Tunnel-based networks such as Multi-protocol Label switching (MPLS) are suitable for providing diversity guarantees to different service classes or customers. Based on the number of active tunnels to handle, router capabilities can be taxed due to the limited amount of memory and/or processing power of these routers. In this paper, we present a mixed-integer linear program formulation for a traffic engineering problem where such tunnel restrictions are taken into account in addition to standard capacity constraints while addressing diversity requirement of services. Due to large size of the formulation, we also present an accompanied solution approach based on Lagrangian relaxation and sub-gradient optimization. We then present results towards impact of diversity constraint upon the tunneling and capacity restrictions. We observed that the networks having higher amounts of capacity and demands with higher level of survivability are much more sensitive to number of allowed tunnels in t...