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Analysing and modelling traffic is one important step in the performance evaluation of communication systems. In this paper we focus on first responder (FR) networks. The goal is to figure out models that can be used to generate realistic synthetic push to talk voice traffic for single talk groups to be used in network simulation. Our work is based on an empirical long-time measurement of one FR channel. The analysis of the trace shows significant short- and long-range correlations as well as variations of load over time. As the characteristics analysed are similar to ones observed in disaster area (DA) traces, we consider n-state and 3-state (semi)-Markov models. After fitting the parameters of these models to the traces, synthetic traffic streams for the different models are generated and finally evaluated by both visual and statistical analysis.