A model is proposed for forecasting the performance of a Satellite-Relay with Routing Function (SRRF) in a prospective LEO Communications System (LEOCS), using queuing theory tools. This model accounts for SRRF displacement relative to subscribers, the dependency of subscriber-to-subscriber conversations, and variations in conversation duration. In the proposed model, the incoming flow of requests simulates message packets from subscribers. This flow is characterized by a Markov queue with a finite number of states and a matrix of conditional flow rates. The forecasted performance metrics include the probability of all SRRF links being busy, or a pre-set number of links being busy, as well as the probability of message packet loss. Additionally, a technique is proposed to set a threshold for message packet loss probability in the SRRF link. The proposed model is compared with a model that assumes a simple Poisson request flow.