## Abstract

Network operators are facing hard competition for opportunities in the
telecommunications market, forcing network investments to be carefully evaluated
before the decision-making process. A great part of core network operators’ revenues
comes from the provisioned connectivity services. Taking this premise as our starting
point, we first examine the provisioning of differentiated services in current
shared-path protection (SPP) environments. This analysis reveals that current
resource assignment policies are only able to provide a very poor grade of service to
the supported best-effort traffic. Aiming to improve this performance, a novel
resource partitioning scheme called *diff-WS* is proposed, which
differentiates those wavelengths supporting each class of service in the network. As
a major goal of this paper, the benefits of *diff-WS* over current
resource assignment policies are assessed from an economic perspective. For this
purpose, the network operator revenues maximization (NORMA) problem is presented to
design the optical network such that the operator’s revenues are maximized. To solve
NORMA, we derive statistical models to obtain, given a certain grade of service, the
highest traffic intensity for each class of service and resource partitioning scheme.
These models turn NORMA into a nonlinear problem, which is finally addressed as an
iterative approach, solving an integer linear programming (ILP) subproblem at each
iteration. The obtained numerical results on several network topologies illustrate
that *diff-WS* maximizes resource utilization in the network and,
thus, the network operator’s profit.

© 2011 OSA

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### Equations (21)

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(1)
$${R}_{BE}^{\ast}=\bigcup _{\forall i\in WL}\underset{BE}{\overset{i}{R}}\left(\underset{SP}{\overset{i}{G}}\right).$$
(2)
$$P\left({R}_{BE},{G}_{SP}\right)=\frac{\mid {R}_{BE}^{\ast}\mid}{\mid {R}_{BE}\mid}.$$
(3)
$$P{b}_{BE}=\frac{\mid {R}_{BE}\mid -\mid {R}_{BE}^{\ast}\mid}{\mid {R}_{BE}\mid}+f(G,{I}_{SP},{I}_{BE})\cdot \frac{\mid {R}_{BE}^{\ast}\mid}{\mid {R}_{BE}\mid}\ge 1-P\left({R}_{BE},{G}_{SP}\right).$$
(4)
$$\left(\text{NORMA}\right)\phantom{\rule{1em}{0ex}}\underset{\forall k\in K}{\text{Maximize}}\phantom{\rule{1em}{0ex}}{\text{REVENUES}}^{k}.$$
(5)
$$b{t}_{j}^{k}=\mid N\mid \cdot \frac{\Delta t}{ia{t}_{j}^{k}}\cdot (1-P{b}_{j})\cdot (h{t}_{j}^{k}\cdot {\rho}_{j}^{k})=\mid N\mid \cdot {I}_{j}^{k}\cdot {\rho}_{j}^{k}\cdot (1-P{b}_{j})\cdot \Delta t,$$
(6)
$${\text{REVENUES}}^{k}=\sum _{\forall j\in S}b\underset{j}{\overset{k}{t}}\cdot {C}_{j}=\sum _{\forall j\in S}\left(\mid N\mid \cdot \underset{j}{\overset{k}{I}}\cdot {\rho}_{j}^{k}\cdot \left(1-P{b}_{j}\right)\cdot \Delta t\cdot {C}_{j}\right).$$
(7)
$${I}_{j}^{k}=\frac{1{0}^{\alpha (k,j)}\cdot \mid E{\mid}^{\beta (k,j)}}{{h}^{\gamma (k,j)}}\pm \epsilon (k,j).$$
(8)
$$\text{MaximizeREVENUES}}^{k}\equiv \text{Maximize}\phantom{\rule{0.2em}{0ex}}\sum _{\forall j\in S}\frac{\underset{j}{\overset{k}{\theta}}\cdot \mid E{\mid}^{\beta (k,j)}}{{h}^{\gamma (k,j)}$$
(9)
$$\begin{array}{cc}\sum _{\forall j\in S}\frac{\underset{j}{\overset{k}{\theta}}\cdot \mid {E}_{2}{\mid}^{\beta (k,j)}}{\underset{2}{\overset{\gamma (k,j)}{h}}}>\sum _{\forall j\in S}\frac{\underset{j}{\overset{k}{\theta}}\cdot \mid {E}_{1}{\mid}^{\beta (k,j)}}{\underset{1}{\overset{\gamma (k,j)}{h}}}\hfill & \begin{array}{c}\forall \beta (k,j)>1\hfill \\ \forall \gamma (k,j)>1\hfill \\ \hfill \end{array},\hfill \end{array}$$
(10)
$$\left(\text{NORMA}\right)\phantom{\rule{0.2em}{0ex}}\text{minimize}\phantom{\rule{1em}{0ex}}h=\frac{1}{\mid D\mid}\sum _{\forall d\in D}\sum _{\forall e\in E}\underset{e}{\overset{d}{\omega}}$$
(11)
$$\sum _{\forall e\in \Omega \left(n\right)}\underset{e}{\overset{d}{\omega}}=1\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall n\in \{{s}_{d},{t}_{d}\},$$
(12)
$$\sum _{\forall e\in \Omega \left(n\right)}\underset{e}{\overset{d}{\omega}}\le 2\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall n\in N-\{{s}_{d},{t}_{d}\},$$
(13)
$$\sum _{\genfrac{}{}{0ex}{}{\forall {e}^{\prime}\in \Omega \left(n\right)}{{e}^{\prime}\ne e}}\underset{{e}^{\prime}}{\overset{d}{\omega}}\ge \underset{e}{\overset{d}{\omega}}\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall n\in N-\{{s}_{d},{t}_{d}\}\phantom{\rule{0.2em}{0ex}}\forall e\in \Omega \left(n\right),$$
(14)
$$\sum _{\forall e\in \Omega \left(n\right)}\underset{e}{\overset{d}{\kappa}}=1\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall n\in \{{s}_{d},{t}_{d}\},$$
(15)
$$\sum _{\forall e\in \Omega \left(n\right)}\underset{e}{\overset{d}{\kappa}}\le 2\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall n\in N-\{{s}_{d},{t}_{d}\},$$
(16)
$$\sum _{\genfrac{}{}{0ex}{}{\forall {e}^{\prime}\in \Omega \left(n\right)}{{e}^{\prime}\ne e}}\underset{{e}^{\prime}}{\overset{d}{\kappa}}\ge \underset{e}{\overset{d}{\kappa}}\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall n\in N-\{{s}_{d},{t}_{d}\}\phantom{\rule{0.2em}{0ex}}\forall e\in \Omega \left(n\right),$$
(17)
$${\omega}_{e}^{d}+{\kappa}_{e}^{d}\le 1\phantom{\rule{2em}{0ex}}\forall d\in D\phantom{\rule{1em}{0ex}}\forall e\in E,$$
(18)
$$\sum _{\forall d\in D}\left(\underset{e}{\overset{d}{\omega}}+\underset{e}{\overset{d}{\kappa}}\right)\le M\cdot {\zeta}_{e}\phantom{\rule{2em}{0ex}}\forall e\in E,$$
(19)
$$\sum _{\forall e\in E}{\zeta}_{e}=a,$$
(20)
$$\sum _{\forall e\in E}{\zeta}_{e}\cdot \underset{e}{\overset{x}{\phi}}\le 1\phantom{\rule{2em}{0ex}}\forall x\in X,$$
(21)
$$\sum _{\forall e\in \Omega \left(n\right)}{\zeta}_{e}\le {\delta}_{\mathrm{max}}\phantom{\rule{2em}{0ex}}\forall n\in N.$$