Requests Satisfaction in a Virtual Web Services System

This paper defines analytical models for a Web services system, with two stations on tandem queue, for evaluating the request satisfaction involving two exponential servers, each having its own waiting queue. The first waiting queue is unlimited. The arrivals of requests follow a Poisson process, and after service completion, they can either leave the system or join the second line. The obtained model has not a product form; and the only way to obtain its performances is by computing its steady-state probabilities. To this end, we must use balance equations that give us unlimited equations with unlimited unknowns. In this case the only solution is the use of approximation methods. In this paper we use the truncation method to approximate the performances of our model with the performances of a truncated model. We also use the strong stability method to estimate the error of this approximation. Furthermore, we compute the system's response time, and the average number of clients in the system in terms of the arrival rate of clients requests.