Robust Distributed Server Selection Model Against Delay Uncertainty

In real-time applications under wide-area networks, providing a demanded quality of service for end users is an issue. Recent studies adopt distributed processing for server selection problems to reduce data synchronization delay and total interaction delay, assuming that link delays over the distributed system are exactly known. No study has addressed the problem of such a distributed server selection in properly handling the delay uncertainty. This paper proposes a robust optimization model for the distributed server selection problem against the delay uncertainty. We handle the delay uncertainty of user-server and server-server links by defining two -ellipsoidal uncertainty sets. The proposed model determines allocated servers for multiple users to minimize the weighted sum of data synchronization delay and total interaction delay over the distributed system. We formulate the proposed model as a mixed integer second-order cone programming problem. We prove that the distributed server selection problem with uncertain delays is NP-complete. We compare the proposed model with baseline models, focusing on delay uncertainty and distributed processing. The numerical results show that the proposed model can achieve a lower objective value than the baseline models, indicating the benefit of utilizing -ellipsoidal uncertainty sets to handle delay uncertainty.