The General Packet Radio Service (GPRS) extends the Global System Mobile Communication (GSM), by introducing a packet-switched transmission service. This paper analyses the GPRS behavior under critical conditions. In particular, we focus on outages, which significantly impact the GPRS dependability. In fact, during outage periods the cumulative number of users trying to access the service grows proportionally over time. When the system resumes its operations, the overload caused by accumulated users determines a higher probability of collisions on resources assignment and therefore a degradation of the overall QoS. This paper adopts a Stochastic Activity Network modeling approach for evaluating the dependability of a GPRS network under outage conditions. The major contribution of this study lies in the novel perspective the dependability study is framed in. Starting from a quite classical availability analysis, the network dependability figures are incorporated into a very detailed service model that is used to analyze the overload effect GPRS has to face after outages, gaining deep insights on its impact on user's perceived QoS. The result of this modeling is an enhanced availability analysis, which takes into account not only the bare estimation of unavailability periods, but also the important congestion phenomenon following outages that contribute to service degradation for a certain period of time after operations resume.