Optimal Scalability of FiWi Networks Based on Multistage Stochastic Programming and Policies

Arturo Peralta; Esteban Inga; Roberto Hincapié

doi:10.1364/JOCN.9.001172

Journal of Optical Communications and Networking
Vol. 9,
Issue 12,
pp. 1172-1183
(2017)
•https://doi.org/10.1364/JOCN.9.001172

Optimal Scalability of FiWi Networks Based on Multistage Stochastic Programming and Policies

Arturo Peralta, Esteban Inga, and Roberto Hincapié

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Arturo Peralta, Esteban Inga, and Roberto Hincapié, "Optimal Scalability of FiWi Networks Based on Multistage Stochastic Programming and Policies," J. Opt. Commun. Netw. 9, 1172-1183 (2017)

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Abstract

The large demand of bandwidth due to new and future applications from services being implemented such as smart grid (SG), smart cities (SC), and the Internet of Things has triggered a focus of interest from the scientific community on issues related to the planning and scalability of the communications infrastructure. In this paper, we present three new and important contributions regarding the deployment of FiWi networks that support users who benefit from the services provided by SG and SC. We first propose a planning model, and then formulate a mixed linear programming optimization model using multistage stochastic programming, and finally propose an algorithm, called MOA–FiWi, which has the capacity to handle medium and large instances of the problem and give feasible solutions for the optimization process, where scalability indices between 85%–95% are reached with respect to the projected stochastic values. The proposed model considers the scalability and capital and operating expense, as well as the uncertainty management in the different stages of time–space through multistage stochastic programming. The proposed model presents flexibility in decision making as the time stages progress. This allows for the planning of green fields, as well as the updating of networks that already have communication infrastructure.

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Carrier aggregation	Intra-carriers
Carrier aggregation	Inter-carriers
Spatial multiplexing using techniques	MIMO
	MISO
	SIMO
	SISO
Relay nodes	Microcells
Relay nodes	Femtocells
Fronthaul/backhaul	NG-PON1
	NG-PON2
	DWDM
	UDWDM

Name	Domain	Interpretation
Sets
$A$	$\subseteq R^{3}$	Planning Area, divided into pixels
$C$	$\in Z$	Set of candidate cells for coverage
$F$	$\in Z$	Set of $m$ flows
Tree Scenario
$N$		Set of MSPT nodes
$P (n)$	$\in (0, 1]$	Probability at node $n$
$p (n)$	$\in N$	Parent node at MSPT
Coefficients and Parameters
$M$	$\in R ≫ 0$	It is a sufficiently large number $> ‖ F ‖$
$K^{n}$	$\in Z$	Construction limit at node $n$
$α^{n}$	$\in [0,1]$	Coverage requirement parameter
$W_{j}^{n}$	$\in [0,1]$	Weight on a pixel in node $n$
${\hat{I}}_{j}^{n}$	$\in R \geq 0$	Revenue per pixel at node $n$
${\hat{C}}_{i}^{capex, n}$	$\in R \geq 0$	NPV of CAPEX in cell $i$ at node $n$
${\hat{C}}_{i}^{opex, n}$	$\in R \geq 0$	NPV of OPEX in cell $i$ at node $n$
$D_{p, q}^{n}$	$\in R \geq 0$	Distance for link $p ⇆ q$ at node $n$
${\hat{C}}_{p, q}^{capex, n}$	$\in R \geq 0$	NPV of CAPEX for link $p ⇆ q$ at node $n$
${\hat{C}}_{p, q}^{opex, n}$	$\in R \geq 0$	NPV of OPEX for link $p ⇆ q$ at node $n$
Decision Variables
$Y_{i}^{n}$	$\in {0,1}$	Cell $i$ is active at node $n$
$X_{s j}^{n}$	$\in {0,1}$	UDAP $j$ is covered at node $n$
$Z_{p, q}^{n}$	$\in {0, 1}$	Link $p ⇆ q$ is active at node $n$
$C^{n}$	$\in {0, 1}$	Fulfillment of coverage at node $n$

Step: 1	Generate:
		$M S P T (n, t)$
Step: 2	Generate:
		$ξ_{0}^{'} \subseteq ξ$
Step: 3	Generate:
		$π_{0}^{*} (ξ_{0}^{'}) \forall M S P T (n, t)$
Step: 4	Calculate:
		$E (ξ_{0}^{'}) = \tilde{R} {π_{0}^{*}}$
Step: 5	Generate new:
		$ξ_{k + 1}^{'} = f_{1} (ξ_{k}^{'}, ξ)$
Step: 6	Modify:
		Set Covered
		Dijkstra
		$π_{k + 1}^{*} = f_{2} (π_{k}^{'}, ξ_{k}^{'}) \forall M S P T (n, t)$
Step: 7	Apply:
		Metaheuristic brute force Decision criterion & Stopped
Step: 8	Go to Step 5:
		If criterion does not meet
Step: 9	Return:
		$D^{*} : a r g m a x E {R}$

Annual Benefit per UDAP	$400.00
CAPEX OLT, with capacity for 1000 users, type XG–PON	$45,000.00
CAPEX eNodeB/ONU	$25,000.00
CAPEX per meter includes optical fiber, supports, pipes, and ducts	$15.00
Annual OPEX of eNodeB/ONU	$200.00
Annual OPEX per meter optical fiber	$1.20

Year	0	1	2	3	4
Scenario 1—Conservative Type
${MSPT}_{n}$	1	2	3	6	10
$P (n)$	1.000	1.000	0.392	0.392	0.222
Covered UDAP	124	253	326	481	645
eNodeB active	2	4	4	6	8
Meters of fiber optics	730.943	1878.020	1878.020	2575.353	4039.069
$E {{MSPT}_{n}}$	$−56,364.152	$22,367.979	$41,580.464	$36,314.909	$26,541.632
Scenario 2—Conservative Type
${MSPT}_{n}$	1	2	3	6	11
$P (n)$	1.000	1.000	0.392	0.392	0.171
Covered UDAP	124	253	326	481	684
eNodeB active	2	4	4	6	9
Meters of fiber optics	730.943	1878.020	1878.020	2575.353	4482.632
$E {{MSPT}_{n}}$	$−56,364.152	$22,367.979	$41,580.464	$36,314.909	$18,086.502
Scenario 3—Realistic Type
${MSPT}_{n}$	1	2	4	7	12
$P (n)$	1.000	1.000	0.423	0.256	0.256
Covered UDAP	124	253	370	523	739
eNodeB active	2	4	5	7	10
Meters of fiber optics	730.943	1878.020	2156.580	3337.963	5022.704
$E {{MSPT}_{n}}$	$−56,364.152	$22,367.979	$39,589.036	$25,229.900	$31,575.068
Scenario 4—Realistic Type
${MSPT}_{n}$	1	2	4	8	13
$P (n)$	1.000	1.000	0.423	0.167	0.167
Covered UDAP	124	253	370	605	841
eNodeB active	2	4	5	8	12
Meters of fiber optics	730.943	1878.020	2156.580	3920.261	5422.150
$E {{MSPT}_{n}}$	$−56,364.152	$22,367.979	$39,589.036	$15,771.690	$22,335.897
Scenario 5—Optimistic Type
${MSPT}_{n}$	1	2	5	9	14
$P (n)$	1.000	1.000	0.185	0.185	0.074
Covered UDAP	124	253	422	624	989
eNodeB active	2	4	6	8	18
Meters of fiber optics	730.943	1878.020	2504.900	3686.283	8547.029
$E {{MSPT}_{n}}$	$−56,364.152	$22,367.979	$15,358.243	$23,858.840	$1,441.696
Scenario 6—Optimistic Type
${MSPT}_{n}$	1	2	5	9	15
$P (n)$	1.000	1.000	0.185	0.185	0.111
Covered UDAP	124	253	422	624	905
eNodeB active	2	4	6	8	14
Meters of fiber optics	730.943	1878.020	2504.900	3686.283	6139.293
$E {{MSPT}_{n}}$	$−56,364.152	$22,367.979	$15,358.243	$23,858.840	$11,322.930

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Journal of Optical Communications and Networking