Optimal capacity allocation for Web systems with end-to-end delay guarantees

Providing quality of service guarantees have become a critical issue during the rapid expansion of the e-Commerce area. We consider the problem of finding the optimal capacity allocation in a clustered Web system environment so as to minimize the cost while providing the end-to-end performance guarantees. In particular, we consider constraints on both the average and the tail distribution of the end-to-end response times. We formulate the problem as a nonlinear program to minimize a convex separable function of the capacity assignment vector. We show that under the mean response time guarantees alone, the solution has a nice geometric interpretation. Various methods to solve the problem are presented in detail. For the problem with tail distribution guarantees, we develop an approximation method to solve the problem. We also derive bounds and show that the solution is asymptotically optimal when the service requirement becomes stringent. Numerical results are presented to further demonstrate the robustness of our solutions under data uncertainty.