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This paper addresses the routing of backup tunnels with bandwidth guarantee in MPLS networks. Backup tunnels implemented by the packet layer in MPLS are seen as a useful alternative (or addition) to the schemes offered by a SONET/SDH layer in particular for providing protection for real time packet services such as voice over IP. Many schemes have been proposed, working with MPLS, to provide the switching architecture for backup tunnels. However, the routing of the tunnels in these schemes is not clearly defined and hence the motivation for this work. This paper investigates the use of the p-cycle scheme to route the bandwidth-guaranteed backup tunnels, a scheme that was originally devised for optical transport networks and IP/MPLS networks as well. We demonstrate that the problem (as for all but trivial p-cycle schemes) is too large to solve optimally and propose a relaxation method that pre-selects candidate cycles that are likely to provide a good solution. Furthermore, we show that working load distributions can significantly affect the performance of a p-cycle scheme and compare two routing algorithms to show how good distribution of working load can help increase the efficiency of the system.