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Recently, emphasis has been placed on integrated communication facilities capable of handling both line-switching and packet-switch-ing digital traffic. The problem of dynamically allocating the bandwidth of a trunk to both types of traffic is formulated as a Markovian decision process. Line switching is modeled as a time division multiplexing loss scheme over a varying portion of a fixed time frame. Packet-switching traffic is served through the remaining portion of the frame and requires queueing at the multiplexer-concentrator. Two different cost criteria are examined involving probability of blocking for line switching and average queueing delay for packets. The corresponding optimization problems are presented under reasonable simplifying assumptions. The movable boundary scheme suggested for commercial implementation of integrated multi-plexers is shown to offer optimal or near-optimal performance.