Long running software systems are known to experience an aging phenomenon called software aging, one in which the accumulation of errors during the execution of software leads to performance degradation and eventually results in failure. To counteract this phenomenon a proactive fault management approach, called software rejuvenation, is particularly useful. It essentially involves gracefully terminating an application or a system and restarting it in a clean internal state. In this paper, we evaluate dependability performance of a communication network system with the software rejuvenation under the assumption that the requests arrive according to a Markov modulated Poisson process (MMPP). Three dependability measures, steady-state availability, loss probability of requests and mean response time on tasks, are derived through the hidden Markovian analysis based on the time-based software rejuvenation scheme. In numerical examples, we investigate the sensitivity of some model parameters to the dependability measures.