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A novel analytical framework for the accurate and efficient evaluation of the performance of channel resource management strategies for low Earth orbit mobile satellite systems (LEO-MSSs) supporting multiparty traffic is presented. By considering a fixed channel reservation (FCR) scheme as a benchmark, an efficient and accurate analytical approach is developed for obtaining the performance of multiparty traffic under various quality-of-service (QoS) performance measure criteria. The proposed approach is based on a Markovian queuing model, and its correctness and accuracy have been verified by means of computer simulations. To improve the overall performance of LEO-MSS, two novel resource management techniques are introduced and analyzed. The first one is an efficient adaptive channel reservation (ACR) scheme, which allows priority to be given to handover requests that are generated by multiparty traffic. The second one is a new call queuing (NCQ) policy, which efficiently reduces the new call blocking probability with little impact on other system performance measures, such as call dropping probability and unsuccessful call probability. Various performance results show that when ACR is used in conjunction with NCQ, extremely low blocking and handover failure probabilities can be achieved for multiparty traffic.