Stochastic bounds for performance evaluation of Web services

We propose new techniques to simplify the computation of the end-to-end delay for an evaluation of a Web services model. The simplification processes are associated with stochastic comparisons of random variables. Thus, the simplified models are stochastic bounds for the original ones. In this study, we consider that the Web service model can be represented by an acyclic directed graph. Thus, we propose upper and lower bounds on the response times by considering in one case special random variables for service times and in the other case we substitute the precedence graph by another one. We prove that the response times computed on the bounding models are really upper and lower bounds on the considered models. We also propose to generalize the model by considering the contention time when several executions of composite Web services are invocated. We propose in this case upper and lower bounds on response times by proposing bounding models. The response times are easier to compute on these new models. We give the corresponding proofs based on stochastic comparisons. We present several numerical results in order to show the accuracy of our bounds