Regeneration and grooming in MPLS over WDM networks

Bruna Nogueira; Ricardo Mendes; Lúcia Martins; Lúcia Martins; Teresa Gomes; Teresa Gomes; Rita Girão-Silva; Rita Girão-Silva; João Santos; Tibor Cinkler

doi:10.1364/JOCN.11.000465

Journal of Optical Communications and Networking
Vol. 11,
Issue 8,
pp. 465-477
(2019)
•https://doi.org/10.1364/JOCN.11.000465

Regeneration and grooming in MPLS over WDM networks

Bruna Nogueira, Ricardo Mendes, Lúcia Martins, Teresa Gomes, Rita Girão-Silva, João Santos, and Tibor Cinkler

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Bruna Nogueira, Ricardo Mendes, Lúcia Martins, Teresa Gomes, Rita Girão-Silva, João Santos, and Tibor Cinkler, "Regeneration and grooming in MPLS over WDM networks," J. Opt. Commun. Netw. 11, 465-477 (2019)

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Abstract

This work addresses the grooming, routing and wavelength assignment with regeneration (GRWAR) problem for meshed networks in static traffic scenarios. It focuses primarily on the grooming and routing with regeneration (GRR) problem. Physical impairments were considered in the model, imposing a limit in lightpath lengths without regeneration. This creates the opportunity to strategically place transponders for both grooming and regeneration. The GRR problem is tackled lexicographically, which means that for a given network topology and a traffic matrix, the goal is to route and groom connection requests in a way that minimizes the number of transponders and, for that number of transponders, throughout minimum length routes. To solve this problem, an integer linear programming (ILP) formulation was developed considering undirected networks and explicitly including the relationship between the different network layers. The results of the ILP model are used to validate a heuristic suited to be included in a software-defined network (SDN) platform in a multilayer core network. The GRWAR problem is addressed after a solution for the GRR problem is obtained, using a first-fit approach to assign wavelengths to the lightpaths obtained by the ILP and the heuristic. The wavelength assignment problem is less critical due to the large number of wavelengths per fiber. The ILP and the heuristic were compared for small networks, with the heuristic providing good results in very short time, proving to be efficient and better suited for larger problems, as is confirmed through a set of proposed bounds.

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Physical Layer
$G (N, A)$	Graph representing a network topology
$N$	Set of nodes in the network
$k, m, n \in N$	End nodes of an optical link
$A$	Set of arcs in the network
$(m, n) \in A$	Directed arc connecting nodes $m$ and $n$ (with $m \neq n$ )
$c_{m n}$	Cost of arc $(m, n)$
$p_{m n}$	Path originating at node $m$ and terminating at node $n$
$N (p_{m n})$	Set of nodes of the path $p_{m n}$
$A (p_{m n})$	Set of arcs of the path $p_{m n}$
$c (p_{m n})$	Cost of the path $p_{m n}$
$p_{m k} ♢ p_{k n}$	Concatenation of paths $p_{m k}$ and $p_{k n}$
$W$	Number of wavelengths of each arc
Virtual Layer
$G^{'} (N, L)$	Virtual topology
$L$	Set of lightpaths
$i, j, k$	End nodes of a lightpath
$l_{i j}$	Set of lightpaths originating at node $i$ and terminating at node $j$
$l_{i j}^{t}$	$t$ -th lightpath of $l_{i j}$
$p_{l_{i j}^{t}}$	Optical lightpath associated with $l_{i j}^{t}$
$o_{l_{i j}^{t}}$	Occupied capacity associated with $l_{i j}^{t}$
$C$	Maximum bandwidth that may be carried by a lightpath
$l_{i k}^{t_{1}} ◯ ⋄ l_{k j}^{t_{2}}$	Concatenation of lightpaths $l_{i k}^{t_{1}}$ and $l_{k j}^{t_{2}}$
$V_{i j}$ or $\| l_{i j} \|$	Number of lightpaths between node $i$ and node $j$
$λ_{i j, t}^{s d, y, v}$	Binary variable: 1 if $Λ_{y, s d}^{v}$ uses $l_{i j}^{t}$ as an intermediate virtual link; 0 otherwise
Relation between the Layers
Paths in $G (N, A)$ are mapped as links in $G^{'} (N, L)$
$l (m, n)$	Set of translucent lightpaths using the arc $(m, n)$
$P_{m n}^{i j, t}$	Binary variable: 1 if $l_{i j}^{t}$ is routed through arc $(m, n)$ ; 0 otherwise
Demands
$s, d$	Source and destination nodes of an end-to-end connection request
$Λ$	Set of traffic matrices
$Λ_{y}$	Traffic matrix of a service class with bandwidth $y$
$Λ_{s d}$	Set of traffic matrices between source node $s$ and destination node $d$
$Λ_{y, s d}$	Subset of the demands in $Λ_{s d}$ with bandwidth $y$
$Λ_{y, s d}^{v}$	$v$ -th demand in $Λ_{y, s d}$
Miscellany
$Δ$	Regeneration impairment threshold

Input Data						ILP (Lexi) / Heuristic					Bounds for Transp.
Network	$\| N \|$	$\| A \|$	$\| Λ \|$	$Δ$	$W$	Avg LP Cost [km]	Capacity Usage (%)	$W_{m a x}$	Transp. + Reg.	Time [s]	LB	LBA	UB
polska	6	6	17	1000	48	322.65 / 491.04	3.12 / 4.51	2 / 4	14 + 0 / 14 + 0	496.30 / 0.681	12	14	18
			34			415.97 / 466.95	5.90 / 6.94	4 / 5	20 + 0 / 22 + 0	2537.67/ 0.984	18	20	28
			51			373.90 / 430.45	7.99 / 10.07	5 / 5	30 + 0 / 32 + 0	time-out / 1.49	26	28	42
			68			433.37 / 459.77	10.76 / 11.81	7 / 8	36 + 0 / 38 + 0	time-out / 1.72	34	34	50
	7	8	24			305.74 / 432.89	3.12 / 5.21	2 / 4	18 + 0 / 22 + 0	25620.21 / 1.71	14	20	26
	7	8	48			368.50 / 380.18	6.51 / 5.99	5 / 4	30 + 0 / 28 + 0	time-out / 1.66	24	28	40
	8	10	32			324.90 / 397.71	3.54 / 5.41	3 / 5	24 + 0 / 30 + 0	time-out / 1.81	18	24	38
abilene	12	15	75	3000	48	1434.84 / 1558.69	9.44 / 8.75	12 / 10	72 + 0 / 66 + 0	time-out / 7.66	38	50	102

Input Data					Heuristic								Bounds for Transp.
Network	$\| N \|$	$\| A \|$	$\| Λ \|$	$Δ$	$T$	$T_{Δ}$	Avg LPCost [km]	Avg LPHops	Avg SPHops	Max SPHops	Time [s] GR	$nSP > Δ$	LB	LBA	UB
abilene	12	15	75	3000	66	66	1558.69	1.91	2.64	6	7.699	21	38	50	102
abilene	12	15	150	3000	92	110	1719.94	2.05	2.64	6	10.61	21	92	82	164
polska	12	18	75	1000	66	66	490.63	2.18	2.2	5	9.78	1	40	54	94
polska	12	18	150	1000	94	94	485.576	2.19	2.2	5	14.21	1	74	84	152
dfn-bwin	10	45	51	1000	46	46	406.26	1	1	1	5.06	0	28	90	90
dfn-bwin	10	45	102	1000	64	64	407.42	1	1	1	8.28	0	52	90	90
nobel_eu	28	41	434	1500	368	476	1063.96	2.42	3.61	8	281.47	197	222	248	852
nobel_eu	28	41	868	1500	526	822	1088.5	2.42	3.61	8	206.98	197	430	450	1324
india	35	80	684	3000	604	694	2038.94	2.37	3.23	9	1132.28	294	330	394	1130
india	35	80	1368	3000	844	1144	2130.14	2.47	3.23	9	1402.19	294	644	700	1788

(a) polska_6_6_17				(b) polska_7_8_24				(c) polska_8_10_32
S	D	BW	Link	S	D	BW	Link	S	D	BW	Link
0	1	10	n	0	1	10	n	0	1	10	n
0	2	40	n	0	2	10	n	0	2	40	y
0	3	10	n	0	3	10	n	0	3	40	n
0	4	40 + 10	y	0	4	10	n	0	4	10	n
0	5	40 + 10	n	0	5	40	y	0	5	10	n
1	2	10	n	0	6	40 + 10	n	0	6	40 + 10	y
1	3	10	y	1	2	40	n	0	7	40 + 10	n
1	4	40	y	1	3	10	n	1	2	10	y
1	5	40	n	1	4	10	n	1	3	10	n
2	3	10	n	1	5	40	y	1	4	10	y
2	4	10	y	1	6	10	y	1	5	40	n
2	5	40	y	2	3	40 + 10	y	1	6	40	y
3	4	10	n	2	4	40	n	1	7	40	n
3	5	10	y	2	5	40	n	2	3	40	n
4	5	40	n	2	6	40 + 10	y	2	4	10	n
				3	4	10	n	2	5	40 + 10	y
				3	5	10	n	2	6	10	n
				3	6	40	y	2	7	40	n
				4	5	10	y	3	4	40	n
				4	6	10	n	3	5	10	n
				5	6	40	y	3	6	10	y
								3	7	40	y
								4	5	40 + 10	y
								4	6	10	n
								4	7	10	y
								5	6	10	n
								5	7	10	n
								6	7	40	n

Physical Layer
$G (N, A)$	Graph representing a network topology
$N$	Set of nodes in the network
$k, m, n \in N$	End nodes of an optical link
$A$	Set of arcs in the network
$(m, n) \in A$	Directed arc connecting nodes $m$ and $n$ (with $m \neq n$ )
$c_{m n}$	Cost of arc $(m, n)$
$p_{m n}$	Path originating at node $m$ and terminating at node $n$
$N (p_{m n})$	Set of nodes of the path $p_{m n}$
$A (p_{m n})$	Set of arcs of the path $p_{m n}$
$c (p_{m n})$	Cost of the path $p_{m n}$
$p_{m k} ♢ p_{k n}$	Concatenation of paths $p_{m k}$ and $p_{k n}$
$W$	Number of wavelengths of each arc
Virtual Layer
$G^{'} (N, L)$	Virtual topology
$L$	Set of lightpaths
$i, j, k$	End nodes of a lightpath
$l_{i j}$	Set of lightpaths originating at node $i$ and terminating at node $j$
$l_{i j}^{t}$	$t$ -th lightpath of $l_{i j}$
$p_{l_{i j}^{t}}$	Optical lightpath associated with $l_{i j}^{t}$
$o_{l_{i j}^{t}}$	Occupied capacity associated with $l_{i j}^{t}$
$C$	Maximum bandwidth that may be carried by a lightpath
$l_{i k}^{t_{1}} ◯ ⋄ l_{k j}^{t_{2}}$	Concatenation of lightpaths $l_{i k}^{t_{1}}$ and $l_{k j}^{t_{2}}$
$V_{i j}$ or $\| l_{i j} \|$	Number of lightpaths between node $i$ and node $j$
$λ_{i j, t}^{s d, y, v}$	Binary variable: 1 if $Λ_{y, s d}^{v}$ uses $l_{i j}^{t}$ as an intermediate virtual link; 0 otherwise
Relation between the Layers
Paths in $G (N, A)$ are mapped as links in $G^{'} (N, L)$
$l (m, n)$	Set of translucent lightpaths using the arc $(m, n)$
$P_{m n}^{i j, t}$	Binary variable: 1 if $l_{i j}^{t}$ is routed through arc $(m, n)$ ; 0 otherwise
Demands
$s, d$	Source and destination nodes of an end-to-end connection request
$Λ$	Set of traffic matrices
$Λ_{y}$	Traffic matrix of a service class with bandwidth $y$
$Λ_{s d}$	Set of traffic matrices between source node $s$ and destination node $d$
$Λ_{y, s d}$	Subset of the demands in $Λ_{s d}$ with bandwidth $y$
$Λ_{y, s d}^{v}$	$v$ -th demand in $Λ_{y, s d}$
Miscellany
$Δ$	Regeneration impairment threshold

Abstract

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Tables (9)

Equations (23)

Journal of Optical Communications and Networking