Multi-step migration of optical connections to minimize disruption time in flex-grid networks

Tuấn Khải Nguyễn; Ronald Romero Reyes; Thomas Bauschert

doi:10.1364/JOCN.463702

Journal of Optical Communications and Networking
Vol. 14,
Issue 10,
pp. 866-881
(2022)
•https://doi.org/10.1364/JOCN.463702

Multi-step migration of optical connections to minimize disruption time in flex-grid networks

Tuấn Khải Nguyễn, Ronald Romero Reyes, and Thomas Bauschert

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Tuấn Khải Nguyễn, Ronald Romero Reyes, and Thomas Bauschert, "Multi-step migration of optical connections to minimize disruption time in flex-grid networks," J. Opt. Commun. Netw. 14, 866-881 (2022)

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Abstract

Migration of optical connections in flex-grid networks has become increasingly necessary as the arrivals and departures of optical connection requests are more dynamic. To mitigate disruptions of existing connections during migration, former research applies the resource dependency digraph (RDD) model to allow for sequential migration of optical connections. In this paper, we argue that, in this RDD model, each connection has a quota of one migration step only and that this one-step-quota constraint can be safely lifted to accomplish even lower disruption time due to the greater degree of migration freedom. We consider the whole migration process to be composed of multiple lightpath assignment states, each of which is to be determined individually. We show that this consideration can drastically reduce disruption time and hence the ensuing service level agreement violation penalties, even when it is already minimized under the one-step-quota constraint. For that, we propose two mathematical models. The first model, namely, multi-step optical connection migration (MOCM), adopts a layer-based abstraction in which each lightpath assignment state is represented as a layer, and the transition between two consecutive layers constitutes a migration step. In the second model, namely, MOCM2, to improve the solution efficiency, we readopt the concept of RDD and integrate multiple RDDs into MOCM to further enable even larger migration freedom. This way, the transition between two consecutive layers may involve multiple so-called meta-migration steps. As a use case, the proposed approaches are applied to perform connection migration for spectrum defragmentation. The results show that our multi-step migration scheme notably reduces disruption time as compared with the one-step-quota RDD-based approaches.

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Type	Symbol	Definition
Set	$S$	Set of optical fiber links
	$K$	Set of existing optical connections
	$P_{k}$	Set of candidate paths for connection $k$
Parameter	$ν$	Number of spectrum slots in each link
	$b_{k}$	Number of spectrum slots occupied by an optical connection $k$
	$I_{s}^{p}$	Binary, 1 if path $p$ spans link $s$ , 0 otherwise
	$ψ$	Maximum number of allowed migration steps
	$α$	Weight of the subordinate objective part
Variable	$x^{(k, p, w, t)}$	Binary: 1 if $w$ is the smallest spectrum slot index in path $p$ occupied by connection $k$ in layer $t$ , 0 otherwise
	$μ^{(t)}$	Binary: 1 if the transition from the $(t - 1)$ th layer to the $t$ th layer qualifies as one migration step in MOCM,
		at least one migration step in MOCM2, 0 otherwise
	$d_{A}^{(k, t)}$	Binary: 1 if connection $k$ is type-A-disrupted from layer $(t - 1)$ to layer $t$ , 0 otherwise (applicable to MOCM only)
	$d_{B}^{(k, t)}$	Binary: 1 if connection $k$ is type-B-disrupted from layer $(t - 1)$ to layer $t$ , 0 otherwise (applicable to MOCM only)
	$u^{(t)}$	Integer: number of migration steps from the $(t - 1)$ th layer to the $t$ th layer (applicable to MOCM2 only)
	$e^{(k, \tilde{k}, t)}$	Binary: 1 if an arc exists from $\tilde{k}$ to $k$ in the RDD from the $(t - 1)$ th layer to the $t$ th layer, 0 otherwise
		(applicable to MOCM2 only)
	$d^{(k, t)}$	Integer: number of migration steps from the $(t - 1)$ th layer to the $t$ th layer during which $k$ is disrupted
		(applicable to MOCM2 only)
	${ahc}^{(k, t)}$	Integer: AHC of connection $k$ during the transition from the $(t - 1)$ th layer to the $t$ th layer
		(applicable to MOCM2 only)

Variable	Complexity
$x^{(k, p, w, t)}$	$O (\| K \| \cdot K \cdot ν \cdot ψ)$
$μ^{(t)}$ , $u^{(t)}$	$O (ψ)$
$e^{(k, \tilde{k}, t)}$	$O (\| K \|^{2} \cdot ψ)$
$d^{(k, t)}$ , $d_{A}^{(k, t)}$ , $d_{B}^{(k, t)}$ , ${ahc}^{(k, t)}$	$O (K \cdot ψ)$

Constraint	Complexity
C1	$O (\| K \| \cdot K \cdot ν \cdot ψ)$
C2	$O (\| N_{S} \| \cdot \| K \| \cdot K \cdot ν \cdot ψ)$
C3, C7, C8, C9	$O (\| K \| \cdot ψ)$
C4	$O (\| S \| \cdot ν \cdot ψ)$
C5	$O (\| N_{S} \| \cdot \| K \|^{2} \cdot ν \cdot ψ)$
C6	$O (\| K \|^{2} \cdot ψ)$
C10	$O (ψ)$

Type	Symbol	Definition
Set	$S$	Set of optical fiber links
	$K$	Set of existing optical connections
	$P_{k}$	Set of candidate paths for connection $k$
Parameter	$ν$	Number of spectrum slots in each link
	$b_{k}$	Number of spectrum slots occupied by an optical connection $k$
	$I_{s}^{p}$	Binary, 1 if path $p$ spans link $s$ , 0 otherwise
	$ψ$	Maximum number of allowed migration steps
	$α$	Weight of the subordinate objective part
Variable	$x^{(k, p, w, t)}$	Binary: 1 if $w$ is the smallest spectrum slot index in path $p$ occupied by connection $k$ in layer $t$ , 0 otherwise
	$μ^{(t)}$	Binary: 1 if the transition from the $(t - 1)$ th layer to the $t$ th layer qualifies as one migration step in MOCM,
		at least one migration step in MOCM2, 0 otherwise
	$d_{A}^{(k, t)}$	Binary: 1 if connection $k$ is type-A-disrupted from layer $(t - 1)$ to layer $t$ , 0 otherwise (applicable to MOCM only)
	$d_{B}^{(k, t)}$	Binary: 1 if connection $k$ is type-B-disrupted from layer $(t - 1)$ to layer $t$ , 0 otherwise (applicable to MOCM only)
	$u^{(t)}$	Integer: number of migration steps from the $(t - 1)$ th layer to the $t$ th layer (applicable to MOCM2 only)
	$e^{(k, \tilde{k}, t)}$	Binary: 1 if an arc exists from $\tilde{k}$ to $k$ in the RDD from the $(t - 1)$ th layer to the $t$ th layer, 0 otherwise
		(applicable to MOCM2 only)
	$d^{(k, t)}$	Integer: number of migration steps from the $(t - 1)$ th layer to the $t$ th layer during which $k$ is disrupted
		(applicable to MOCM2 only)
	${ahc}^{(k, t)}$	Integer: AHC of connection $k$ during the transition from the $(t - 1)$ th layer to the $t$ th layer
		(applicable to MOCM2 only)

Variable	Complexity
$x^{(k, p, w, t)}$	$O (\| K \| \cdot K \cdot ν \cdot ψ)$
$μ^{(t)}$ , $u^{(t)}$	$O (ψ)$
$e^{(k, \tilde{k}, t)}$	$O (\| K \|^{2} \cdot ψ)$
$d^{(k, t)}$ , $d_{A}^{(k, t)}$ , $d_{B}^{(k, t)}$ , ${ahc}^{(k, t)}$	$O (K \cdot ψ)$

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Equations (13)

Journal of Optical Communications and Networking