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Call blocking probabilities (CBP) are a key index of quality of service assessment in multi-rate networks. We focus on the CBP calculation in single link loss models where calls of each service-class come from finite sources and compete for the available link bandwidth under the complete sharing policy. We review the Engset multi-rate loss model (EnMLM) and the single-retry loss model for finite sources (f-SRM) in which blocked calls of a service-class may immediately retry once, in order to be connected in the system, with reduced bandwidth and increased service time requirements. We extend the f-SRM to the multi-retry loss model for finite sources (f-MRM) to cover multiple retrials. Furthermore, we propose the single- and multi-threshold finite source models (f-STM, f-MTM) in which calls, prior to being blocked, may adjust their traffic requirements according to a common set of thresholds, which indicate the …