On the arrival theorem for queueing networks operating under a just-in-time protocol

This note shows that the arrival theorem that is well-known for networks of the BCMP-type can be extended to queueing network models for just-in-time production protocols. Such models have a product form stationary distribution that satisfies backward local balance. The statement of the arrival theorem is that a customer routing among the queues observes the equilibrium distribution of the network containing one customer extra. This is shown to naturally correspond to the just-in-time protocol.