In this work, we analyze the power saving and its impact on web traffic performance when customers adopt the continuous connectivity paradigm. To this end, we provide a model for packet transmission and cost. We model each mobile user's traffic with a realistic web traffic profile, and study the aggregate behavior of the users attached to a base station by means of a processor-shared queueing system. In particular, we evaluate user access delay, download time and expected economy of energy in the cell. Our study shows that dramatic energy saving can be achieved by mobile devices and base stations, e.g., as much as 70%-90% of the energy cost in cells with realistic traffic load and the considered parameter settings.