[[abstract]]A per-connection end-to-end call admission control (CAC) problem is solved in this paper to allocate network resources to an input session to guarantee its quality of service (QoS) requirements. In conjunction with the solution of the CAC problem, a traffic descriptor is proposed to describe the loss rate and the delay bound QoS requirements of the connection to be set up as well as the statistical characteristics of the associated input traffic which is modeled as a linear mean function plus a (zero-mean) fractional Brownian motion. The information in the traffic descriptor is sufficient to determine the allocation of channel bandwidth and buffer space to the input traffic in a network which employs leaky bucket shapers and scheduling algorithms to guarantee the QoS requirements. The CAC problem is solved by an iterative algorithm of which there are two stages in each iteration: one is responsible for the search of a candidate end-to-end routing path and the other for the verification of the legitimacy of this candidate path to meet the QoS requirements and for the allocation of resources in such a legitimate path
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