Journal of Optical Communications and Networking
Vol. 7,
Issue 7,
pp. 644-655
(2015)
•https://doi.org/10.1364/JOCN.7.000644

Impact of Wavelength and Modulation Conversion on Translucent Elastic Optical Networks Using MILP

X. Wang, M. Brandt-Pearce, and S. Subramaniam

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X. Wang, M. Brandt-Pearce, and S. Subramaniam, "Impact of Wavelength and Modulation Conversion on Translucent Elastic Optical Networks Using MILP," J. Opt. Commun. Netw. 7, 644-655 (2015)

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Abstract

Compared to legacy wavelength division multiplexing networks, elastic optical networks (EONs) have added flexibility to network deployment and management. EONs can include previously available functionality, such as signal regeneration and wavelength conversion, as well as new features such as finer-granularity spectrum assignment and modulation conversion. Yet each added feature adds to the cost of the network. In order to quantify the potential benefit of each functionality, we present a link-based mixed-integer linear programming (MILP) formulation to solve the optimal resource allocation problem. We then propose a recursive model in order to either augment existing network deployments (spectrum and regenerators) or speed up the resource allocation computation time for larger networks with higher traffic demand requirements than can be solved using an MILP. We show through simulation that systems equipped with signal regenerators or wavelength converters require a notably smaller total bandwidth, depending on the topology of the network. We also show that the suboptimal recursive solution speeds up the calculation and makes the running time more predictable, compared to the optimal MILP.

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$N$	Set of nodes in the network.
$L$	Set of unidirectional links in the network. Each link $L_{i j}$ is represented by its source and destination node, $L_{i j} \in L$ .
$D$	Set of unidirectional traffic demands. Each demand $D_{s d}$ is represented by its source node $s$ and destination node $d$ , $D_{s d} \in D$ .

$b_{s d}$	Bit rate requested by demand $D_{s d}$ .
$η_{s d}$	Spectrum efficiency according to particular modulation scheme (e.g., 2 for QPSK).
$S_{n, s d}$	Relationship between nodes and demands: $S_{n, s d} = - 1$ if node $n$ is the source node of demand $D_{s d}$ (i.e., $n = s$ ); $S_{n, s d} = 1$ if node $n$ is the destination node of demand $D_{s d}$ (i.e., $n = d$ ); $S_{n, s d} = 0$ otherwise (i.e., $n \neq s$ , $n \neq d$ ).
$G$	Guard band in gigahertz.

$F_{s d}$	Starting frequency index of demand $D_{s d}$ .
$V_{i j, s d}$	Link assignment: $V_{i j, s d} = 1$ if link $L_{i j}$ is assigned to demand $D_{s d}$ ; $V_{i j, s d} = 0$ otherwise.
$δ_{s d, s^{'} d^{'}}$	Order of the starting frequency index of demand $D_{s d}$ and $D_{s^{'} d^{'}}$ .^a $δ_{s d, s^{'} d^{'}} = 1$ if $F_{s d} \leq F_{s^{'} d^{'}}$ ; $δ_{s d, s^{'} d^{'}} = 0$ if $F_{s d} > F_{s^{'} d^{'}}$ .
$c$	Highest frequency index required by the network traffic.

$ℓ_{i j}$	Length of link $L_{i j}$ in kilometers.
$R_{s d}$	Transmission reach of demand $D_{s d}$ according to particular spectral efficiency, e.g., in Eq. (1)
$N^{r}$	Set of regeneration nodes.

$Y_{n, s d}$	$Y_{n, s d} = 0$ if node $n$ is not on the lightpath assigned to demand $D_{s d}$ . Otherwise, $Y_{n, s d}$ is the physical distance from node $n$ on the lightpath to the beginning of that transparent segment for demand $D_{s d}$ .
$U_{i j, s d}$	$U_{i j, s d} = 0$ if the entire link $L_{i j}$ is not assigned to demand $D_{s d}$ ( $V_{i j, s d} = 0$ ). Otherwise, $U_{i j, s d}$ is the physical distance from node $i$ to the beginning of the transparent segment for demand $D_{s d}$ . Equivalently, if we were not restricted to linear functions, we could have defined $U_{i j, s d} = V_{i j, s d} Y_{i, s d}$ .

$I_{n}$	Regeneration nodes: $I_{n} = 1$ if node $n$ is used as a regeneration node; $I_{n} = 0$ otherwise.
$N_{n, c}$	Number of regeneration devices used on node $n$ .
$I_{n, s d}$	Regeneration at node $n$ : $I_{n, s d} = 1$ if demand $D_{s d}$ is regenerated at node $n$ , $I_{n, s d} = 0$ otherwise. For $I_{n, s d} = 1$ , node $n$ has to be a regeneration node, i.e., $I_{n} = 1$ , but also its regeneration circuit has to be used by demand $D_{s d}$ .
$X_{i j, s d}$	Distance used to calculate $Y_{n, s d}$ based on whether regeneration occurs at node $i$ : $X_{i j, s d} = U_{i j, s d}$ if $I_{i, s d} = 0$ , $X_{i j, s d} = 0$ otherwise.

$F_{i j, s d}$	Starting frequency index of demand $D_{s d}$ on link $L_{i j}$ .
$η_{s d, i j}^{- 1}$	Inverse spectral efficiency of demand $D_{s d}$ on link $L_{i j}$ .

Number of Variables		Number of Constraints
Nonrecursive	Recursive	Nonrecursive	Recursive
$(1 + L + \| D \|) \times \| D \| + 1$	$(1 + L + \| D \| / S) \times \| D \| / S$	$\| D \| + N \| D \| + (1 + 2 L) \times {\| D \|}^{2}$	$\| D \| / S + N \| D \| / S + (1 + 2 L) \times {(\| D \| / S)}^{2}$

Impact of Wavelength and Modulation Conversion on Translucent Elastic Optical Networks Using MILP

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Journal of Optical Communications and Networking