Slide 9 of 10
Notes:
Using Link-to-Route-Dependency we can establish two types of relationship between links - equivalency and parent-child relationship.
Two or more links are equivalent if they have the same sets of dependent Routes.
For example, links 1 and 2 are equivalent, because both these links have the same set of dependent Routes -- AD_North and FC. For the set of equivalent links we use notation: (1,2). Another examples of equivalent link sets are (9,10,11) and (12,13).
From DCR perspective cut of any link from the equivalent link set gives the same loss of capacity. That is why to save a time we will use only one link from the equivalent link set to make a cut simulation, and this link cut “represents” all other link cuts from the set.
Link I is higher in hierarchy than link J, if the set of dependent Routes for link I includes (but not equal to) the set of dependent Routes for link J. In this case we also call a link I as a parent of a link J, and a link J as a child of a link I. We use arrow from parent to child to indicate this relationship. It is many-to-many relationship: a link can have no, one or several children and/or parents. The chief-link is the link that has the highest position in this hierarchy (has no parents).
For example, link 5 is a parent of the link 6 (and link 6 is a child of link 5), because a set of dependent Routes for link 5 (AD_South, FC, HK_North and LG) includes a set of dependent Routes for link 6 (AD_South and LG). Also, link 5 is a chief-link, because it has no parents.
From DCR perspective there is a dependency in results of cut simulations of parent and child links. If, for example, number of Blocked Calls (BC) is within threshold for a cut of a parent link, we can guarantee, that BC number will be within threshold also for a cut of a child link.
That is why we should select for cut simulation only highest level links (links without parents, or chief-links).
To illustrate this hierarchy relationship we can present all links as nodes in a directed graph. Each node in this graph represents a link or a set of equivalent links. This graph can have several components (clusters). For a sample set we select one chief-link from each cluster.