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Fragmentation Metrics

This section describes the different metrics that are used to measure spectrum fragmentation in EONs. Spectrum loss can be a metric to measure fragmentation; it occurs when a free slot cannot be utilized. Spectrum loss is demand sensitive as larger granularities are more likely to be blocked than smaller granularities. Therefore, it is not considered to estimate the level of fragmentation effect in EONs; other metrics are essential. The most commonly used metric to estimate fragmentation is the blocking ratio; it is the ratio of the number of blocked requests to the number of offered requests in the network. The assumption is that if the blocking ratio is less, the fragmentation effect is also less. However, the blocking ratio is not a complete measure of fragmentation as the blocking ratio is also impacted by several system parameters, such as a lack of resources, quality of transmission, and holding time. Therefore, it is necessary to identify other comparison metrics to measure the blocking caused by spectrum fragmentation.

Measuring Fragmentation in a Link

In the following, we discuss the metrics that are used to estimate spectrum fragmentation in each link. Let i be a block of available contiguous slots, f be the number of available contiguous slots in block i, and / be a set of blocks of available contiguous slots, in each link. In the case that there is one slot whose neighbor slot(s) are not available, we also consider it as a block i € / with f = 1. We express A = max,fj and В =

External Fragmentation Metric

External fragmentation metric f 154,155] has been well studied in memory fragmentation management. It can also be used to measure the fragmentation effect in each link, which is defined by (6.1)

where A and В are the maximum number of available contiguous slots, and the number of all available slots, respectively, in each link. The concept of the external fragmentation metric is explained by the example shown in Fig. 6.2.

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