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The provision of quality of service to different service types in broadband packet networks requires techniques for the evaluation of the probabilities of packet delays and loss. The authors analyse the multiplexing of independent and homogeneous Markovian ON-OFF traffic sources into a single buffer, extending earlier work. The resulting closed-form equation provides a virtually zero-complexity approach to the calculation of the buffer overflow probability via the burst-scale decay rate of the buffer state probabilities. Graphical results are provided, comparing our expression with the results from simulations and the -standard- formula of Anick, Mitra and Sondhi. These show that our new formula provides excellent accuracy for medium to high loads, i.e. those load values at which queuing becomes important. This makes it ideal for quick calculations, with practical utility when dimensioning checks are required in many networking situations involving the accurate estimation of loss probabilities in e.g. buffer multiplexing VoIP traffic sources.