Multimedia applications require support from the underlying broadband network at the end-to-end communication level. Multicasting is an important paradigm of end-to-end communication. The root node of a multicasting session is responsible for controlling the session including monitoring, maintenance, and the implementation of the multicasting protocol. The job that controls the multicasting session executes as a group of tasks at the root node of a multicasting tree. The scheduling scheme at the root node should give support to a multicasting session by improving the completion time of the jobs controlling the multicasting session, hence increasing throughput and the probability of admitting new multicast sessions. We model the tasks that carry out the multicasting session monitoring and maintenance as a fork-join job executing on a multiprocessor system. We assume that an executing task blocks for device I/O as a part of the activities associated with sending and receiving data packets. We develop two analytic models for scheduling a session control job on a multiprocessor system. The first allows incoming job tasks to multiplex processors with existing tasks of another multicasting session; the other model schedules a task of the incoming job to an idle processor. We assume that the overhead of rescheduling a task to another processor is large. We compare the performance of both models and show the range of conditions under which a model outperforms the other. The results can be used in the design of an adaptive scheduler that uses both models to improve throughput and the probability of admitting new multicast sessions.