Graph-Model-Based Dynamic Routing and Spectrum Assignment in Elastic Optical Networks

Ching-Fang Hsu; Yuan-Chih Chang; Siou-Ci Sie

doi:10.1364/JOCN.8.000507

Journal of Optical Communications and Networking
Vol. 8,
Issue 7,
pp. 507-520
(2016)
•https://doi.org/10.1364/JOCN.8.000507

Graph-Model-Based Dynamic Routing and Spectrum Assignment in Elastic Optical Networks

Ching-Fang Hsu, Yuan-Chih Chang, and Siou-Ci Sie

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Ching-Fang Hsu, Yuan-Chih Chang, and Siou-Ci Sie, "Graph-Model-Based Dynamic Routing and Spectrum Assignment in Elastic Optical Networks," J. Opt. Commun. Netw. 8, 507-520 (2016)

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Abstract

In recent years, the concept of the elastic optical network (EON) was proposed and very quickly became an attractive solution for flexible channel bandwidth utilization. Analogous to the routing and wavelength assignment (RWA) problem in traditional wavelength-routed networks, routing and spectrum assignment (RSA) is the most basic and critical resource management issue in EONs. In this work, we exploit and modify the layered graph model, which is a well-known RWA model, to design two RSA heuristic algorithms named LG-FF and LG-SP. Additionally, we also derive an analytical model to estimate the number of required layered graphs. Numerical results demonstrate that LG-SP can achieve the same blocking performance level with significant time complexity reduction as compared to the near-optimal solution. Whether we care about blocking performance or aim at saving computational time, the layered graph is an important representation model of resource utilization status to efficiently solve the RSA problem.

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Notation	Meaning
$G_{i d x} = (V_{i d x}, E_{i d x})$	The layered graph for slot $i d x$ , where $V_{i d x}$ and $E_{i d x}$ stand for the sets of vertices and edges in $G_{i d x}$ , respectively.
$v_{i, i d x}$	The corresponding vertex of $v_{i} \in V (e_{i} \in E)$ in $G_{i d x}$ .
$e_{i, i d x}$	The corresponding edge of $e_{i} \in E$ in $G_{i d x}$ if frequency slot $i d x$ is not occupied on $e_{i}$ .
$Λ$	The ordered set of layered graphs; sorted in ascending order of layered graph indices.
Head/Tail index	The indices of the first and the last elements of $Λ$ .
$G_{l_i d x}^{u_i d x} = (V_{l_i d x}^{u_i d x}, E_{l_i d x}^{u_i d x})$	The filter graph of slot range $[l_i d x, u_i d x]$ , where $V_{l_i d x}^{u_i d x} = {v_{i, l_i d x}^{u_i d x} \| \forall v_{i} \in V}$ and $E_{l_i d x}^{u_i d x} = {e_{i, l_i d x}^{u_i d x} \| \forall i ∋ e_{i, j} \in E_{j}$ for all $j \in [l_i d x, \min (u_i d x, the tail index)]$ and $G_{j} = (V_{j}, E_{j}) \in Λ}$ .
$p_{l_i d x}^{u_i d x}$	A corresponding path in $G_{l_i d x}^{u_i d x}$ .
$u_{i}$	A Boolean value to assess the necessity of a layered graph.
$θ_{i}$	The number of allocated spectrum segments starting at frequency slot $i$ .
$κ_{i}$	The number of allocated spectrum segments ending at frequency slot $i - 1$ .

Notation	Meaning
$G_{i d x} = (V_{i d x}, E_{i d x})$	The layered graph for slot $i d x$ , where $V_{i d x}$ and $E_{i d x}$ stand for the sets of vertices and edges in $G_{i d x}$ , respectively.
$v_{i, i d x}$	The corresponding vertex of $v_{i} \in V (e_{i} \in E)$ in $G_{i d x}$ .
$e_{i, i d x}$	The corresponding edge of $e_{i} \in E$ in $G_{i d x}$ if frequency slot $i d x$ is not occupied on $e_{i}$ .
$Λ$	The ordered set of layered graphs; sorted in ascending order of layered graph indices.
Head/Tail index	The indices of the first and the last elements of $Λ$ .
$G_{l_i d x}^{u_i d x} = (V_{l_i d x}^{u_i d x}, E_{l_i d x}^{u_i d x})$	The filter graph of slot range $[l_i d x, u_i d x]$ , where $V_{l_i d x}^{u_i d x} = {v_{i, l_i d x}^{u_i d x} \| \forall v_{i} \in V}$ and $E_{l_i d x}^{u_i d x} = {e_{i, l_i d x}^{u_i d x} \| \forall i ∋ e_{i, j} \in E_{j}$ for all $j \in [l_i d x, \min (u_i d x, the tail index)]$ and $G_{j} = (V_{j}, E_{j}) \in Λ}$ .
$p_{l_i d x}^{u_i d x}$	A corresponding path in $G_{l_i d x}^{u_i d x}$ .
$u_{i}$	A Boolean value to assess the necessity of a layered graph.
$θ_{i}$	The number of allocated spectrum segments starting at frequency slot $i$ .
$κ_{i}$	The number of allocated spectrum segments ending at frequency slot $i - 1$ .

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Equations (8)

Journal of Optical Communications and Networking