The Advantage of Small Machines in a Stochastic Fluid Production Process

摘要

We consider a stochastic fluid production model, where m machines which are subject to breakdown and repair, produce a fluid at rate p > 0 per machine if it is working. This fluid is fed into an infinite buffer with stochastic output rate. Under the assumption that the machine processes are independent and identically distributed, we prove that the buffer content at time t is less or equal in the increasing convex ordering to the buffer content at time t of a model with m' ≤ m machines and production rate p' = m/m'p. This formulation includes a conjecture posed by Mitra [6]. Moreover, it is shown how to extend this result to Brownian flow systems, systems obtained by diffusion approximation and simple stochastic flow networks like tandem buffer and assembly systems.