Robust scheduling in a flexible fork-join network

We consider a general flexible fork-join processing network, in which jobs are modeled as directed acyclic graphs with nodes representing tasks, and edges representing precedence constraints among tasks. Both servers and tasks are flexible in the sense that each task can be processed by several servers, which in turn can serve multiple task types. The system model is motivated by the problem of efficient scheduling of both sequential and parallel tasks in a flexible processing environment, which arises in application areas such as healthcare, cloud computing, and manufacturing. A major challenge in designing efficient scheduling policies is the lack of reliable estimates of system parameters such as arrival and/or service rates. We call a policy robust if it does not depend on system parameters such as arrival and service rates. In this paper, we propose a robust scheduling policy for the flexible fork-join network model, and prove that it is rate stable when service rates can be written as products of a task-dependent quantity and a server-dependent quantity. We also provide a detailed simulation study to demonstrate the performance of the proposed policy.