Static multi-sourced data retrieval in elastic optical networks

Juzi Zhao; Vinod M. Vokkarane; Vinod M. Vokkarane

doi:10.1364/JOCN.465019

Journal of Optical Communications and Networking
Vol. 14,
Issue 10,
pp. 792-804
(2022)
•https://doi.org/10.1364/JOCN.465019

Static multi-sourced data retrieval in elastic optical networks

Juzi Zhao and Vinod M. Vokkarane

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Juzi Zhao and Vinod M. Vokkarane, "Static multi-sourced data retrieval in elastic optical networks," J. Opt. Commun. Netw. 14, 792-804 (2022)

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History
- Original Manuscript: May 24, 2022
- Revised Manuscript: August 1, 2022
- Manuscript Accepted: August 26, 2022
- Published: September 14, 2022

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Abstract

Extreme-scale science applications are highly innovative and constantly evolving. They are expected to generate data in the petabyte and exabyte ranges. Erasure coding has been widely adopted for data storage in data center networks, where the data are encoded and stored in multiple locations. Therefore, an efficient data retrieval service is needed to transfer encoded data from selected multiple stored nodes to a single destination. Elastic optical networks are a promising backbone technology for data center communication due to their capability to efficiently and flexibly allocate the huge optical bandwidth to heterogeneous traffic demands. In this paper, the erasure-coded multi-sourced data retrieval routing and scheduling problem is studied for static traffic in elastic optical networks, and the objective is to minimize the total transmission completion time of all the requests. An integer linear programming formulation and low-complexity heuristic are proposed. Furthermore, analytical lower bounds are derived and a meta-heuristic, Tabu Search, is adopted to solve the problem. Numerical results are presented to show the effectiveness of the proposed methods.

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Symbol	Meaning
$T \in N$	Completion time-slot of all requests
$s_{i}^{v} \in B$	$s_{i}^{v} = 1$ if storage node $v$ (one of the $n$ candidate sources) is selected by request $i$
$p_{ij}^{k} \in B$	$p_{ij}^{k} = 1$ if path $k \in K$ candidate paths (with the corresponding source node and destination node) is assigned to data segment $j$ of request $i$
$r_{ij}^{w} \in B$	$r_{ij}^{w} = 1$ if data segment $j$ of request $i$ is assigned $w$ contiguous subcarriers
$q_{ij}^{z} \in B$	$q_{ij}^{z} = 1$ if data segment $j$ of request $i$ is assigned modulation format $z$
$h_{ij}^{t} \in B$	$h_{ij}^{t} = 1$ if the starting transmission time-slot for data segment $j$ of request $i$ is $t$
$τ_{ij}^{t} \in B$	$τ_{ij}^{t} = 1$ if the transmission of data segment $j$ of request $i$ uses time-slot $t$
$π_{ij}^{vt} \in B$	$π_{ij}^{vt} = 1$ if the transmission of data segment $j$ of request $i$ uses a transponder on node $v$ at time-slot $t$
$g_{ij}^{w} \in B$	$g_{ij}^{w} = 1$ if the starting subcarriers allocated to data segment $j$ of request $i$ are $w$
$y_{i j i^{'} j^{'}} \in B$	$y_{i j i^{'} j^{'}} = 1$ if data segment $j$ of request $i$ and data segment $j^{'}$ of request $i^{'}$ share common links and time-slots
$u_{i j i^{'} j^{'}} \in B$	$u_{i j i^{'} j^{'}} = 1$ if $y_{i j i^{'} j^{'}} = 1$ and the ending subcarrier index allocated to data segment $j$ of request $i$ is smaller than the starting subcarrier index allocated to data segment $j^{'}$ of request $i^{'}$
$α_{i j i^{'} j^{'}} \in B$	$α_{i j i^{'} j^{'}} = 1$ if data segment $j$ of request $i$ and data segment $j^{'}$ of request $i^{'}$ share any common link
$σ_{ij} \in B$	$σ_{ij} = 1$ if data segment $j$ of request $i$ is combined with another data segment of $i$ to be transmitted together
$c_{i j j^{'}} \in B$	$c_{i j j^{'}} = 1$ if $σ_{ij} = 0$ and data segments $j$ and $j^{'}$ $(j^{'} > j)$ of request $i$ are combined to be transmitted together, and $c_{i j j^{'}} = 0$ for $j^{'} \leq j$

Symbol	Meaning
$A_{i}^{v} \in B$	$A_{i}^{v} = 1$ if node $v$ is a candidate source node for request $i$
$f_{kl} \in B$	$f_{kl} = 1$ if link $l$ is on path $k$
$E_{ij}^{v} \in B$	$E_{ij}^{v} = 1$ if data segment $j$ of request $i$ is stored on candidate node $v$
$X_{z}$	Spectrum efficiency of modulation scheme $z$ (in terms of bps/Hz)
$z_{k}$	Modulation format of path $k$
$D_{i}^{v} \in B$	$D_{i}^{v} = 1$ if node $v$ is a destination node for request $i$
$θ$	Very large number
$η_{v}^{t}$	Number of transponders equipped on node $v$ at time-slot $t$
$F$	Size of each data segment in GB
$C$	Bandwidth of each subcarrier in GHz
$G$	Number of subcarriers used as the guardband
$Q$	Capacity of each transponder (in Gbps)

Symbol	Meaning
$T \in N$	Completion time-slot of all requests
$s_{i}^{v} \in B$	$s_{i}^{v} = 1$ if storage node $v$ (one of the $n$ candidate sources) is selected by request $i$
$p_{ij}^{k} \in B$	$p_{ij}^{k} = 1$ if path $k \in K$ candidate paths (with the corresponding source node and destination node) is assigned to data segment $j$ of request $i$
$r_{ij}^{w} \in B$	$r_{ij}^{w} = 1$ if data segment $j$ of request $i$ is assigned $w$ contiguous subcarriers
$q_{ij}^{z} \in B$	$q_{ij}^{z} = 1$ if data segment $j$ of request $i$ is assigned modulation format $z$
$h_{ij}^{t} \in B$	$h_{ij}^{t} = 1$ if the starting transmission time-slot for data segment $j$ of request $i$ is $t$
$τ_{ij}^{t} \in B$	$τ_{ij}^{t} = 1$ if the transmission of data segment $j$ of request $i$ uses time-slot $t$
$π_{ij}^{vt} \in B$	$π_{ij}^{vt} = 1$ if the transmission of data segment $j$ of request $i$ uses a transponder on node $v$ at time-slot $t$
$g_{ij}^{w} \in B$	$g_{ij}^{w} = 1$ if the starting subcarriers allocated to data segment $j$ of request $i$ are $w$
$y_{i j i^{'} j^{'}} \in B$	$y_{i j i^{'} j^{'}} = 1$ if data segment $j$ of request $i$ and data segment $j^{'}$ of request $i^{'}$ share common links and time-slots
$u_{i j i^{'} j^{'}} \in B$	$u_{i j i^{'} j^{'}} = 1$ if $y_{i j i^{'} j^{'}} = 1$ and the ending subcarrier index allocated to data segment $j$ of request $i$ is smaller than the starting subcarrier index allocated to data segment $j^{'}$ of request $i^{'}$
$α_{i j i^{'} j^{'}} \in B$	$α_{i j i^{'} j^{'}} = 1$ if data segment $j$ of request $i$ and data segment $j^{'}$ of request $i^{'}$ share any common link
$σ_{ij} \in B$	$σ_{ij} = 1$ if data segment $j$ of request $i$ is combined with another data segment of $i$ to be transmitted together
$c_{i j j^{'}} \in B$	$c_{i j j^{'}} = 1$ if $σ_{ij} = 0$ and data segments $j$ and $j^{'}$ $(j^{'} > j)$ of request $i$ are combined to be transmitted together, and $c_{i j j^{'}} = 0$ for $j^{'} \leq j$

Symbol	Meaning
$A_{i}^{v} \in B$	$A_{i}^{v} = 1$ if node $v$ is a candidate source node for request $i$
$f_{kl} \in B$	$f_{kl} = 1$ if link $l$ is on path $k$
$E_{ij}^{v} \in B$	$E_{ij}^{v} = 1$ if data segment $j$ of request $i$ is stored on candidate node $v$
$X_{z}$	Spectrum efficiency of modulation scheme $z$ (in terms of bps/Hz)
$z_{k}$	Modulation format of path $k$
$D_{i}^{v} \in B$	$D_{i}^{v} = 1$ if node $v$ is a destination node for request $i$
$θ$	Very large number
$η_{v}^{t}$	Number of transponders equipped on node $v$ at time-slot $t$
$F$	Size of each data segment in GB
$C$	Bandwidth of each subcarrier in GHz
$G$	Number of subcarriers used as the guardband
$Q$	Capacity of each transponder (in Gbps)

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Equations (26)

Journal of Optical Communications and Networking