This paper presents a distributed server allocation model with preventive start-time optimization against a single server failure. The presented model preventively determines the assignment of servers to users under each failure pattern to minimize the largest maximum delay among all failure patterns. We formulate the proposed model as an integer linear programming (ILP) problem. We prove the NP-completeness of the considered problem. As the number of users and that of servers increase, the size of ILP problem increases; the computation time to solve the ILP problem becomes excessively large. We develop a heuristic approach that applies simulated annealing and the ILP approach in a hybrid manner to obtain the solution. Numerical results reveal that the developed heuristic approach reduces the computation time by 26% compared to the ILP approach while increasing the largest maximum delay by just 3.4% in average. It reduces the largest maximum delay compared with the start-time optimization model; it avoids the instability caused by the unnecessary disconnection permitted by the run-time optimization model.

This paper proposes a migration model for distributed server allocation. In distributed server allocation, each user is assigned to a server to minimize the communication delay. In the conventional model, a user cannot migrate to another server to avoid instability. We develop a model where each user can migrate to another server while receiving services. We formulate the proposed model as an integer linear programming problem. We prove that the considered problem is NP-complete. We introduce a heuristic algorithm. Numerical result shows that the proposed model reduces the average communication delay by 59% compared to the conventional model at most.