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The routing algorithms used by current operators aim at coping with the demanded QoS requirements while optimizing the use of their network resources. These algorithms rely on the optimal substructure property (OSP), which states that an optimal path contains other optimal paths within it. However, we show that QoS metrics such as queuing delay and buffer consumption do not satisfy this property, which implies that the used algorithms lose their optimality and/or completeness. This negatively impacts the operator economy by causing a waste of network resources and/or violating Service Level Agreements (SLAs). In this paper, we propose a new so-called Mn taxonomy defining new metric classes. An Mn metric corresponds to a metric which requires the knowledge of the n previously traversed edges to compute its value at a given edge. Based on this taxonomy, we present three solutions for solving routing problems with the newly defined classes of metrics. We show that state-of- the-art algorithms based on the OSP indeed lose their original optimality and/or completeness properties while our proposed solutions do not, at the price of an increased computation time.

Routing Metrics Depending on Previous Edges: The Mn Taxonomy and Its Corresponding Solutions