Instability of FIFO queueing networks with quick service times (Q1336584)

A class of open queueing networks is examined, where customers arrive according to a Poisson process with rate \(t\). Each customer proceeds along a prescribed route visiting a subset of \(m \geq 1\) queues and then leaving the system. Customers are served one at a time at each queue with FIFO discipline, with the service times being independent and exponentially distributed. The route may depend on the customer type. The rate a customer is served at a given queue may depend on the position along the route. The author presents a group of examples where the equilibria do not exist for systems whose customers are served more quickly than the rate at which they enter.