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In this paper, we analyze the operating mechanism of a connection-oriented Internet service. Considering the finite buffer size in a connection-oriented Internet service, we establish a Geom/Geom/1/K queueing model with setup-close delay-close down feature for user-initiated sessions. Using a simulation approach, 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 buffer on the performance measures. Findings from such an analysis may potentially be applied in the design, resource assigning, and optimal setting for the next generation Internet.