for $(u, v) \in \cup_{i \in P} T_{i}^{2}$
$r_{i u} \in N^{+}$	Index of the first spatial element assigned to $u \in T_{i}$ in A3, $i \in P$
$z_{u h} \in {0, 1}$	Equals 1 if $u \in T$ in A3 selects candidate $h \in H_{u}$
$γ_{i u v} \in {0, 1}$	Equals 1 if $u$ and $v$ in A3 share any spatial element, $(u, v) \in T_{i}^{2}, i \in P$
$q_{i u v} \in {0, 1}$	Equals 1 if $u$ and $v$ in A3 do not share any spatial element and the indexes of all the spatial elements in $u$ are smaller than those in $v$ , $(u, v) \in T_{i}^{2}, i \in P$
$p_{u v} \in {0, 1}$	Equals 0 if $u$ and $v$ in A3 are both successfully established, $(u, v) \in \cup_{i \in P} T_{i}^{2}$
$κ_{u} \in N^{+}$	Required number of spectral elements by $u \in T$ in A3
$λ_{u} \in N^{+}$	Required number of spatial elements by $u \in T$ in A3

Symbol	Meaning
$P$	Set of PODs
$T$	Set of connection requests
$T^{s}$	A subset of $T$ selected by the spatial element assignment
$Γ$	Set of spatial elements in an SDM fiber
$Ω$	Set of spectral slots per spatial element in an SDM fiber
$T_{i}$	Set of requests connecting POD $i \in P$
$T_{i}^{2}$	$T_{i}^{2} = {(u, v) \| u, v \in T_{i}, u \neq v}$ for $i \in P$
$H_{u}$	Set of candidate spectral–spatial superchannels for connection $u \in T$ in A3, where each element $h \in H_{u}$ has the form of $(κ_{u h}, λ_{u h})$
$f_{u}$	Required number of spectral slots by connection $u \in T$ in A1 and A2
$κ_{u h}$	Number of spectral elements required by the candidate $h \in H_{u}$ of connection $u \in T$ in A3
$λ_{u h}$	Number of spatial elements required by the candidate $h \in H_{u}$ of connection $u \in T$ in A3
$t_{u}$	Requested bit rate of connection $u \in T$
$t_{ave}$	$t_{ave} = \frac{1}{\| T \|} \sum_{u \in T} t_{u}$
$β$	Weight factor in the objective

Symbol	Meaning
$x_{i u k} \in {0, 1}$	Equals 1 if the connection $u \in T$ in A1 uses the spatial element $k \in Γ$ in the fiber connecting POD $i \in P$
$y_{u} \in {0, 1}$	Equals 1 if $u \in T$ is successfully provisioned
$w_{u} \in N^{+}$	Index of the first spectral slot assigned to $u \in T$
$δ_{u v} \in {0, 1}$	Equals 1 if the first spectral slot assigned to $u$ is smaller than the first spectral slot assigned to $v$ for $(u, v) \in \cup_{i \in P} T_{i}^{2}$
$r_{i u} \in N^{+}$	Index of the first spatial element assigned to $u \in T_{i}$ in A3, $i \in P$
$z_{u h} \in {0, 1}$	Equals 1 if $u \in T$ in A3 selects candidate $h \in H_{u}$
$γ_{i u v} \in {0, 1}$	Equals 1 if $u$ and $v$ in A3 share any spatial element, $(u, v) \in T_{i}^{2}, i \in P$
$q_{i u v} \in {0, 1}$	Equals 1 if $u$ and $v$ in A3 do not share any spatial element and the indexes of all the spatial elements in $u$ are smaller than those in $v$ , $(u, v) \in T_{i}^{2}, i \in P$
$p_{u v} \in {0, 1}$	Equals 0 if $u$ and $v$ in A3 are both successfully established, $(u, v) \in \cup_{i \in P} T_{i}^{2}$
$κ_{u} \in N^{+}$	Required number of spectral elements by $u \in T$ in A3
$λ_{u} \in N^{+}$	Required number of spatial elements by $u \in T$ in A3

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Equations (34)

Journal of Optical Communications and Networking