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We present the development, modeling, analysis and performance evaluation of a deterministic call admission control (CAC) protocol for bursty traffic in high-speed broadband integrated services digital networks. This CAC protocol simultaneously satisfies two quality of service (QoS) parameters, namely cell loss ratio (CLR) and delay. The protocol presented is suitable for "on-line" application and provides efficient network resource (buffer space and link capacity) utilization. The end-to-end delay and CLR values are divided among the nodes of the connection. Deterministic models that capture the bursty nature of the traffic supported by the ATM network are developed for the source and the network node. These models satisfy the deterministic burstiness constraint required by ATM usage parameter control (UPC). Analytical expressions at nodes for CLR and delay are developed based on these models. These analytical expressions are used to develop a CAC protocol. This CAC protocol for bursty sources is evaluated by using queuing models.