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The objective of the present paper is to propose a rapid and accurate method for the evaluation of the quality of service (QoS) perceived by the users in the uplink of wireless cellular networks. In doing so we aim to account for the dynamics induced by the arrivals and the departures of the users. In particular, the QoS is evaluated in terms of the blocking probability for streaming users and the throughput of elastic calls. We build some conditions of the feasibility of the resource (power and bandwidth) allocation problem. We first develop a reference feasibility condition (FC) for which the QoS can be evaluated only by long simulations. Then we propose a sufficient feasibility condition (SFC) and an analytical method to evaluate the corresponding QoS. The blocking probability for streaming users is evaluated using the Kaufman-Roberts algorithm whereas the throughput of elastic calls is evaluated using a multi-class processor sharing model. The proposed approach is validated by simulating a CDMA network as well as an OFDMA one.