Optimized Portfolio Contracts for Bidding the Cloud

Amazon EC2 provides two most popular pricing schemes--i) the {\em costly} on-demand instance where the job is guaranteed to be completed, and ii) the {\em cheap} spot instance where a job may be interrupted. We consider a user can select a combination of on-demand and spot instances to finish a task. Thus he needs to find the optimal bidding price for the spot-instance, and the portion of the job to be run on the on-demand instance. We formulate the problem as an optimization problem and seek to find the optimal solution. We consider three bidding strategies: one-time requests with expected guarantee and one-time requests with penalty for incomplete job and violating the deadline, and persistent requests. Even without a penalty on incomplete jobs, the optimization problem turns out to be non-convex. Nevertheless, we show that the portion of the job to be run on the on-demand instance is at most half. If the job has a higher execution time or smaller deadline, the bidding price is higher and vice versa. Additionally, the user never selects the on-demand instance if the execution time is smaller than the deadline. The numerical results illustrate the sensitivity of the effective portfolio to several of the parameters involved in the model. Our empirical analysis on the Amazon EC2 data shows that our strategies can be employed on the real instances, where the expected total cost of the proposed scheme decreases over 45\% compared to the baseline strategy

Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets

. This paper discusses computational complexity of conceptual successive convex relaxation methods proposed by Kojima and Tun¸cel for approximating a convex relaxation of a compact subset F = fx 2 C 0 : p(x) 0 (8p(\Delta) 2 P F )g of the n-dimensional Euclidean space R n . Here C 0 denotes a nonempty compact convex subset of R n , and P F a set of finitely or infinitely many quadratic functions. We evaluate the number of iterations which the successive convex relaxation methods require to attain a convex relaxation of F with a given accuracy ffl, in terms of ffl, the diameter of C 0 , the diameter of F , and some other quantities characterizing the Lipschitz continuity, the nonlinearity and the nonconvexity of the set P F of quadratic functions. Keywords: Complexity, Nonconvex Quadratic Program, Semidefinite Programming, Global Optimization, SDP Relaxation, Convex Relaxation, Lift-and-Project Procedure. 1 Introduction. In their paper [2], Kojima and Tun¸cel proposed a class of..