Comparison of Routing Methods in Telecommunication Networks—An Overview and a New Proposal Using a Multi-criteria Approach Dealing with Imprecise Information

Abstract

The performance evaluation and comparison of routing models in telecommunication networks, normally imply the necessity of evaluating them through multidimensional, potentially conflicting, often incommensurate criteria, frequently involving imprecise information regarding the relative importance of the various network performance criteria. As we will show, this is particularly relevant for flow-oriented, decentralized routing optimization methods, having in mind their inherent limitations. Therefore, we formulate a decision problem focused on the comparison and selection of flow-oriented routing models, evaluated through multiple global network performance measures. A proposal of a multi-criteria/multi-attribute approach for tackling this decision problem, based on the VIP (Variable Interdependent Parameter) software, will be described. The adequacy of the features of the multi-attribute decision analysis model, which uses additive aggregation of criteria with variable interdependent importance parameters, coping with imprecise information, will be discussed. A detailed formulation of the application of the proposed approach to a specific problem involving the choice of a point-to-point routing method in a modern transport telecom network, from a set of height routing models, by considering their performance evaluated in terms of nine global network performance measures, will be presented. Moreover, the extension of the decision analysis model, based on the VIP decision support tool, for dealing with this problem, in the case of face-to-face cooperative group decision, will be addressed. A case study concerning the application of this approach to the aforementioned decision problem, in a setting involving three decision makers, including a facilitator, will be presented. Finally, some conclusions, both from a methodological and practical nature, founded on the application study, will be put forward, highlighting the interest of this type of approach in this important area of telecom-network design.

Appendices

Appendix A—Variants of the Bi-criteria Routing Model

Concerning the bi-criteria routing model, in two of the considered variants, a₁, a₂, the aggregation of the bi-criteria preferences was performed by using preference regions in the objective function space. These regions were obtained by defining required and acceptable values m ⁱ_req , m ⁱ_ac (i = 1, 2), specified by the coordinates corresponding to points at distances, taken from the optimal point coordinates, at 1/3 and 2/3 of the variation range of the corresponding function mⁱ(r_s), as shown below (cf. Eq. A3). In these variants, the non-dominated paths were obtained by calculating k-shortest paths, using the additive path cost function (A1), and choosing the first solution in the highest non-empty priority region:

$$ min_{{r_{s} }} m(r_{s} ) = \sum\limits_{{l_{k} \in r_{s} }} {(m_{k}^{*1} + m_{k}^{*2} )} $$

(A1)

where $m_{k}^{*i} = \varepsilon_{i} m_{k}^{i}$ is the normalized value of the cost function mⁱ at arc l_k, (i = 1, 2). The normalizing coefficients ε_i (such that ε₁ + ε₂ = 1) were calculated in two different forms, in the various variants of the model. Let opⁱ de the minimal value of the two path metrics mⁱ(r_s) (i = 1, 2), and $\Delta^{i}$ the range of values of mⁱ(r_s) defined in terms of the Nadir point (M¹, M²), in the objective function space:

$$ \Delta^{i} = M^{i} - op^{i} ;\;M^{i} = m^{i} \left( {\arg \left\{ {\hbox{min} \;m^{j} (r_{s} )} \right\}} \right)\;({\text{i}} = 1,2)\; \wedge {\text{j}} \ne {\text{i}} $$

(A2)

Therefore, the required and acceptable values m ⁱ_req , m ⁱ_ac (i = 1, 2) were calculated as follows:

$$ m_{ac}^{i} = op^{i} + \frac{2}{3}\Delta^{i} ;\;m_{req}^{i} = op^{i} + \frac{1}{3}\Delta^{i} $$

(A3)

Concerning the first set of normalizing coefficients, WA, it is obtained by equalizing the two ranges $\varepsilon_{i} \Delta_{i} \;(i = 1,2)$, leading to:

$$ \varepsilon_{i} = \frac{1}{{\Delta^{i} }}\left( {\sum\limits_{k = 1}^{2} {\frac{1}{{\Delta^{k} }}} } \right)^{ - 1} \;i = (1,\,2) $$

(A4)

Note that these coefficients are calculated each time a VC (node to node virtual connection) is established.

The second set of normalizing coefficients, WB, is calculated (cf. Martins et al. 2013) by considering the average of each path metric, for the current state of the network links l_k:

$$ \overline{{m_{k}^{i} }} = \frac{{\sum\nolimits_{{I_{k} \in L}} {m_{k}^{i} } }}{\left| L \right|} $$

(A5)

where L is the set of network links, $\left| L \right|$ denotes the cardinal of L and m ⁱ_k is the cost associated with metric mⁱ, considering all current occupations in link l_k. The equalization of the variation ranges, considering these averages $\overline{{m_{k}^{i} }}$ leads to:

$$ \varepsilon_{1} = \frac{1}{{1 + \overline{{m_{k}^{1} }} }}\quad\!\!\!\!\!; \varepsilon_{2} = 1 - \varepsilon_{1} $$

Note that, in this case, the coefficients don´t have to be calculated for each VC since they depend on the average metric values.

The other variants of the routing model seek non-dominated solutions which minimize either the Euclidian or the Chebyschev distance to the ideal optimum, also considering the two different sets of normalizing coefficients WA, WB, determined as explained above. This leads two four variants of the routing model, a₃, a₄, a₅, a₆. Further details can be seen in (Martins et al. 2013).

Appendix B—Results for Decision Maker DM3

Fig. 13

Summary of results for S3

Fig. 14

Confrontation table for S3

Fig. 15

Min-max ranges for S3

Acknowledgement: This work was financially supported by FEDER Funds and National Funds through FCT—‘Fundação para a Ciência e a Tecnologia’ under the projects UID/MULTI/00308/2019 and CENTRO-01-0145-FEDER-029312.