Providing efficient workload management is an important issue for a large-scale heterogeneous distributed computing environment where a set of periodic applications is executed. The considered distributed system is expected to operate in an environment where the input workload is likely to change unpredictably, possibly invalidating a resource allocation that was based on the initial workload estimate. The tasks consist of multiple application strings, each made up of an ordered sequence of applications. There are quality of service (QoS) constraints that must be satisfied for each string. This work addresses the problem of finding a robust initial allocation of resources to application strings that is able to absorb some level of unknown input workload increase without rescheduling. An allocation feasibility analysis is presented followed by four heuristics for finding a near-optimal allocation of resources. The performance of the proposed heuristics is evaluated and compared using simulation. The proposed heuristics also are compared to a mathematically derived upper bound.