Optimization Model for Backup Resource Allocation in Middleboxes

Abstract

Network function virtualization paradigm enables us to implement network functions provided in middleboxes as software which runs on commodity servers. This paper proposes a backup resource allocation model for middleboxes with considering failure probabilities of network functions and backup servers. Multiple backup servers, each of which is allowed to protect several functions, can be assigned to protect one function. When a function fails, one of the corresponding servers providing protection is required to recover it, if the function is protected by any server. We aim to find an assignment of servers to functions where the unavailability of the function that is in the worst case is minimized. We formulate the backup resource allocation problem as a mixed integer linear programming problem. We prove that the backup resource allocation problem is NP-complete by showing that the partition problem is reducible to it. A heuristic algorithm is introduced to solve the same optimization problem. We analyze the computational time complexity of the heuristic algorithm as a polynomial. We show the comparison results obtained by the heuristic algorithm and by solving the mixed integer linear programming problem in terms of deviation and computational time. The results reveal that the heuristic algorithm needs about 10•5 times computational time, compared to that of solving the mixed integer linear programming problem, to obtain a solution, where the worst unavailability over all the functions is about 1.6 times of the optimal value in average in our examined scenarios.