Optimization Model for Multiple Backup Resource Allocation With Workload-Dependent Failure Probability

Abstract

This paper proposes a multiple backup resource allocation model with a workload-dependent failure probability to minimize the maximum expected unavailable time (MEUT) under a protection priority policy. The workload-dependent failure probability is a non-decreasing function which reveals the relationship between the workload and the failure probability. The proposed model adopts hot backup and cold backup strategies to provide protection. For protection of each function with multiple backup resources, it is required to adopt a suitable priority policy to determine the expected unavailable time. We analyze the superiority of the protection priority policy for multiple backup resources in the proposed model; we provide the theorems that clarify the influence of policies on MEUT. We formulate the optimization problem as a mixed integer linear programming (MILP) problem. We provide a lower bound of the optimal objective value in the proposed model. We prove that the decision version of the multiple resource allocation problem in the proposed model is NP-complete. A heuristic algorithm inspired by the water-filling algorithm is developed with providing an upper bound of the expected unavailable time obtained by the algorithm. The numerical results show that the proposed model reduces MEUT compared to baselines. The priority policy adopted in the proposed model suppresses MEUT compared with other priority policies. The developed heuristic algorithm is approximately 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> times faster than the MILP approach with 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> performance penalty on MEUT.