Service Mapping and Scheduling With Uncertain Processing Time in Network Function Virtualization

This article proposes an optimization model for the network service (NS) mapping and scheduling problem with uncertain processing time in network function virtualization. We model processing time uncertainty through the
$\Gamma$
-robustness approach, which provides different degrees of robustness against processing time uncertainty. We formulate the problem with the objective to minimize the worst-case makespan over the given uncertainty set. We show the NP-hardness of considered problem. A heuristic that divides the problem into subproblems is presented to tackle it. For the subproblem in which mapping and scheduling decisions are given, we develop an algorithm with polynomial time complexity to calculate the worst-case makespan over the uncertainty set, which has a better scalability than the corresponding mixed integer linear programming (MILP) problem and obtains the same worst-case makespan with the MILP problem. The numerical results show that the proposed model outperforms the conventional model with deterministic parameters in terms of worst-case makespan.