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The issue of providing QoS guarantees in an ad hoc wireless network is a challenging problem. Irrespective of the nature of the routing and reservation protocol used in the QoS scheme, there is an inherent limitation on the kind of QoS guarantees that can be provided. Unlike existing studies which analyze the transport capacity, we focus on the achievable capacity. The framework that we assume is that of a TDMA-based network. In this paper, we investigate the achievable capacity and the influence of routing protocols on it. The metrics that we consider are the call acceptance probability and the system saturation probability. We derive general bounds for the case of multiple-classes of users in the network. These bounds indicate the number of calls of the highest priority class that can be admitted into the network. Simulation studies were performed to study the effect of load, hopcount, and the routing protocol on the call acceptance. The increase of the call acceptance with the introduction of load-balancing highlights the importance of load-balancing in enhancing the system performance.