Journal of Optical Communications and Networking
Vol. 10,
Issue 11,
pp. 823-831
(2018)
•https://doi.org/10.1364/JOCN.10.000823

Robust Regenerator Allocation in Nonlinear Flexible-Grid Optical Networks With Time-Varying Data Rates

Li Yan, Yuxin Xu, Maïté Brandt-Pearce, Nishan Dharmaweera, and Erik Agrell

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Li Yan, Yuxin Xu, Maïté Brandt-Pearce, Nishan Dharmaweera, and Erik Agrell, "Robust Regenerator Allocation in Nonlinear Flexible-Grid Optical Networks With Time-Varying Data Rates," J. Opt. Commun. Netw. 10, 823-831 (2018)

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History
- Original Manuscript: March 23, 2018
- Revised Manuscript: July 28, 2018
- Manuscript Accepted: July 30, 2018
- Published: September 4, 2018

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Abstract

Predeployment of regenerators in a selected subset of network nodes allows service providers to achieve rapid provisioning of traffic demands, high utilization, and reduced network operational costs, while still guaranteeing lightpath quality of transmission. Enabled by bandwidth-variable transceivers in flexible-grid optical networks, optical channel bandwidths are no longer fixed but constantly changing according to real-time communication requirements. Consequently, the data-rate-variable traffic together with other new network features introduced by flexible-grid networks will render the regenerator allocation very difficult due to the complicated network states. In this paper, we investigate how to allocate regenerators robustly in flexible-grid optical networks to combat physical-layer impairments when the data rates of traffic demands are random variables. The Gaussian noise model and a modified statistical network assessment process framework are used to characterize the probabilistic distributions of physical-layer impairments for each demand, based on which a heuristic algorithm is proposed to select a set of regenerator sites with minimum blocking probabilities. Our method achieves the same blocking probabilities with on average 10% less regenerator sites compared with the greedy constrained-routing regenerator allocation method, and obtains blocking probabilities two orders of magnitude lower than that of the routing and reach method with the same number of regenerator sites.

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Parameter Type	Symbol	Meaning
Input	$V$	The set of nodes
	$E$	The set of links
	$M$	The name of the modulation format used in the network
	$G$	The PSD (in $W \cdot {THz}^{- 1}$ ) used for all the traffic demands
	$b_{sub}$	The subcarrier bandwidth (in GHz) in the network
	$c$	The spectral efficiency of $M$
	${SNR}_{th}$	The SNR threshold of $M$ to achieve an acceptable QoT
	$T$	The set of traffic demands
	$R_{t}$	A random variable representing the data rate (in Gbps) of demand $t \in T$
	$p_{R_{t}} (r_{t})$	The PDF of the data rate for demand $t \in T$
	$Δ b_{t}$	The optical channel bandwidth (in GHz) of demand $t \in T$
	$F_{\max}$	The maximum number of RSs in the network
Output	$S (F_{\max})$	The set of output RSs whose total number is constrained by $F_{\max}$

Symbol	Meaning
$P_{t}$	The ordered set of links on the route of $t \in T$
$Q_{t}$	The ordered set of intermediate nodes on the route of $t \in T$
$L (T)$	The ordered list of randomly shuffled demands in $T$
$N_{MC}$	The number of Monte Carlo repetitions
$N_{t, l}$	The random noise of the demand $t \in T$ on the link $l \in P_{t}$
$p_{N_{t, l}} (n)$	The PDF of $N_{t, l}$
$f_{i}$	A binary indicator that equals 1 if node $i \in V$ is an RS and 0 otherwise
$f$	$f = {f_{1}, \dots, f_{\| V \|}}$ is a vector of $f_{i}$ for $i \in V$
$H_{t} (f)$	The BP of the demand $t \in T$
$Seg (t, f)$	The set of transparent segments on the route of the demand $t \in T$ that is divided by the RS allocation $f$
$Seg (t)$	The set of all possible transparent segments on the route of the demand $t \in T$
$N_{t}^{s}$	A random variable denoting the accumulated noise of the demand $t \in T$ at the end of the transparent segment $s \in Seg (t)$
$p_{N_{t}^{s}} (n)$	The PDF of $N_{t}^{s}$
$H_{t}^{s}$	The BP of the demand $t \in T$ on the transparent segment $s \in Seg (t)$
$src (x)$	The source of $x$ , where $x$ can be a demand, link, or a transparent segment
$dst (x)$	The destination of $x$ , where $x$ can be a demand, link, or a transparent segment
${\bar{V}}_{t}$	${\bar{V}}_{t} = {src (t), dst (t)} \cup Q_{t}$ for $t \in T$
$w_{s}$	The weight associated with the link $s \in Seg (t)$
${\bar{D}}_{t}$	The auxiliary weighted complete graph ${\bar{D}}_{t} = ({\bar{V}}_{t}, Seg (t))$ with weight $w_{s}$ for the link $s \in Seg (t)$
$S_{t}$	The set of promising RS allocations for $t \in T$
$S_{t, k}$	The set of promising RS allocations with exactly $k$ transparent segments for $t \in T$
$K$	The maximum number of different solutions that will be collected in $S_{t, k}$
$u_{s}$	A binary variable that equals 1 if the transparent segment $s \in Seg (t)$ has its source and destinations as RSs, the source, or the destination of $t \in T$ and 0 otherwise
$u_{s}^{κ}$	The value of $u_{s}$ in the $κ$ -th element of $S_{t, k}$ for $κ \in {1, \dots, \| S_{t, k} \|}$
$U_{t}$	$U_{t} = {1, \dots, \| S_{t} \|}$ , the set of indices for elements in $S_{t}$
$f^{t, κ}$	The $κ$ -th element in $S_{t}$ for $κ \in U_{t}$
$y_{t, κ}$	The binary variable that equals 1 if the pre-calculated solution $f^{t, κ} \in S_{t}$ is chosen by the overall RS allocation, and 0 otherwise, $κ \in U_{t}$
$z_{i}$	The binary variable that equals 1 if the node $i \in V$ is chosen by the overall RS allocation, and 0 otherwise
$θ$	A large enough real number

SNR Threshold	TR (km)
14.60	1300
9.49	2000
7.03	2700
5.58	3400

Parameter Type	Symbol	Meaning
Input	$V$	The set of nodes
	$E$	The set of links
	$M$	The name of the modulation format used in the network
	$G$	The PSD (in $W \cdot {THz}^{- 1}$ ) used for all the traffic demands
	$b_{sub}$	The subcarrier bandwidth (in GHz) in the network
	$c$	The spectral efficiency of $M$
	${SNR}_{th}$	The SNR threshold of $M$ to achieve an acceptable QoT
	$T$	The set of traffic demands
	$R_{t}$	A random variable representing the data rate (in Gbps) of demand $t \in T$
	$p_{R_{t}} (r_{t})$	The PDF of the data rate for demand $t \in T$
	$Δ b_{t}$	The optical channel bandwidth (in GHz) of demand $t \in T$
	$F_{\max}$	The maximum number of RSs in the network
Output	$S (F_{\max})$	The set of output RSs whose total number is constrained by $F_{\max}$

Symbol	Meaning
$P_{t}$	The ordered set of links on the route of $t \in T$
$Q_{t}$	The ordered set of intermediate nodes on the route of $t \in T$
$L (T)$	The ordered list of randomly shuffled demands in $T$
$N_{MC}$	The number of Monte Carlo repetitions
$N_{t, l}$	The random noise of the demand $t \in T$ on the link $l \in P_{t}$
$p_{N_{t, l}} (n)$	The PDF of $N_{t, l}$
$f_{i}$	A binary indicator that equals 1 if node $i \in V$ is an RS and 0 otherwise
$f$	$f = {f_{1}, \dots, f_{\| V \|}}$ is a vector of $f_{i}$ for $i \in V$
$H_{t} (f)$	The BP of the demand $t \in T$
$Seg (t, f)$	The set of transparent segments on the route of the demand $t \in T$ that is divided by the RS allocation $f$
$Seg (t)$	The set of all possible transparent segments on the route of the demand $t \in T$
$N_{t}^{s}$	A random variable denoting the accumulated noise of the demand $t \in T$ at the end of the transparent segment $s \in Seg (t)$
$p_{N_{t}^{s}} (n)$	The PDF of $N_{t}^{s}$
$H_{t}^{s}$	The BP of the demand $t \in T$ on the transparent segment $s \in Seg (t)$
$src (x)$	The source of $x$ , where $x$ can be a demand, link, or a transparent segment
$dst (x)$	The destination of $x$ , where $x$ can be a demand, link, or a transparent segment
${\bar{V}}_{t}$	${\bar{V}}_{t} = {src (t), dst (t)} \cup Q_{t}$ for $t \in T$
$w_{s}$	The weight associated with the link $s \in Seg (t)$
${\bar{D}}_{t}$	The auxiliary weighted complete graph ${\bar{D}}_{t} = ({\bar{V}}_{t}, Seg (t))$ with weight $w_{s}$ for the link $s \in Seg (t)$
$S_{t}$	The set of promising RS allocations for $t \in T$
$S_{t, k}$	The set of promising RS allocations with exactly $k$ transparent segments for $t \in T$
$K$	The maximum number of different solutions that will be collected in $S_{t, k}$
$u_{s}$	A binary variable that equals 1 if the transparent segment $s \in Seg (t)$ has its source and destinations as RSs, the source, or the destination of $t \in T$ and 0 otherwise
$u_{s}^{κ}$	The value of $u_{s}$ in the $κ$ -th element of $S_{t, k}$ for $κ \in {1, \dots, \| S_{t, k} \|}$
$U_{t}$	$U_{t} = {1, \dots, \| S_{t} \|}$ , the set of indices for elements in $S_{t}$
$f^{t, κ}$	The $κ$ -th element in $S_{t}$ for $κ \in U_{t}$
$y_{t, κ}$	The binary variable that equals 1 if the pre-calculated solution $f^{t, κ} \in S_{t}$ is chosen by the overall RS allocation, and 0 otherwise, $κ \in U_{t}$
$z_{i}$	The binary variable that equals 1 if the node $i \in V$ is chosen by the overall RS allocation, and 0 otherwise
$θ$	A large enough real number

Robust Regenerator Allocation in Nonlinear Flexible-Grid Optical Networks With Time-Varying Data Rates

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Equations (15)

Journal of Optical Communications and Networking