Relationships between Cycle and Working Path

A typical FIPP p-cycle network design involves a number of cycles. Each FIPP p-cycle has a protection relationship with one or more working paths. The cycle and corresponding path set form a configuration. More specifically, there are two main relationships between a working path and the cycle which can protect it. Note that the relationship between a cycle and a working path only exists when the two end nodes of the working path are both on the cycle. In other words, only on this premise, the cycle is capable of protecting the working path.

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On-Cycle Relationship

On-cycle relationship is specified when a working path has at least one common link with the cycle. In this way, the cycle can provide at most one protection path for this working path. This relationship can be classified further into two cases. Imagine that a working path is completely along a cycle, that is to say, all links of the working path belong to the cycle simultaneously. The protection path is definitely the remaining part of the cycle in such a case. It is called a fully on-cycle relationship. The opposite case to this, the partially on-cycle relationship, occurs when at least one of the links on the working path is not shared by the cycle. The protection that the cycle can provide all depends on the specific position of the common links.

To illustrate, Figure 11a shows a fully on-cycle working path and its protecting cycle, while in Figure 11b illustrates how the cycle protects the affected working path in the

case of a link failure. The involved traffic will be diverted along the cycle in the opposite direction. The arrowed solid curve represents the protection path supplied by the cycle in case the failure occurs along the dashed working path. Again, the traffic demand on the working path can be restored not only under link failure but also under intermediate node failure.

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Figure 12 is an example of a partial on-cycle case. With respect to the cycle, the two end nodes of the working path break the path into two segments, defined as left and right segments respectively. Common links are all distributed on one of the segments (right segment in this case) and leaves the other segment unoccupied. Thus, no matter which link or transit node fails, the left segment will always survive and become the protection path.

There is also another case that common links are distributed on both segments. The

whole working path shapes like a letter “Z” on the cycle. Under a single element failure

assumption, just one of the segments will be affected and the other one will remain intact and be utilized as in the fully on-cycle cases. The problem is, there is no way to know in advance which one will survive until an actual failure occurs. Attempts to include such cases will sacrifice the failure independency of the protection scheme. This situation depicted in Figure 13 has a vivid description in the literature: “z-case” or “z-form”. The arrowed curve has common links with both the left and right segment. Thus, which segment can be the protection path depends on the specific failure location. In other words, the cycle cannot provide link-disjoint protection path to a “z-form”

working path. Tradeoffs exist between additional capacity efficiency and complete failure independency.

Figure 12 a) Partially on-cycle relationship b) The protection path provided by the left segment

“Left”

“Right”

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Straddling Relationship

It becomes more straightforward with regard to straddling relationships. The working path has no common elements with the cycle except that its two end nodes are on-cycle. So the cycle and the working path are mutually disjoint (except for the two end nodes). It means that any failure on the working path cannot cause damage on the cycle. The two segments of the cycle both will survive and can be assigned to route the affected traffic. Therefore, the cycle can provide two protection paths simultaneously. Or from the capacity point of view, a single unit cycle can afford two unit capacities for traffic restoration. Figure 14a shows a full straddling working path and its corresponding protecting cycle. Figure 14b demonstrates how the two segments of the cycle turn out to be protection paths for the working path by simple protection switching at the two end nodes. The straddling relationship is one of the main advantages and contributes to the high capacity efficiency of p-cycles.

Figure 13 z-Case

“Right”

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The basic algorithm we used to determine the protection relationship between a cycle and a working path is as follows:

is_z_case(Cycle k, Path q) {

break cycle k into two segment L and R according to the two end nodes of path q;

For each link i that belongs to path q{ If link i belongs to L

Mark Left;

Elseif link i belongs to R Mark Right;

}

If Left and Right are both marked Return true;

Return false; }

Figure 15 Algorithms for Cycle-Path protection relationship

Protect_Cycle_Path_Ind(Cycle k, Path q) {

If not both end nodes of path q on cycle k Return 0;

If path q is disjoint from cycle k Return 2;

If z-case should be avoided

Return ((is_z_case(Cycle k, Path q)) ? 0 : 1);

Else Return 1; }

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