Methodology to Obtain a Fast and Accurate Estimator for Blocking Probability of Optical Networks

Danilo R. B. de Araújo; Carmelo J. A. Bastos-Filho; Joaquim F. Martins-Filho

doi:10.1364/JOCN.7.000380

Journal of Optical Communications and Networking
Vol. 7,
Issue 5,
pp. 380-391
(2015)
•https://doi.org/10.1364/JOCN.7.000380

Methodology to Obtain a Fast and Accurate Estimator for Blocking Probability of Optical Networks

Danilo R. B. de Araújo, Carmelo J. A. Bastos-Filho, and Joaquim F. Martins-Filho

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Danilo R. B. de Araújo, Carmelo J. A. Bastos-Filho, and Joaquim F. Martins-Filho, "Methodology to Obtain a Fast and Accurate Estimator for Blocking Probability of Optical Networks," J. Opt. Commun. Netw. 7, 380-391 (2015)

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Abstract

The assessment of optical networks considering physical impairments is frequently accomplished by using time-consuming analysis tools. We propose in this paper to use artificial neural networks to predict the blocking probability of optical networks with dynamic traffic by using topological metrics and general information of the physical layer. The training process is accomplished by supervised learning based on a historical database of networks. We also propose a new and simple topological property to represent the capacity of the network to distribute traffic. From the results, we found that this novel topological property improves the estimator accuracy. We compared the results of our proposal with the outcome of a discrete event simulator for optical networks. The simulator provides an estimate for blocking probability of all-optical networks considering physical impairments. We show that our approach is faster than discrete event simulators; we obtained a speedup of greater than 7500 times, with comparable estimation errors.

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Index	Variable	Definition
$X_{1}$	$W$	Number of wavelengths
$X_{2}$	$δ$	OXC isolation factor
$X_{3}$	CC	Clustering coefficient
$X_{4}$	$d$	Density
$X_{5}$	$I (\hat{F})$	Entropy of the DFT of the Laplacian eigenvalues
$X_{6}$	AC	Algebraic connectivity
$X_{7}$	NC	Natural connectivity
$X_{8}$	$\hat{k}$	Average degree
$X_{9}$	APL	Average path length (hops)
$X_{10}$	$D$	Diameter
$X_{11}$	$I (G)$	Entropy
$X_{12}$	$D_{km}$	Diameter (km)
$X_{13}$	${APL}_{km}$	Average path length (km)
$X_{14}$	$ρ$	Spectral radius
$X_{15}$	CR	Concentration of routes

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—

Parameter	Value	Definition
$OSN R_{in}$	30 dB	Input optical signal-to-noise ratio
${OSNR}_{TH}$	19 dB	Minimum OSNR at the receiver
$B_{o}$	100 GHz	Optical filter bandwidth
$Δ f$	100 GHz	Channel spacing
$λ_{i}$	1529 nm	First wavelength of the grid
$α$	$0.2 dB / km$	Fiber loss coefficient
$L_{Mux}$	3 dB	Multiplexer loss
$L_{Demux}$	3 dB	Demultiplexer loss
$L_{Switch}$	3 dB	Optical switch loss
$W_{MIN}$	4	Minimum number of wavelengths per link
$W_{MAX}$	40	Maximum number of wavelengths per link

Class	Lower Bound	Upper Bound
1	$1 E - 5$	$1 E - 3$
2	$1 E - 3$	0.01
3	0.01	0.10
4	0.10	0.20
5	0.20	0.30
6	0.30	0.40
7	0.40	0.50
8	0.50	0.60
9	0.60	0.70
10	0.70	0.80
11	0.80	0.90
12	0.90	1.00

	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$	$X_{6}$	$X_{7}$	$X_{8}$	$X_{9}$	$X_{10}$	$X_{11}$	$X_{12}$	$X_{13}$	$X_{14}$	$X_{15}$
$X_{1}$	1.00	0.41	0.29	0.32	−0.32	0.30	0.30	0.32	−0.29	−0.24	−0.08	−0.44	−0.46	−0.15	−0.43
$X_{2}$	0.41	1.00	0.19	0.20	−0.18	0.20	0.21	0.20	−0.12	−0.07	−0.08	−0.30	−0.34	−0.02	−0.18
$X_{3}$	0.29	0.19	1.00	0.93	−0.86	0.87	0.93	0.93	−0.81	−0.72	0.05	−0.40	−0.61	−0.21	−0.59
$X_{4}$	0.32	0.20	0.93	1.00	−0.95	0.97	1.00	1.00	−0.85	−0.75	−0.07	−0.42	−0.64	−0.29	−0.62
$X_{5}$	−0.32	−0.18	−0.86	−0.95	1.00	−0.92	−0.93	−0.95	0.86	0.78	0.11	0.43	0.62	0.36	0.64
$X_{6}$	0.30	0.20	0.87	0.97	−0.92	1.00	0.97	0.97	−0.74	−0.64	−0.24	−0.37	−0.58	−0.15	−0.50
$X_{7}$	0.30	0.21	0.93	1.00	−0.93	0.97	1.00	1.00	−0.80	−0.70	−0.08	−0.40	−0.62	−0.23	−0.57
$X_{8}$	0.32	0.20	0.93	1.00	−0.95	0.97	1.00	1.00	−0.85	−0.75	−0.07	−0.42	−0.64	−0.29	−0.62
$X_{9}$	−0.29	−0.12	−0.81	−0.85	0.86	−0.74	−0.80	−0.85	1.00	0.95	−0.22	0.42	0.61	0.59	0.77
$X_{10}$	−0.24	−0.07	−0.72	−0.75	0.78	−0.64	−0.70	−0.75	0.95	1.00	−0.23	0.36	0.52	0.60	0.71
$X_{11}$	−0.08	−0.08	0.05	−0.07	0.11	−0.24	−0.08	−0.07	−0.22	−0.23	1.00	0.01	−0.00	−0.37	−0.20
$X_{12}$	−0.44	−0.30	−0.40	−0.42	0.43	−0.37	−0.40	−0.42	0.42	0.36	0.01	1.00	0.83	0.24	0.54
$X_{13}$	−0.46	−0.34	−0.61	−0.64	0.62	−0.58	−0.62	−0.64	0.61	0.52	−0.00	0.83	1.00	0.29	0.64
$X_{14}$	−0.15	−0.02	−0.21	−0.29	0.36	−0.15	−0.23	−0.29	0.59	0.60	−0.37	0.24	0.29	1.00	0.55
$X_{15}$	−0.43	−0.18	−0.59	−0.62	0.64	−0.50	−0.57	−0.62	0.77	0.71	−0.20	0.54	0.64	0.55	1.00

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—

Principal Component	Eigenvalue	% Variance	Cumulative % Variance
1	8.72	58.13	58.13
2	1.82	12.15	70.27
3	1.66	11.04	81.31
4	0.77	5.12	86.43
5	0.66	4.42	90.84
6	0.54	3.58	94.43
7	0.29	1.92	96.35
8	0.22	1.47	97.82
9	0.13	0.86	98.68
10	0.10	0.65	99.33
11	0.06	0.37	99.70
12	0.03	0.19	99.89
13	0.01	0.10	99.99
14	0.00	0.01	100.00
15	0.00	0.00	100.00

Variable	PC 1	PC 2	PC 3
$X_{1}$	−0.43	0.08	−0.64
$X_{2}$	−0.26	0.22	−0.62
$X_{3}$	−0.91	0.13	0.17
$X_{4}$	−0.96	0.18	0.18
$X_{5}$	0.95	−0.12	−0.16
$X_{6}$	−0.90	0.36	0.19
$X_{7}$	−0.94	0.23	0.19
$X_{8}$	−0.96	0.18	0.18
$X_{9}$	0.92	0.28	−0.15
$X_{10}$	0.84	0.35	−0.18
$X_{11}$	−0.02	−0.79	0.06
$X_{12}$	0.57	0.05	0.61
$X_{13}$	0.76	0.01	0.46
$X_{14}$	0.43	0.72	0.02
$X_{15}$	0.76	0.37	0.20

$p$	Input Layer	$\bar{MSE}$	$σ_{MSE}$	Variance	Time (minutes)
2	$W$ , $δ$	$4.02 E - 3$	$4.6 E - 5$	—	57
3	$W$ , $δ$ , $d$	$5.62 E - 4$	$2.4 E - 4$	0.86	70
4	$W$ , $δ$ , $d$ , CR	$3.23 E - 4$	$1.6 E - 5$	0.43	82
5	$W$ , $δ$ , $d$ , CR, CC	$2.83 E - 4$	$1.5 E - 5$	0.12	93
6	$W$ , $δ$ , $d$ , CR, CC, $I (\hat{F})$	$2.66 E - 4$	$6.8 E - 6$	0.06	104
7	$W$ , $δ$ , $d$ , CR, CC, $I (\hat{F})$ , APL (km)	$2.57 E - 4$	$9.7 E - 6$	0.03	118

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—

Methodology to Obtain a Fast and Accurate Estimator for Blocking Probability of Optical Networks

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Equations (10)

Journal of Optical Communications and Networking

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	—	4	2	0	0	0	0	4	0	0	0	0	0	0
2	4	—	9	19	0	0	0	0	0	0	0	0	0	0
3	2	9	—	0	0	7	0	0	0	0	0	0	0	0
4	0	19	0	—	15	0	0	0	0	0	12	0	0	0
5	0	0	0	15	—	5	16	0	0	0	0	0	0	0
6	0	0	7	0	5	—	0	0	0	7	0	0	0	4
7	0	0	0	0	16	0	—	17	0	0	0	0	0	0
8	4	0	0	0	0	0	17	—	21	0	0	0	0	0
9	0	0	0	0	0	0	0	21	—	8	0	15	5	0
10	0	0	0	0	0	7	0	0	8	—	0	0	0	0
11	0	0	0	12	0	0	0	0	0	0	—	11	3	0
12	0	0	0	0	0	0	0	0	15	0	11	—	0	12
13	0	0	0	0	0	0	0	0	5	0	3	0	—	2
14	0	0	0	0	0	4	0	0	0	0	0	12	2	—