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This paper studies the packet data transmission performance in Terrestrial Trunked Radio (TETRA) networks, giving particular emphasis on the performance of applications characterized by occasionally transmitting small messages between radio terminals and a fixed server. Such applications are constantly increasing in public safety networks and so does the need to dimension and configure TETRA networks in order to meet their reliability, delay and loss requirements. That was the main motivation of our performance analysis. We present simulation results for a variety of practical scenarios and we quantify key performance indicators such as the delay and loss rate characteristics. Our results can help in dimensioning and planning TETRA networks, and in particular in determining the number of packet data terminals that can be supported in a cell for a given traffic profile and QoS requirements.