This paper provides a performance evaluation of the TETRAPOL random access protocol. The results are based on a Markovian model which is also presented. The Markovian model is used to derive quality of service parameters, e.g. mean throughput, waiting probability, and mean random access delay. The analytical results are compared to results based on stochastic simulation. Our prototypic implementation of the TETRAPOL protocol stack uses the Specification and Description Language (SDL). The simulation results correspond to the analytical results with only small differences. Furthermore, these results are compared to the maximum number of users which can be served by TETRA systems. In case of one Control Channel (CCH) and a typical traffic load, up to approx. 300 mobile stations can be served by one TETRAPOL base station.