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Failure-independent path-protecting (FIPP) p-cycle is an extension of the span-protecting p-cycle, and an alternative approach for providing fully pre-connected protection paths with end-to-end failure-independent path protection (Kodian and Gorver, J. of Lightwave Technol., vol. 23, no. 10, pp. 3241-3259). We study the unavailability of end-to-end traffic in FIPP-based mesh networks, which are designed to protect against single failures, and present an availability-aware network design method. Our design method allocates FIPP p -cycles such that the end-to-end unavailability of the protected demands is bounded by an upper limit which we can control. Our study will also focus on determining whether FIPP p-cycles will maintain their resource efficiency advantages over span p -cycles when the network design is based on limiting the unavailability. Our results first show that the length of the FIPP p-cycle plays a vital role in determining the availability of the working path(s). Similar to span-protecting p-cycles, higher service working path(s) availability is obtained when the FIPP p-cycle(s) contains fewer hops. Results also indicate the important role of the number of demands protected by the same FIPP p-cycle. We notice that the higher the desired availability is, the less efficient the FIPP method becomes. This relationship is due to the fact that, to achieve higher service availability, the design will limit the number of demands sharing the same FIPP cycle. Accordingly, we affirm that, when the network design limits the service unavailability, FIPP tends to be less efficient, and its redundancy is 8-13% higher than span-protecting p-cycles. Additionally, we observe that, when we do not limit the unavailability, the average availability for span-protecting p-cycles tends to be more than the FIPP p -cycle method. We present our findings.