For the Internet, system developers often have to estimate the QoS by simulation techniques or mathematical analysis. Probabilistic model checking can evaluate performance, dependability and stability of information processing systems with random behaviors. We apply a hybrid analysis approach onto real-time distributed systems. In the hybrid analysis approach, we perform stepwise analysis using probabilistic models of target systems in different abstract levels. First, we create a probabilistic model with detailed behavior of the system (called detailed model), and apply simulation on the detailed model. Next, based on the simulation results, we create a probabilistic model in an abstract level (called simplified model). Then, we verify qualitative properties using the probabilistic model checking techniques. This prevents from state-explosion. We evaluate the validity of our approach by comparing to simulation results of NS-2 using a case study of a video data streaming system. The experiments show that the result of the proposed approach is very close to that of NS-2 simulation. The result encourages the approach is useful for the performance analysis on various domain.

Model checking techniques are useful for design of high-reliable information systems. The well-known problem of state explosion, however, might occur in model checking of large systems. Such explosion severely limits the scalability of model checking. In order to avoid it, several abstraction techniques have been proposed. Some of them are based on CounterExample-Guided Abstraction Refinement (CEGAR) loop technique proposed by E. Clarke et al.. This paper proposes a concrete abstraction technique for timed automata used in model checking of real time systems. Our technique is based on CEGAR, in which we use a counter example as a guide to refine the abstract model. Although, in general, the refinement operation is applied to abstract models, our method modifies the original timed automaton. Next, we generate refined abstract models from the modified automaton. This paper describes formal descriptions of the algorithm and the correctness proof of the algorithm.