Performance analysis of a multiple vehicle tandem system with inter-vehicle buffers and blocking

We analyze a new tandem system in which items are transported through a sequence of stations from an origin to a destination via a series of vehicles that move back and forth between consecutive stations. Each pair of consecutive stations is connected by a single vehicle with unit capacity that travels back and forth between the upstream and downstream station. Each vehicle travels with an item in the downstream direction and without an item in the upstream direction. The stations act as holding areas for items awaiting further transport within the system. Stations may have non-identical capacities. We model this system as a continuous time Markov chain and develop a recursive algorithm for generating the state transition matrix. After solving for the steady state probabilities using the Gauss–Seidel method, we compute the average throughput rate, average number of items in the system, and average sojourn time for various system configurations.