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The operating mechanism of a connection-oriented Internet service is analyzed. Considering the finite buffer in connection-oriented Internet service, we establish a Geom/G/1/K queueing model with setup-close delay-close down for user-initiated session. Using the approach of an embedded Markovian chain and supplementary variables, we derive the probability distribution for the steady queue length and the probability generating function for the waiting time. Correspondingly, we study the performance measures of quality of service (QoS) in terms of system throughput, system response time, and system blocking probability. Based on the simulation results, we discuss the influence of the upper limit of close delay period and the capacity of the queueing model on the performance measures, which have potential application in the design, resource assigning, and optimal setting for the next generation Internet.