A Simple Proof of the Equivalence of Input and Output Intervals in Jackson Networks of Single Server Nodes

In this paper, we provide a simple proof that the distributions of an input and an output interval in a stationary Jackson network of single server nodes are equivalent. The proof also applies to Gordon and Newell networks of single server nodes. The proof's key idea is that the reverse process of a Jackson network's stationary queue length process is also a Jackson network's stationary queue length process.