Finite buffer polling models with routing

This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue lengths at polling instants are determined by solving a system of recursive equations, and an embedded Markov chain analysis and numerical inversion are used to derive the queue length distributions. This system may be used to represent production models with setups and lost sales or expediting.