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Dual-failures are considered as the main contributors to service unavailability in p-cycle based mesh networks that are designed to withstand single failures. Methods such as post-failure reconfiguration and prefailure provisioning of additional protection capacity have been considered to add another level of protection against dual-failures. In this paper, we present availability-aware service provisioning method in networks designed to only withstand single failures. The approach we discuss builds upon previous work in and uses the concept of ??cutsets method?? to categorize failures that cause overall service outage; we discuss some subtle issues which make existing methods inaccurate. We then develop an improved non-joint optimization ILP model for solving the service provisioning problem under the assumption of fully loaded p-cycles. We also address the scalability issue by introducing several techniques to speed up the run time of the model. We evaluate the sources of inaccuracy in different scenarios. We also investigate the tradeoff between capacity investment and reducing the link outage time and its effect on service availability in different scenarios. Our results indicate that the ILP solutions of our models outperform the prior work in terms of estimating service path unavailability in all considered network and traffic scenarios.