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Application opportunities associated with video, voice, and data triple-play result in a dramatic demand increase in metro transport networks, with traffic patterns becoming increasingly dynamic and difficult to predict. This is driving the need of core networks with a high degree of flexibility and multigranularities to carry traffic. We propose to investigate the question of what this means in terms of dynamic protection provisioning. In other words, we want to study how stable are the protection structures under dynamic traffic, i.e., how much and how often they need to be updated in a dynamic survivable WDM network. While most studies on the stability of protection structures have been conducted on p-cycles and link shared protection, we propose to investigate here the stability of failure-independent path-protecting (FIPP) p-cycles under dynamic traffic. For doing so, we design and develop an original scalable mathematical model that we solve using large-scale optimization tools. Numerical results show that FIPP p-cycles are remarkably stable under the evaluation of the number of required optical bypass reconfigurations under dynamic traffic.