Mathematical analysis of a shuttle system based on two interdependent queues

This is an analysis of a multishuttle system, using a car ferry as the example, to develop mathematical models of shuttle systems. Poisson-exponential mathematical models for the single- and two-shuttle systems are formulated as interdependent queueing systems. The vector (X_A, X_B) representing the number of cars waiting at shore A and shore B respectively, at the end of an unloading at one of the shores is shown to form a bivariate Markov chain; thus the long run probability distributions of (X_A, X_B) can be evaluated using classical Markov chain theory.