In this paper, we study the cost of protection in Time-Domain Wavelength Interleaved Network (TWIN), an optical burst switching technology for transport networks with active edge nodes, passive core nodes, and time slotted operation. For the first time, an optimal network dimensioning with protection is proposed for TWIN, allowing to allocate the needed resources for dedicated and shared path protection. The dimensioning model is in the form of a 0-1 Integer Linear Program (0-1 ILP), and addresses both the routing and wavelength assignment problem, and the scheduler calculation. The cost of protection is studied for centralized and distributed traffic models, and it is shown that the shared path protection in TWIN is the most cost efficient.