  Survivable design of cross-layer networks, such as the cloud computing
infrastructure, lies in its resource deployment and allocation and mapping of
the logical (virtual datacenter/IP) network into the physical infrastructure
(cloud backbone/WDM) such that link or node failure(s) in the physical
infrastructure would not result in cascading failures in the logical network.
Most of the prior approaches for survivable cross-layer network design aim at
single-link failure scenario, which are not applicable to the more challenging
multi-failure scenarios. Also, as many of these approaches use the cross-layer
cut concept, enumeration of all cuts in the network is required and thus
introducing exponential number of constraints. To overcome these difficulties,
we investigate in this paper survivable mapping approaches against multiple
physical link failures and its special case, Shared Risk Link Group (SRLG)
failure. We present the necessary and sufficient conditions based on both
cross-layer spanning trees and cutsets to guarantee a survivable mapping when
multiple physical link failures occur. Based on the necessary and sufficient
conditions, we propose to solve the problem through (1) mixed-integer linear
programs which avoid enumerating all combinations of link failures, and (2) an
algorithm which generates/adds logical spanning trees sequentially. Our
simulation results show that the proposed approaches can produce survivable
mappings effectively against both $k$- and SRLG-failures.
