Optimal stopping of multi-project software testing in the context of software cybernetics

Software cybernetics explores the interplay between control theory/engineering and software theory/engineering. The controlled Markov chains (CMC) approach to software testing follows the idea of software cybernetics and treats software testing as a control problem. The software under test serves as a controlled object and the software testing strategy serves as the corresponding controller. The software under test and the software testing strategy make up a closed-loop feedback control system, and the theory of controlled Markov chains can be used to design and optimize software testing strategies in accordance with testing/reliability goals given a priori. In this paper we apply the CMC approach to the optimal stopping problem of multi-project software testing. The problem under consideration assumes that a single stopping action can stop testing of all the software systems under test simultaneously. The theoretical results presented in this paper describe how to test multiple software systems and when to stop testing in an optimal manner. An illustrative example is used to explain the theoretical results. The study of this paper further justifies the effectiveness of the CMC approach to software testing in particular and the idea of software cybernetics in general.

Numerical Solutions for Optimal Control of Stochastic Kolmogorov Systems

This work is concerned with controlled stochastic Kolmogorov systems.Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control,this paper is devoted to designing numerical methods for approximation.Different from the existing literature on numerical methods for stochastic controls,the Kolmogorov systems take values in the first quadrant.That is,each component of the state is nonnegative.The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent)the controlled diffusion.The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works.Convergence of the numerical scheme is proved under suitable conditions.

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.